I need help with this math question (complex fractions and rational expressions). For the answer, I need a step-by-step explanation so I can understand it, thank you :) I tried putting it into Symbolab to understand it but that wasn't very helpful so I think human assistance would be more beneficial haha. - [tex](\frac{(7x^{2} + 5x) }{x^{2} + 1 } ) - (\frac{5x}{x^{2} -6})[/tex]

Answer:

Step-by-step explanation:

l^2=[(7-V2)/2]^2+(9-V2/2)^2=

49-7V2+2/4+81-9V2+2/4=

49+81+4/4-16V2=

131-16V2=108.4 ft

so l=V108.4≈10.4ft

Answer:

126 meters

Step-by-step explanation:

First, let's find the circumference of the pond. We know that C = πd, π = 3.14 and d = 10 so the circumference is 3.14 * 10 = 31.4 meters. However, the person walks around the pond 4 times so the answer is 31.4 * 4 = 125.6 meters which rounds to about 126 meters.

Answer:

area = 2236 in²

Step-by-step explanation:

area of a triangle = 1/2 b h

b = 86

h = 52

plug in values

area = 1/2 * 86 * 52

area = 2236 in²

Answer:

60h +16 is the answer. If you wanna simpifiy it and the rule still applies then 60 times 4 =240 plus 16 which is 256. 256 is the Simplest anwser.

Step-by-step explanation:

Answer:

10:14

Step-by-step explanation:

10lions:14tigers

Answer:

5:7

Step-by-step explanation:

Answer:

B) approximately normal with mean 2.3 and standard deviation 2

Step-by-step explanation:

Given the following :

Mean crimes per day = 2.3

Standard deviation = 2

Number of samples = 100

Sampling distribution of the mean:

According to the central limit theorem:

Sample mean = population mean

2.3 = 2.3

The standard deviation of the sample (s) : ratio of the population standard deviation and square root of the sample size.

s = population standard deviation / √sample size

s = 2 / √100

s = 2 / 10

s = 0.2

The central limit theorem also posits that once ths sample size is large enough, the sampling of the sample mean will be approximately normal.

Hence, the distribution is approximately normal, with mean of 2.3 and standard deviation of 0.2

Answer:

537.2 ft^2

Step-by-step explanation:

For this problem, we need to find the area of both the inner and outer circle and subtract the area of the outer circle from the area of the inner circle.

The equation for the area of a circle is:

A = πr^2

So we are given the diameters of the circles.  We know that the diameter of a circle is twice the radius.

Let's find the area of the 10ft diameter circle:

A_Little = π(10/2)^2 = π(5)^2 = 25π

Let's find the area of the 28ft diameter circle:

A_Big = π(28/2)^2 = π(14)^2 = 196π

So the area of the big circle excluding the inner circle would be as follows:

196π - 25π = 171π

So 171π in terms of decimals rounded to the nearest tenth would be 537.2.

Cheers.

Area of big remain circle is 536.94 feet²

Given that;

Diameter of big circle = 28 feet

Diameter of small circle = 10 feet

Find:

Area of big remain circle

Computation:

Radius of big circle = 28 / 2 = 14 feet

Radius of small circle = 10 / 2 = 5 feet

Area of big remain circle = π(R1² - R2²)

Area of big remain circle = 3.14(14² - 5²)

Area of big remain circle = 3.14(171)

Area of big remain circle = 536.94 feet²

Find out more information about 'Area of circle'

https://brainly.com/question/1238286?referrer=searchResults

Hello,

4. you have sequences defined by the first term and a recursive relation.

[tex]a_1=3\\\\a_n=2a_{n-1} \ \ \text{ for n}> 1[/tex]

Take n = 2, it gives

[tex]a_2=2a_1[/tex] , right?

But you know [tex]a_1=3[/tex]

so [tex]a_2=2a_1=2*3=6[/tex]

This is the second term. You are asked to find the first three terms.

Now, let's take n = 3

[tex]a_3=2a_2=2*6=12[/tex]

So the first three terms are 3, 6, 12.

6.

[tex]a_1=12\\\\a_2=\dfrac{1}{2}a_1+1=\dfrac{12}{2}+1=6+1=7 \\ \\a_3=\dfrac{1}{2}a_2+1=\dfrac{7}{2}+1=\dfrac{9}{2}[/tex]

8.

[tex]a_1=10\\ \\a_2=-3a_1=-3*10=-30\\\\a_3=-3a_2=-3*(-30)=90[/tex]

10.

[tex]a_1=2\\\\a_2=-1\\\\a_3=a_2+a_1=-1+2=1\\\\a_4=a_3+a_2=1-1=0[/tex]

Do not hesitate if you have any question.

Thank you

Answer:

We can conclude that there is sufficient evidence to state that the companies claim is not false      

Step-by-step explanation:

From the question we are told that

    The  population proportion is  [tex]p = 0.35[/tex]

   The  level of significance is  [tex]\alpha = 0.10[/tex]

    The sample  size is  n  =  50

Generally the  sample proportion is mathematically represented as

     [tex]\r p = \frac{16}{50 }[/tex]

    [tex]\r p = 0.32[/tex]

The null hypothesis is  [tex]H_o : p\ge 0.35[/tex]

The  alternative  hypothesis is  [tex]H_a : p< 0.35[/tex]

Generally the standard error is evaluated as

      [tex]SE = \sqrt{ \frac{0.35 (1- 0.35 )}{ \sqrt{50 } } }[/tex]

      [tex]SE = 0.067[/tex]

So  

    The test statistics is  evaluated as

                [tex]t = \frac{\r p - p }{ SE }[/tex]

=>             [tex]t = \frac{0.32 - 0.35 }{ 0.067 }[/tex]

=>             [tex]t = -0.45[/tex]

The  p-value is obtained from the z-table  , the values is  

       [tex]P( Z < -0.45) = 0.32636[/tex]

From the calculation we see that

        [tex]p-value > \alpha[/tex] so we fail to reject the null hypothesis

Hence we can conclude that there is sufficient evidence to state that the companies claim is not false

Answer:

11 bags of spoons and 3 bags of forks

Step-by-step explanation:

figure out what common number that multiples of 6 and multiples of 22 share

that number is 66

6x11 = 66 spoons total

22x3= 66 forks total

Answer: B

Step-by-step explanation:

Answer:

Solution : Option B

Step-by-step explanation:

Taking a look at the graph, we can see that the parabola has the following features.

Vertex : (3, - 4)

y - intercept : (0, 5)

x - intercept : (1, 0) and (5, 0)

axis of symmetry : x = 3

The vertex, y - intercept, and x - intercept can all be determined through the intersection of the graph at a certain point. However the axis of symmetry is the line with which splits this parabola into two " similar " parts.

Your solution is option b.

Answer:

a) 22 pine trees

b) x² = 2² + 0.75²

Step-by-step explanation:

a) The volume of a cube is given as:

Volume of cube = length³

The length of the cube = length of the edges = 3 inches, hence:

Volume of cube = (3 inches)³  = 27 in³

The pine tree is the shape of a cone with diameter of 1.5 inches and a height (h) of 2 inches. The radius (r) = diameter / 2 = 1.5 inches / 2 = 0.75 inches.

The volume of the cone = πr²(h/3) = π × (0.75)² × (2/3) = 1.178 in³

The number of pine trees that the artist can make = Volume of cube / Volume of cone = 27 / 1.178 = 22.9

The number of pine trees that can be made = 22

b) The yam length need to extend from the top of the tree to the base is the same as the slant height of the cone.

Let the yam length be x, therefore:

x² = height² + radius²

x² = 2² + 0.75²

x² = 4 + 0.5625 = 4.5625

x = √4.5625 = 2.136 in

The yam length is 2,136 in

Answer: 3

Step-by-step explanation:

Given:  A recipe for a pizza that serves 12 people calls for 2 cups of shredded cheese.

12 people = 2 cups of shredded cheese.

Multiply 4 on both sides , we get

48 people = 8 cups of shredded cheese.

So we require 8 cups of shredded cheese  to make pizza for 48 people.

Since, each bag of shredded cheese contains 3 cups.

Then minimum number of bags required = [tex]\dfrac{8}{3}=2.67\approx3[/tex]

Hence, minimum 3 bags required to make pizza for 48 people.

Answer:

48

Step-by-step explanation:

add the values of the ages of the lecturers which should give you 434 then divide by the number of lecturers in question

=480/10

=48

Answer:

48.

Step-by-step explanation:

There are a total of 10 lecturers in the list

You find the mean by dividing the sum of all the ages by 10.

The mean age = 480/10 = 48.

PEMDAS is the order of operation, and is what you follow to solve a expression/equation.

PEMDAS =

Parenthesis

Exponents: This step also includes solving for any roots.

Multiplication

Division

Addition

Subtraction

Answer:

the answer is

Step-by-step explanation:

Parenthesis

Exponents

Multiplication

Division

Addition

Subtraction

Answer:

x=1

Step-by-step explanation:

the line is one unit up from the x axis

Answer: x=-150

Step-by-step explanation:

To solve for x, we would need to use our order of operations.

0.3x+18=-27                       [subtract both sides by 18]

0.3x=-45                              [divide both sides by 0.3]

x=-150

Answer:

[tex]9y+2y-5y=6y[/tex]

Step-by-step explanation:

So we have the expression:

[tex]9y+2y-5y[/tex]

To simplify, simply combine the like terms. Therefore:

[tex]9y+2y-5y\\=11y-5y\\=6y[/tex]

Further notes:

To understand why we can combine like terms in the first place, we just need to use the distributive property. So we have the expression:

[tex]9y+2y-5y[/tex]

Now, factor out a y from the three terms:

[tex]=y(9+2-5)[/tex]

Do all the operations inside the parenthesis:

[tex]y(9+2-5)\\=y(11-5)\\=y(6)=6y[/tex]

And we moved the y back to the front!

This is the same result as before. When combining like terms, this is what we're essentially doing but without doing the distributive property manually. I hope you understand a bit better on how and why we can combine like terms!

Answer:

6y

Step-by-step explanation:

We are given the expression:

9y+2y-5y

and asked to simplify.

Each term in the expression has the same variable, a "y". Therefore, all three terms are like terms. We can combine the like terms in the expression.

First, factor out a y from each term.

9y+2y-5y

(9+2-5)*y

Solve inside the parentheses first. Add 9 and 2.

(11-5)*y

Subtract 5 from 11.

(6)*y

6y

The expression 9y+2y-5y simplified is 6y.

Answer:

one large box equals 15.75kg

one small box equals 13.75kg

Step-by-step explanation:

First, identify your variables:

Let "l" represent the weight of one large box.

Let"s" represent the weight of one small box.

Then, stack the two equations on top of each other:

[tex]5l+3s=120\\7l+9s=234[/tex]

Next, multiply the first equation by 3 so we can use elimination of the "s" variable to find the "l" variable first:

[tex]3(5l+3s=120)\\7l+9s=234\\\\15l+9s=360\\7l+9s=234[/tex]

Now, subtract the two equations to cancel out the s-variable and find the l-variable:

[tex]15l+9s=360\\-(7l+9s=234)\\8l=126\\\frac{8l}{8}=\frac{126}{8}\\l=15.75[/tex]

Then, substitute your l-variable in the original first equation to find the s-variable:

[tex]5l+3s=120\\5(15.75)+3s=120\\78.75+3s=120\\78.85-78.75+3s=120-78.75\\3s=41.25\\\frac{3s}{3}=\frac{41.25}{3}\\s=13.75[/tex]

With all the information that is collected, you find that one large box weighs 15.75kg and one small box weighs 13.75kg.

Answer:

(a) The cumulative frequency curve for the data is attached below.

(b) (i) The inter-quartile range is 10.08.

(b) (ii) The 70th percentile class scores is 0.

(b) (iii) the probability that a student scored at most 50 on the examination is 0.89.

Step-by-step explanation:

(a)

To make a cumulative frequency curve for the data first convert the class interval into continuous.

The cumulative frequencies are computed by summing the previous frequencies.

The cumulative frequency curve for the data is attached below.

(b)

(i)

The inter-quartile range is the difference between the third and the first quartile.

Compute the values of Q₁ and Q₃ as follows:

Q₁ is at the position:

[tex]\frac{\sum f}{4}=\frac{100}{4}=25[/tex]

The class interval is: 34.5 - 39.5.

The formula of first quartile is:

[tex]Q_{1}=l+[\frac{(\sum f/4)-(CF)_{p}}{f}]\times h[/tex]

Here,

l = lower limit of the class consisting value 25 = 34.5

(CF)[tex]_{p}[/tex] = cumulative frequency of the previous class = 24

f = frequency of the class interval = 20

h = width = 39.5 - 34.5 = 5

Then the value of first quartile is:

[tex]Q_{1}=l+[\frac{(\sum f/4)-(CF)_{p}}{f}]\times h[/tex]

     [tex]=34.5+[\frac{25-24}{20}]\times5\\\\=34.5+0.25\\=34.75[/tex]

The value of first quartile is 34.75.

Q₃ is at the position:

[tex]\frac{3\sum f}{4}=\frac{3\times100}{4}=75[/tex]

The class interval is: 44.5 - 49.5.

The formula of third quartile is:

[tex]Q_{3}=l+[\frac{(3\sum f/4)-(CF)_{p}}{f}]\times h[/tex]

Here,

l = lower limit of the class consisting value 75 = 44.5

(CF)[tex]_{p}[/tex] = cumulative frequency of the previous class = 74

f = frequency of the class interval = 15

h = width = 49.5 - 44.5 = 5

Then the value of third quartile is:

[tex]Q_{3}=l+[\frac{(3\sum f/4)-(CF)_{p}}{f}]\times h[/tex]

     [tex]=44.5+[\frac{75-74}{15}]\times5\\\\=44.5+0.33\\=44.83[/tex]

The value of third quartile is 44.83.

Then the inter-quartile range is:

[tex]IQR = Q_{3}-Q_{1}[/tex]

        [tex]=44.83-34.75\\=10.08[/tex]

Thus, the inter-quartile range is 10.08.

(ii)

The maximum upper limit of the class intervals is 69.5.

That is the maximum percentile class score is 69.5th percentile.

So, the 70th percentile class scores is 0.

(iii)

Compute the probability that a student scored at most 50 on the examination as follows:

[tex]P(\text{Score At most 50})=\frac{\text{Favorable number of cases}}{\text{Total number of cases}}[/tex]

                                 [tex]=\frac{10+4+10+20+30+15}{100}\\\\=\frac{89}{100}\\\\=0.89[/tex]

Thus, the probability that a student scored at most 50 on the examination is 0.89.

Answer:

Answer is C

Step-by-step explanation:

This is because Lithium =2.8.1

Sodium=2.8.8.1

Valence electron is the electron located in the last shell

Hope this is correct and helpful

HAVE A GOOD DAY!

Answer:

Step-by-step explanation:

The equation is y = slope + or - y-intercept

Slope = mx

So the slope is -4

The slope can be found also by having 2 points and doing (y2 - y1)/(x2 - x1). Also, you can do rise over run. These are options for if you have a graph.

Hope this helped,

Kavitha

Answer:

-4

Step-by-step explanation:

y= -4x + 9

y= mx + C

comparing

m= -4

S = Total students

B = number that had bikes

M = number that had a master card

P = number that had a phone

S = 200

B = 110

M = 25

P = 130

BM = 50

MP = 30

BP = 60

BMP = 10

B + M + P = 110 + 25 + 130 = 265

BM + MP + BP - BMP = 50 + 30 + 60 -10 = 130

265 - 130 = 135

Students that had none of the three = 200 - 135 = 65

Answer:

E(Y) = √a + √(a+12)

Step-by-step explanation:

X1 and X2 are independent variables while Y is the dependent variable, such that

Y = f(X1, X2)

Meaning Y is a function of X1 and X2

In this case,

Y = 2√X1X2

When (X1, X2) = (a, 1) ; Y = 2√a

When (X1, X2) = (a+12, 1) ; Y = 2√a+12

The expected value of Y is

[2√a + 2√a+12] ÷ 2  = √a + √a+12

Hello, let's note

[tex]f(x)=x^4-3x^3+x^2+3x-2\\\\f(1)=1-3+1+3-2=0[/tex]

So we can put (x-1) in factor. We are looking for a and b such that

[tex]f(x)=(x-1)(x^3+ax^2+bx+2)=x^4+(a-1)x^3+(b-a)x^2+(2-b)x-2[/tex]

We identify the like terms, it comes

a-1=-3 <=> a = -2

b-a=1 <=> b = 1 + a = -1

2-b=3

So it comes.

[tex]f(x)=(x-1)(x^3-2x^2-x+2)[/tex]

And we can go further using the same method to find that

[tex]x^3-2x^2-x+2=(x-1)(x^2-x-2)[/tex]

The sum of the zeroes is 1=2-1 and the product is -2=(-1)*2, so, we can factorise.

[tex]\boxed{f(x)=(x-1)^2(x+1)(x-2)}[/tex]

The sign of f(x) is the same as the sign of (x+1)(x-2) as a square is always positive.

To find the sign of a product, we can apply the following.

"- multiplied by - gives +"

"+ multiplied by + gives +"

"- multiplied by + gives -"

"+ multiplied by - gives -"

This is this what we are doing below.

[tex]\begin{array}{|c|ccccccc}x&-\infty&&-1&&2&&+\infty\\---&---&---&---&---&---&---&---\\x+1&-&-&0&+&3&+&+\\---&---&---&---&---&---&---&---\\x-2&-&-&-3&-&0&+&+\\---&---&---&---&---&---&---&---\\f(x)&+&+&0&-&0&+&+\\\end{array}[/tex]

So, to answer the question

[tex]\Large \boxed{\sf \bf \ f(x) < 0 <=> -1 < x < 2 \ }[/tex]

Thank you.

Answer: 10,000,000

Step-by-step explanation: when anything rasied to the power you take what ever the Exponaten is and take how everything was there for example 10⁷ 10x10x10x10x10x10x10. And you multiply that.

Answer:

The answer is: 10,000,000

You would do 10 x 10 x 10 x 10 x 10 x 10 x 10

Answer:

Step-by-step explanation:

In the attached figure, we have defined LM to be length x. Then the other lengths on side AC are ...

  AM = LR = x/√3

  RC = (2/√3)RK = (2/√3)(2/√3)x = 4/3x

Then the sum of lengths along AC is ...

  AC = AM +ML +LR +RC

  1 = x(1/√3 +1 +1/√3 +4/3) = x(7/3 +2/√3) = x(7√3 +6)/(3√3)

Then the value of x is ...

  [tex]x=\dfrac{3\sqrt{3}}{7\sqrt{3}+6}=\dfrac{3\sqrt{3}(7\sqrt{3}-6)}{(7\sqrt{3})^2-6^2}=\dfrac{3(21-6\sqrt{3})}{3(49-12)}\\\\\boxed{MN=\dfrac{21-6\sqrt{3}}{37}}\\\\RK=\dfrac{2\sqrt{3}}{3}MN\\\\\boxed{RK=\dfrac{14\sqrt{3}-12}{37}}[/tex]

Answer:

See below.

Step-by-step explanation:

We are given the equation:

[tex]x+y=2[/tex]

And we subtracted x from both sides to acquire:

[tex]y=2-x[/tex]

Notice that this is the slope-intercept form:

[tex]y=mx+b[/tex]

Where m is the slope and b is the y-intercept.

If we rearrange our equation, we acquire:

[tex]y = -(1)x+(2)[/tex]

Therefore, m = -1 and b = 2.

In other words, the slope is -1 and the y-intercept is 2.

Answer:

[tex]\Large \boxed{{m=-1, \ b=2}}[/tex]

Step-by-step explanation:

x + y = 2

We need the equation in the form y = mx + b.

m = slope

b = y-intercept

Solve for y by subtracting x from each side.

y = 2 - x

The -x can be written as -1x.

y = 2 - 1x

Rearrange the expression.

y = -1x + 2

The equation is in form y = mx + b.

The slope is -1.

The y-intercept is 2.

Answer:

(BD/DA) = (CE/EA)

slope is calculated using rise over run, and the ratios represent the rise over the run

Answer:

3.64

Step-by-step explanation:

Identify the hundredth:

3.642

Check the value of the thousandth:

3.642

2 is less than four, therefore, we will round down.

3.642 ≈ 3.64