Find the mean
7\8,2/3,9/4,3/4,1/2

Answer:

x−2x4+2x3−7x2−8x+12=x3+4x2+x−6

The rational root theorem suggests that other possible roots may be -6, 6, -3, 3, -2, 2, -1, and 1. It turns out that x=-2x=−2 is a root, since (-2)^3+4(-2)^2+(-2)-6=0(−2)3+4(−2)2+(−2)−6=0 , so x+2x+2 is also a factor and we have

\dfrac{x^4+2x^3-7x^2-8x+12}{(x-2)(x+2)}=x^2+2x-3(x−2)(x+2)x4+2x3−7x2−8x+12=x2+2x−3

Finally, we can factorize the remaining quotient easily:

x^2+2x-3=(x+3)(x-1)x2+2x−3=(x+3)(x−1)

so the other factors are x+2x+2 , x+3x+3 , and x-1x−1 .

The given equation has more than one solutions and can be represented by (0.65 , -10.65).

What is an equation with one solution ?

Equation with one solution is that who has only one value for the variable that makes the equation true.

It is given that the equation is (x+5)² - 32 = 0.

We know that to check that the equation has one solution or many solutions we need to simplify the equation.

So :

(x+5)² - 32 = 0
(x + 5)² = 32

x + 5 = √32

x = √32  - 5

or

x = ± 5.65 - 5

So , value of x will be equal to :

x = 0.65

or

x = - 10.65

This equation has more than one solutions.

Therefore , the given equation has more than one solutions and can be represented by (0.65 , -10.65).

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The temperature at the bottom of the mountain is 50.9 °C.

Let's work through the given information step by step to find the temperature at the bottom of the mountain.

The temperature in the hotel is 21 °C.

The temperature in the hotel is 26.7 °C warmer than at the top of the mountain.

Let's denote the temperature at the top of the mountain as T_top.

So, the temperature in the hotel can be expressed as T_top + 26.7 °C.

The temperature at the top of the mountain is 3.2 °C colder than at the bottom of the mountain.

Let's denote the temperature at the bottom of the mountain as T_bottom.

So, the temperature at the top of the mountain can be expressed as T_bottom - 3.2 °C.

Now, let's combine the information we have:

T_top + 26.7 °C = T_bottom - 3.2 °C

To find the temperature at the bottom of the mountain (T_bottom), we need to isolate it on one side of the equation. Let's do the calculations:

T_bottom = T_top + 26.7 °C + 3.2 °C

T_bottom = T_top + 29.9 °C

Since we know that the temperature in the hotel is 21 °C, we can substitute T_top with 21 °C:

T_bottom = 21 °C + 29.9 °C

T_bottom = 50.9 °C

Therefore, the temperature at the bottom of the mountain is 50.9 °C.

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In order to create 728 millilitres of the medication, 273 millilitres of component A are required.

A compound in chemistry is a material comprised of two or more separate chemical elements mixed together in a certain proportion. Chemical connections that are challenging to break are created when the elements interact with one another.

Compound A:Compound B ratio in the medication is 3:5. In other words, there are 3 millilitres of compound A and 5 millilitres of compound B for every 3+5=8 millilitres of the medicine.

We may set up a percentage using the ratio of compound A to the total volume of the medicine to determine how much compound A is required to make 728 millilitres of the drug:

3 ml x 3 ml x 3 ml

-------- = ----------

728 ml total, 8 ml overall

If we cross-multiply, we obtain:

8(x) = 3(728)

To find x, we use the formula x = 3(728)/8 = 273

In order to create 728 millilitres of the medication, 273 millilitres of component A are required.

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273 milliliters of compound A are needed to make 728 milliliters of the drug.

What are proportions?

In mathematics, a proportion is a statement that two ratios are equal. It expresses the relationship between two or more quantities that are directly proportional to each other. A proportion can be represented as an equation of the form:

a/b = c/d

To determine the amount of compound A needed to make 728 milliliters of the drug, we need to use the given ratio of 3 milliliters of compound A to 5 milliliters of compound B.

Let's start by finding the ratio of compound A to the total amount of ingredients (A+B) in the drug:

3 : (3+5) or 3:8

This means that for every 8 milliliters of the drug, 3 milliliters of compound A are used.

To find out how many milliliters of compound A are needed for 728 milliliters of the drug, we can set up a proportion:

3/8 = x/728

where x represents the amount of compound A needed.

To solve for x, we can cross-multiply:

8x = 3*728

8x = 2184

x = 273

Therefore, 273 milliliters of compound A are needed to make 728 milliliters of the drug.

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The midpoint is 26.

Midpoint in this scenario = mean

(23+29)/2 = 26

Answer:

-6

Step-by-step explanation:

the value of x is  16.97

Given that:

The right angled triangle has hypotenuse of 18 units

Its one other side measures 6 units.

The length of unknown side is denoted by length x units.

To find:

Value of x

The Pythagoras theorem states that:

"In a right angled triangle, the square of length of its hypotenuse is equal to sum of square of other two sides' lengths"

Using Pythagoras theorem for given right triangle we have:

Thus, for given right triangle, the value of x is given as:

18²=\(x^{2} +\)6²

324=\(x^{2}\)+36

\(x^{2}\)=324-36

\(x^{2}\)=288

\(x\)=√288

\(x\)=16.97

the value of x is  16.97

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Mean ≈ 0.874

Median ≈ 0.877

Maximum = 0.933

Minimum = 0.83

Mode = None

To find the mean, median, maximum, minimum, and mode of the given numbers:

Mean: The mean is the average of a set of numbers.

To calculate the mean, add up all the numbers and divide the sum by the total count.

Mean = (0.834 + 0.861 + 0.927 + 0.877 + 0.831 + 0.925 + 0.912 + 0.83 + 0.849 + 0.933 + 0.884) / 11

Mean ≈ 0.874

Median: The median is the middle value when the numbers are arranged in ascending or descending order.

Since there are 11 numbers, the median would be the 6th number when arranged in order.

Arranging the numbers in ascending order:

0.83, 0.831, 0.834, 0.849, 0.861, 0.877, 0.884, 0.912, 0.925, 0.927, 0.933

Median ≈ 0.877

Maximum: The maximum is the largest value among the given numbers.

Maximum = 0.933

Minimum: The minimum is the smallest value among the given numbers.

Minimum = 0.83

Mode: The mode is the value(s) that appear most frequently in the given numbers.

If there is no value that appears more than once, there is no mode.

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The required answers are 1) \($$A = x^2 + 28x + 192$$\) 2) 300000 3) \($$x^2 + 28x + 192 = (x + 14 - 2\sqrt{19})(x + 14 + 2\sqrt{19})$$\).

area of the land purchased is given as 480m², and the dimensions of the land are (x+12)mx(x+16)m. Therefore, the area of the land can be expressed as:

\($$A = (x+12)(x+16)$$\)

Expanding this expression, we get:

\($$A = x^2 + 28x + 192$$\)

Hence, the area of the land purchased is given by the polynomial expression \($x^2 + 28x + 192$\).

The total budget for the expenses is Rs. 5,00,000. If Mr. Chand's daughter is ready to share 3/5 of the expenses, then the fraction of the expenses she will pay is:

\($\frac{3}{5}=\frac{x}{500000}$$\)

Simplifying this expression, we get:

\($x = \frac{3}{5}\times 500000 = 300000$$\)

Therefore, Mr. Chand's daughter will pay Rs. 3,00,000 towards the expenses.

We can solve the polynomial \($x^2 + 28x + 192$\) into different factors by using the quadratic formula:

\($x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$\)

Here, the coefficients of the polynomial are:

\($$a = 1, \quad b = 28, \quad c = 192$$\)

Substituting these values in the quadratic formula, we get:

\($x = \frac{-28 \pm \sqrt{28^2 - 4\times 1 \times 192}}{2\times 1}$$\)

Simplifying this expression, we get:

\($$x = -14 \pm 2\sqrt{19}$$\)

Therefore, the polynomial \($x^2 + 28x + 192$\) can be factored as:

\($$x^2 + 28x + 192 = (x - (-14 + 2\sqrt{19}))(x - (-14 - 2\sqrt{19}))$$\)

or

\($$x^2 + 28x + 192 = (x + 14 - 2\sqrt{19})(x + 14 + 2\sqrt{19})$$\)

So, we have factored the polynomial into two factors.

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Answer:

\((-\infty,2)\)

Step-by-step explanation:

Since \(-3x+6\nless 0\), then \(x\ngtr 2\), therefore, the domain of the function is \((-\infty,2)\).

After evaluating the expression 58 + (4x12-40) to the power of 2, we get 4356 or 4.356 ×10³ in scientific notation.

An expression or mathematical expression is a finite combination of symbols that are well-formed in accordance with context-dependent rules. To help define the logical syntax and order of operations, mathematical symbols can be used to represent variables, operations, functions, brackets, punctuation, and grouping.

Authors frequently distinguish between a formula and an expression, with the former referring to a mathematical object and the latter to a statement about such an object.

We have been asked to evaluate the Expression

​58 + (4x12-40) to the power of 2

⇒ (​58 + (4x12-40))²

Use (a + b)² = a² + b² + 2ab

= 58² + (4x12-40)² + 2(​58)(4x12-40)

= 3364 + (4x12-40)² + 116(4x12-40)

= 3364 + (48-40)² + 116(48-40)

= 3364 + (8)² + 116(8)

= 3364 + 64 + 928

= 4356

= 4.356 ×10³

Thus, After evaluating the expression 58 + (4x12-40) to the power of 2, we get 4356 or 4.356 ×10³ in scientific notation.

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Answer:

Each car weighs 2,265 pounds

Step-by-step explanation:

Given that the car carrier weighs 35,000 pounds when empty, that is, without cars, and that loading 7 cars its weight is 50,855 pounds, the difference between both values implies the weight of the 7 cars together, which is determined through the following calculation:

50,855 - 35,000 = X

15.855 = X

Thus, the weight of the 7 cars together is 15,855 pounds. In turn, the weight of each particular car is determined from the following division:

15.855 / 7 = X

2,265 = X

Therefore, each car weighs about 2,265 pounds.

Answer:

the answer is 1/6.......

The hypotenuse of a right triangle will be $561$.

What is hypotenuse?

In a right triangle, the hypotenuse is the longest side, an "opposite" side is the one across from a given angle, and an "adjacent" side is next to a given angle.

Lengths of legs of a right triangle are given that are $264$ and $495$.

According to The Pythagorean Theorem,

\(hypotenuse^{2} = lenght^{2} + lenght^{2}\\hypotenuse^{2} = 264^{2} + 495^{2}\\\\hypotenuse^{2} = 69,696 + 245,025\\ hypotenuse^{2} = 314,721\\hypotenuse = 561\)

The hypotenuse of a right triangle will be $561$.

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The solution set of this inequality is {x| x > -6.1}

Here we have the inequality:

2x + 8 > -4.2

To find the solution set, we need to isolate the variable x in one of the sides of the inequality. Doing that we will get:

2x + 8 > -4.2

2x > -4.2 - 8

2x > -12.2

x > -12.2/2

x > -6.1

So the set of all numbers larger than -6.1, this in number form is:

{x| x > -6.1}

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Answer:

A.2 x minus y = negative 6 and 3 x minus y = negative 5

Step-by-step explanation:

A ) 2x-y=-6, and 3x-y=-5

Consider the provided information.

First convert the statement into mathematical representation.Consider the smaller number is x and the larger number is y.

y, is equal to twice the sum of a smaller number and 3.    

This information can be written as: y=2(x+3)

The larger number is also equal to 5 more than 3 times the smaller number.

This information can be written as: y=5+3x

Answer:

A ) 2x-y=-6, and 3x-y=-5

Step-by-step explanation:

Working with the given percentages, we will get:

Here we need to work with percentages.

Let's say that X is last year's attendance. We know that 270 is the 125% of last year's attendance, then we will have the relation:

X*(125%/100%) = 270

X*1.25 = 270

X = 270/1.25 = 216

This means that last year's attendance was of 216 people.

The 25% of that is:

216*(25%/100%) = 216*(0.25) = 54

then we can complete the 3 blanks as:

125% of last year's attendance = 270

25% of last year's attendance = 54

100% of last year's attendance = 216

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Answer: Ned received 86 Points overall on the test and Ned lost 24 points overall on his test.

Step-by-step explanation: Ned got 19 questions correct and 6 questions incorrect. He as well got 10 bonus points for answering a bonus question correctly. We know each of the questions on the test (excluding the bonus question) is worth 4 points.

If Ned got 19 questions correct that means 19 x 4 = he received 76 points.

If Ned got 6 questions incorrect that means 6 x 4 = he lost 24 points.

If Ned got 1 question correct that is worth 10 points, that means he got an additional 10 points to his score.

We can add the amount of points Ned scored to the amount of bonus points he earned; 76 + 10 = 86 points total on his test.

Answer:

Ned received 86 Points on the test and Ned lost 24 points on his test.

Answer:

A. has a right angle

thats one

Answer:

I think it is A and D. Not 100% sure tho.

Answer:

\(x=3\)

Step-by-step explanation:

\(3^{x+2}+3^{x-3}=244\)

\(3^x3^2+\frac{3^x}{3^3} =244\)

\(3^x(9+\frac{1}{27})=244 \)

\(3^x(\frac{244}{27})=244 \)

\(3^x=27\)

\(x=log_3(27)\)

\(x=3\)

The average rate of change of the function over the interval is 4

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

y = 4x + 1

The interval is given as

[-1, 1)

The function is a linear function

This means that it has a constant average rate of change

From y = 4x + 1, we have

Rate = 4

Hence, the rate is 4

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Answer:

A mathematical proof is an inferential argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion.The argument may use other previously established statements, such as theorems; but every proof can, in principle, be constructed using only certain basic or original assumptions known as axioms, along with the accepted rules of inference.

Its got to be in there.

Answer: yes

Step-by-step explanation:

because if you were to ask someone this question they would respond with a number but a lot of people would reply with different answers which shows variability if it were to be compared with other different answers.  A statistical question is one that can be answered by collecting data and where there will be variability in that data.

Answer:240 square feet

Step-by-step explanation:length of rectangle DMLG

= DM = LG = (25 + 5) = 30 feet

width of rectangle DMLG

= ML = 8 feet

area of rectangle DMLG

= length × width

= 30 × 8

= 240 square feet

Answer: length of rectangle DMLG

= DM = LG = (25 + 5) = 30 feet

width of rectangle DMLG

= ML = 8 feet

area of rectangle DMLG

= length × width

= 30 × 8

= 240 square feet

wish that helped :)

Step-by-step explanation:

The surface area of the cylinder is 131.88 in².

A cylinder is a three-dimensional figure that has a radius and a height.

The volume of a cylinder is given as:

Example:

The volume of a cup with a height of 5 cm and a radius of 2 cm is

Volume = 3.14 x 2 x 2 x 5 = 62.8 cubic cm

We have,

The surface area of the cylinder = 2B + P h

Where B is the base area and P is the perimeter.

B = πr² and P = 2πr

Now,

We will assume that,

The radius of the cylinder = 3 in.

The height of the cylinder = 4 in.

So,

The surface area of the cylinder.

= 2B + P h

= 2πr² + 2πrh

= 2 x 3.14 x 3² + 2 x 3.14 x 3 x 4

= 56.52 + 75.36

= 131.88 in²

Thus,

131.88 in² is the surface area of the cylinder.

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Answer:-16

Step-by-step explanation:

Answer:

D. Multiply the top equation by -3.

Step-by-step explanation:

2x – 4y= 5           -3(2x – 4y= 5)          -6x + 12y= -15

6x - 3y=10                                                6x - 3y=10

No you can eliminate -6 and 6

Answer:

The answer is D.

Step-by-step explanation:

D. Multiply the top equation by -3.

This works because if you multiply the top equation by -3 then it will be

-3(2x – 4y= 5) which is -6x + 12y = -15

now our equation is : -6x +12y = -15

                                     6x - 3y = 10

As you can see we can eliminate -6x and 6x if we add those two equation together.

The length of BD is 22.

In the given scenario, let's consider the following information.

AD = 8

AE = 6

EC is 12 more than BD.

To find the length of BD, we can utilize the Intercepted Arcs Theorem, which states that when two secants intersect outside a circle, the measure of an intercepted arc formed by those secants is equal to half the difference of the measures of the intercepted angles.

From the given information, we know that AD = 8 and AE = 6.

Since these are the lengths of the secants, we can use them to calculate the intercepted arcs.

First, let's find the intercepted arc corresponding to AD:

Intercepted Arc ADB = 2 \(\times\) AD = 2 \(\times\) 8 = 16

Similarly, we can find the intercepted arc corresponding to AE:

Intercepted Arc AEC = 2 \(\times\) AE = 2 \(\times\) 6 = 12

Now, we know that EC is 12 more than BD.

Let's assume the length of BD as x.

BD + 12 = EC

Now, let's consider the intercepted arcs theorem:

Intercepted Arc ADB - Intercepted Arc AEC = Intercepted Angle B - Intercepted Angle C

16 - 12 = Angle B - Angle C

4 = Angle B - Angle C.

Since Angle B and Angle C are vertical angles, they are congruent:

Angle B = Angle C.

Therefore, we can say:

4 = Angle B - Angle B

4 = 0

However, we have reached an inconsistency here.

The equation does not hold true, indicating that the given information is not consistent or there may be an error in the problem statement.

As a result, we cannot determine the length of BD based on the given information.

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\(\\ \sf\longmapsto 4\left(\dfrac{7}{8}\right)+7\left(\dfrac{3}{4}+\dfrac{1}{8}\right)-10\)

\(\\ \sf\longmapsto \dfrac{4(7)}{8}+7\left(\dfrac{6+1}{8}\right)-10\)

\(\\ \sf\longmapsto \dfrac{28}{8}+7\times \dfrac{7}{8}-10\)

\(\\ \sf\longmapsto \dfrac{28}{8}+\dfrac{49}{8}-10\)

\(\\ \sf\longmapsto \dfrac{28+49-80}{8}\)

\(\\ \sf\longmapsto \dfrac{78-80}{8}\)

\(\\ \sf\longmapsto \dfrac{-2}{80}\)

\(\\ \sf\longmapsto \dfrac{-1}{40}\)

Answer:

x = 5

y = 5√2

Step-by-step explanation:

In a 45-45-90 degree right triangle, the two legs form the right angle, and the hypotenuse is opposite the right angle.

The side lengths of a 45-45-90 right triangle are in the ratio

1 : 1 : √2

The legs are congruent, so if one leg has length 5, the other leg also has length 5.

The hypotenuse is √2 times the length of the legs.

x = 5

y = 5√2

(x-9)/(2)=x+1
Multiply both sides by 2
x-9 = 2(x+1)
Distribute the 2
x-9=2x+2
Add 9 to both sides
x=2x+11
Subtract 2x from both sides
-x=11
Divide both sides by -1
x=-11

(-11 - 9)/2 = -10 = -11 + 1

It is correct when substituted back in.