The sum of three numbers is 125. The first number is 7 more than the first. The third number is 4 times the second.What are the numbers

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:

B

Step-by-step explanation:

This is because to write a polynomial in standard form they are arranged from the highest degree to the lowest degree.

[tex] {x}^{3} \: carries \:the \: \: highest \: degree\: which \: is \: 3.[/tex]

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

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:

see below (I hope this makes sense and I hope it helps!)

Step-by-step explanation:

Points are found in the form (x, y) where x represents the x - value which is basically how far you move from the origin on the x-axis, and the same goes for y except it represents how far you move from the origin on the y-axis. A positive x means you move right, a negative x means you move left, a positive y means you move up and a negative y means you move down. Following these rules, to plot (2, 3), you move 2 units right and 3 units up from the origin and to plot (3, 2), you move 3 units right and 2 units up from the origin. The difference between plotting the two points is that first of all, they are different points so they are in different locations and second, their coordinates are "flipped"; what I mean by that is the x-coordinate of the first point is the y-coordinate of the second point and vice versa. Therefore, you move the same amount but in different directions.

These points are similar.

They both lie in quadrant 1.

However, the x coordinate is different in each ordered pair.

So (3, 2) moves farther from the origin than (2 , 3).

However, (2, 3) moved farther up than (3, 2).

Take a look below.

Answer:

9√3

Step-by-step explanation:

simpilify the expression by multiplying exponents

= 3 1/9

using a m/n = n√a^m, transform to  9√3

Answer:

Option B

Step-by-step explanation:

(3^2/3)^1/6

=> Multiply the powers

=> 3^2/18

=> 3^1/9

In the above answer, 9 is the root. 1 is the power of 3

=> 9th root of 3.

So, the answer is B

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: 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:

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: 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:

(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:

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.

Answer:

(BD/DA) = (CE/EA)

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

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:

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

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:

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:

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

Answer:

10:14

Step-by-step explanation:

10lions:14tigers

Answer:

5:7

Step-by-step explanation:

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: 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:

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:

Largest p value

Step-by-step explanation:

The p value is basically used to check if an effect is in existence. A high p value shows that the evidence is weak and cannot be used to say an effect exists.

A p value that is greater than 0.05 is considered to be large and it shows weak evidence against H0, the null hypothesis.

Therefore of the 10 variables, we can use the criterion of largest p values to eliminate one of the variables.

Answer:

x=1

Step-by-step explanation:

the line is one unit up from the x axis

Answer: 354500m²

Step-by-step explanation:

Area of the recreation park  = 560m x 700m

                                               = 392000m²

Area used for soccer and baseball = 250m x 150m

                                                          = ¹⁵⁰⁰⁰⁰/₄

                                                          = 37500m².

Area of the remaining park  = 392000 - 37500

                                              = 354500m²

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:

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: 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