Fine the length of the side labeled x. Around intermediate values to the nearest tenth. use the rounded values to calculate the next value. round your answer to the nearest tenth.

Answer:

1 * 10 ^ -7

Step-by-step explanation:

Answer:

The  margin of error is  [tex]E = 0.021[/tex]

Step-by-step explanation:

From the question we are told that  

   The  population size is  [tex]n = 2161[/tex]

    The number that showed improvement is  [tex]k = 1214[/tex]

Generally the sample proportion is mathematically represented as

        [tex]\r p = \frac{ 1214}{2161}[/tex]

=>     [tex]\r p = 0.56[/tex]

Given that the confidence level is  95% then the level of significance is mathematically represented as

        [tex]\alpha =(100-95) \%[/tex]

=>     [tex]\alpha =0.05[/tex]

The  critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table is  

      [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]

Generally the margin of error is mathematically represented as

        [tex]E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\r p (1 - \r p )}{n} }[/tex]

=>      [tex]E = 1.96 * \sqrt{\frac{ 0.56(1 - 0.56 )}{2161} }[/tex]

=>      [tex]E = 0.021[/tex]

Answer:

Step-by-step explanation:

Hello, I attached the graph.

This is a parabola, then a line and finally an horizontal line.

The vertex of the parabola is (0,0) and (2,4) is on the graph.

For the second part, draw a line which is passing by (2,4) and (0,4)

Finally, draw the line y = 4

You can see that f is continuous everywhere except in x = 4.

So, for any c real different from 4 the limit of f(x) exists.

Thank you

Answer: Number 1- you make 7 bracelets in 1 hour.

Step-by-step explanation:

Number 1- You divide 35 by 5 and get 7. The hour (5) goes at the denominator and the number of bracelets(35)goes on the numerator and you divide

Answer:

$540

Step-by-step explanation:

We know Damien earned $9 per hour, worked 30 hours a week and was paid every 2 weeks.

We can write an expression to something like this:

(9 x 30) x 2

Which would give us 540

The question asks for the Gross income (the total income, before any taxes or deductions)

Which means that his gross income was $540

Answer:

About $6000  

Step-by-step explanation:

Multiply 689 × 9.

When you are estimating, you should round the numbers off to values that you can easily work in your head.

I would round 9 up to 10 and 689 down to 600 to compensate. Then,

10 credit hours × $600/credit hour ≈ $6000.

It should cost about $6000 to register for 9 credit hours.

Answer:

1.131,5

Step-by-step explanation:

Answer/Step-by-step explanation:

Given:

Line equation => [tex] 2.1x + 9.9y - 9.2 = 0 [/tex]

Required:

x-intercept and y-intercept of the line.

SOLUTION:

The x-intercept is the point where the line intercepts the x-axis. To find the x-intercept of the line for which the equation is given above, set y = 0 and solve for x.

[tex] 2.1x + 9.9(0) - 9.2 = 0 [/tex]

[tex] 2.1x + 0 - 9.2 = 0 [/tex]

[tex] 2.1x - 9.2 = 0 [/tex]

[tex] 2.1x - 9.2 + 9.2 = 0 + 9.2 [/tex]

[tex] 2.1x = 9.2 [/tex]

[tex] \frac{2.1x}{2.1} = \frac{9.2}{2.1} [/tex]

[tex] x = 4.4 [/tex] (approximated)

The y-intercept is the point where the line intercepts the y-axis. At this point, x = 0. Set x = 0 and solve for y to find the y intercept.

[tex] 2.1(0) + 9.9y - 9.2 = 0 [/tex]

[tex] 9.9y - 9.2 = 0 [/tex]

[tex] 9.9y - 9.2 + 9.2 = 0 + 9.2 [/tex]

[tex] 9.9y = 9.2 [/tex]

[tex] y = \frac{9.2}{9.9} [/tex]

[tex] y = 0.9 [/tex] (approximated)

Answer:

minimum is -3,0

Step-by-step explanation:

Answer:

the answer is one twelve 1/12

Answer:

The solution set is {-3, -6}.

Step-by-step explanation:

x^2 + 18 = -9x

x^2 + 9x + 18 = 0

(x + 3)(x + 6) = 0

x = -3, -6.

Step-by-step explanation:

(i) 5 ≤ 2x − 4 ≤ 8 add 4 to all three expressions

9 ≤ 2x ≤ 12 divide by 2

9/2 ≤ x ≤ 6

(ii) −10 < (4 −3y)/− 5 ≤ 4 multiply all sides by -5

-20 ≤ 4 - 3y < 50 subtract 4

-24 ≤ -3y < 46 divide with -3

-46/3 < y ≤ 8

Answer:

Option (A) and Option (D)

Step-by-step explanation:

Point on the parabola is (x, y).

Focus given as (2, -4) and directrix of the parabola is y = -6

Therefore, distance of the point from the directrix will be,

d = |(y + 6)|

Similarly, distance of the point (x, y) from the focus will be,

d = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

  = [tex]\sqrt{(x-2)^2+(y+4)^2}[/tex]

Therefore, Option (A) and Option (D) will be the correct options.

Answer:

[tex]$\frac{51}{5}t$[/tex]

Step-by-step explanation:

Let W = [tex]$(p_0, p_1, p_2)$[/tex]  be orthogonal polynomials which is equal to [tex]$(4, 3t, t^2 -2)$[/tex], which defines the inner products as

[tex]$(f,g)=f(-2)g(-2)+f(-1)g(-1)+f(0)g(0)+f(1)g(1)+f(2)g(2)$[/tex]

Now, we find the orthogonal projection of [tex]$p=3t^3$[/tex] on W.

So the projection is

[tex]$Proj_W p = \frac{(p_0,p)}{(p_0,p_0)}p_0+\frac{(p_1,p)}{(p_1,p_1)}p_1+\frac{(p_2,p)}{(p_2,p_2)}p_2$[/tex]

[tex]$(p_0,p)=p_0(-2)p(-2)+p_0(-1)p(-1)+p_0(0)p(0)+p_0(1)p(1)+p_0(2)p(2)$[/tex]

          [tex]$=4(-24)+4(-3)+4(0)+4(3)+4(24)=0$[/tex]

[tex]$(p_0,p_0)=p_0(-2)p_0(-2)+p_0(-1)p_0(-1)+p_0(0)p_0(0)+p_0(1)p_0(1)+p_0(2)p_0(2)$[/tex]

            [tex]$=4(4)+4(4)+4(4)+4(4)+4(4)=80$[/tex]

[tex]$(p_1,p)=p_1(-2)p(-2)+p_1(-1)p(-1)+p_1(0)p(0)+p_1(1)p(1)+p_1(2)p(2)$[/tex]

          [tex]$=(-6)(-24)+(-3)(-3)+0(0)+3(3)+6(24)=306$[/tex]

[tex]$(p_1,p_1)=p_1(-2)p_1(-2)+p_1(-1)p_1(-1)+p_1(0)p_1(0)+p_1(1)p_1(1)+p_1(2)p_1(2)$[/tex]

            [tex]$=(-6)(-6)+(-3)(-3)+0(0)+3(3)+6(6)=90$[/tex]

[tex]$(p_2,p)=p_2(-2)p(-2)+p_2(-1)p(-1)+p_2(0)p(0)+p_2(1)p(1)+p_2(2)p(2)$[/tex]

         [tex]$=2(-24)+(-1)(-3)+(-2)(0)+(-1)(3)+2(24)=0$[/tex]

[tex]$(p_2,p_2)=p_2(-2)p_2(-2)+p_2(-1)p_2(-1)+p_2(0)p_2(0)+p_2(1)p_2(1)+p_2(2)p_2(2)$[/tex]

            [tex]$=(2)(2)+(-1)(-1)+(-2)(-2)+(-1)(-1)+2(2)=14$[/tex]

Therefore,

[tex]$Proj_W p = \frac{(p_0,p)}{(p_0,p_0)}p_0+\frac{(p_1,p)}{(p_1,p_1)}p_1+\frac{(p_2,p)}{(p_2,p_2)}p_2$[/tex]

              [tex]$=\frac{0}{80}(4)+\frac{306}{90}(3t)+\frac{0}{14}(t^2-2)$[/tex]

              [tex]$=\frac{51}{5}t$[/tex]

Answer:

0.875

Step-by-step explanation:

14÷16= 0.875

divide the mass value by 16

Hi there! :)

Answer:

[tex]\huge\boxed{-5.5q - 7}[/tex]

-(5.5q + 7)

Distribute:

-(5.5q) -(7)

-5.5q - 7

Answer:

Z≥0 = {0, 1, 2, .

Step-by-step explanation:

Just took test

Answer:

a.   [tex]X(T) = 120 (1.058)^T[/tex]

b.   Population after 3 years is 142

c.   50 years

Step-by-step explanation:

Given

Type of growth: Exponential

Initial number of rats = 120

Number of rats (15months) = 280

Solving (a)

Since the growth type is exponential, we make use of the following exponential progression

[tex]X_T = X_0 (1 + R)^T[/tex]

Where Xo is the initial population;

Xo = 125

[tex]X_T[/tex] is the current population at T month

So;

[tex]X_T = 280[/tex]; when [tex]T = 15[/tex]

Substitute these values in the above formula

[tex]280 =120 * (1 + R)^{15}[/tex]

Divide both sides by 120

[tex]\frac{280}{120} =(1 + R)^{15}[/tex]

[tex]2.3333 =(1 + R)^{15}[/tex]

Take 15th root of both sides

[tex]\sqrt[15]{2.3333} =1 + R[/tex]

[tex]1.05811235561 = 1 + R[/tex]

Subtract 1 from both sides

[tex]R = 1.05811235561 - 1[/tex]

[tex]R = 0.05811235561[/tex]

[tex]R = 0.058[/tex] (Approximated)

Plug in values of R and Xo in [tex]X_T = X_0 (1 + R)^T[/tex]

[tex]X_T = 120 (1 + 0.058)^T[/tex]

[tex]X_T = 120 (1.058)^T[/tex]

Write as a function

[tex]X(T) = 120 (1.058)^T[/tex]

Hence, the function is [tex]X(T) = 120 (1.058)^T[/tex]

Solving (b):

Population after 3 years

In this case, T = 3

So:

[tex]X(T) = 120 (1.058)^T[/tex]

[tex]X(3) = 120 (1.058)^3[/tex]

[tex]X(3) = 120 * 1.18466445254[/tex]

[tex]X(3) = 142.159734305[/tex]

[tex]X(3) = 142[/tex] (Approximated)

Solving (c): When population will reach 2000

Here: X(T) = 2000

So:

So:

[tex]2000 = 120 (1.058)^T[/tex]

Divide both sides by 120

[tex]\frac{2000}{120} = 1.058^T[/tex]

[tex]16.667 = 1.058^T[/tex]

Take Log of both sides

[tex]Log(16.667) = Log(1.058^T)[/tex]

Apply law of logarithm

[tex]Log(16.667) = TLog(1.058)[/tex]

Divide both sides by Log(1.058)

[tex]T = \frac{Log(16.667)}{Log(1.058)}[/tex]

[tex]T = 49.9009236926[/tex]

Approximate

[tex]T = 50\ years[/tex]

Answer:

1

Step-by-step explanation:

4^10/4^10 x 7^O =

= 4^(10 - 10) * 1

= 4^0 * 1

= 1 * 1

= 1

Answer:

1

Step-by-step explanation:

4^10/4^10 = 1

7^0 = 1

1 x 1 = 1

Answer:580

Step-by-step explanation:

Answer:

The answer of the question is 10.53%.

Answer: $1.6

Step-by-step explanation:

price × percentage of tax=amount of tax

$20 × 8%=20 × 0.08= $1.6

Hope this helps!! :)

Answer:

125°

Step-by-step explanation:

Sum of angles of triangle equals 180°:

Answer:

x=125

Step-by-step explanation:

because sum of interior angles of a triangle is 180

Answer: Hi!

Since 5 is being multiplied by x, and x is equal to 2, be would multiply 5 and 2. 5 * 2 is equal to 10.

Hope this helps!

Answer:

Step-by-step explanation:

Answer: The Max fun is 9, and the Min fun is -3

Step-by-step explanation:

Please follow the steps carefully;

Let us consider the function f(x,y) = xy -------------- (1)

We will apply the Lagrange multipliers to maximize the function f(x,y) subject to the constraint  g(x,y) = x^2+y^2-xy = 9

By differentiating (1) w.r.t  x,   we get fx(x,y) = y

By differentiating (1) w.r.t  y,   we get fy(x,y) = x

By differentiating g(x,y) w.r.t  x,   we get gx(x,y) = 2x - y

Also By differentiating g(x,y) w.r.t  y,   we get gy(x,y) = 2y - x

let us take

fx = λgx

where y = λ(2x - y)

y/2x - y = λ  ----------- (2)

fy =  λgy

where x = λ(2y - x)

λ = x/2y -x ----------- (2)

Let us equate (2) and (3)

y/2x - y  = x/2y -x

2y² - xy = 2x² - xy

2y² = 2x² after cancelling like terms

y² = x²

So y = ±x

Now let us substitute y = x into the given constraint

x² + y² - xy = 9

x² + x² - x(x) = 9

x² = 9

therefore x = ± 3

We can conclude that when x = ±3, ⇒ y = ±3

The corresponding points are (3,3), (-3,-3)

Substitue y = -x in the given constraint gives

x² + y² - xy = 9

x² + (-x)² -x(-x) = 9

3x² = 9

x² = 3

x = ±√3

The corresponding points are (√3,-√3), (-√3,√3)

The function value is

f(x,y) = xy

f (√3,-√3) = (√3)(-√3) = -3

f (-√3,√3) = (-√3)(√3) = -3

we get;

f(3,3) = (3)(3) = 9

and

f (-3,-3) = (-3)(-3) = 9

We can conclusively say that ;

The Maximum value of the function is 9

The Minimum value of the function is -3

cheers i hope this helped

Answer:

[tex]\huge \boxed{{m=6}}[/tex]

Step-by-step explanation:

Let's take two points,

(12, -4) and (13, 2).

slope = (difference of y) / (difference of x)

m = (2 - - 4) / (13 - 12)

m = (2 + 4) / 1

m = 6 / 1 = 6

The slope of the line is 6.

Answer:

6

Step-by-step explanation:

The slope is the change in y over the change in x

m = ( y2-y1)/(x2-x1)

    = (14-8)/(15-14)

   = 6/1

Answer:

The correct answer is B.

Explanation:

Putting it into your calculator as you see it gives you the correct answer.

Have a good day! :)

Answer:

19

Step-by-step explanation:

first you would combine like terms to get 5x^2-3x-7. plug in -2 into the x's and you will get 19!

Step-by-step explanation:

The approximate equation to convert from liters to quarts is : x • 1.056688.

We enter 65 for x and multiply.

65 • 1.056688 = 68.68472

We round that to the nearest 100th to get our final answer.

Our final answer: 68.68 liters

Answer:

a + (n-1)*4

Step-by-step explanation:

Day n could be any particular day located on the x-axis of the bar chart. Each bar represents the amount of cupcakes sold on each of the four days numbered from 1 to 4. The height of each bar marks the number of cupcakes sold. According to the chart attached, the number of cupcakes sold on each day is listed below:

Day 1 : 1 cupcake sold

Day 2 : 5 cupckaes sold

Day 3: 9 cupcakes sold

Day 4: 13 cupckaes sold

Studying the graph carefully fully, it will be observed that the number of cupcakes sold increases by a margin of 4 after day one.

As such the number of cupcakes sold in n days can be modeled by:

Using the Arithmetic progression formula:

Tn = a + (n-1)d

d = common difference, = 4

a = first term = 1

n = number of days

Hence, number sold in day n:

a + (n-1)*4

Arithmetic progressio

Answer:

3n−1  cupcakes

Step-by-step explanation:

Answer:

[tex]\huge \boxed{f(-2)=6}[/tex]

Step-by-step explanation:

[tex]\sf f(x)=-1x+4[/tex]

Switching x variable with -2.

[tex]\sf f(-2)=-1(-2)+4[/tex]

Evaluating.

[tex]\sf f(-2)=2+4[/tex]

[tex]\sf f(-2)=6[/tex]

Answer:

Step-by-step explanation:

[tex]f(x) = -1x + 4\\\\f(-2) =?\\\\f(-2) = -1(-2) +4\\f(-2) = 2+4\\f(-2) = 6[/tex]