The height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. When graphed, the function gives a line with a slope of −0.4. See the figure below. Suppose that the height of the candle after 11 hours is 16.6 centimeters. What was the height of the candle after 6 hours?

Answer:

The 95 percent Confidence Interval is for the population is (38.911 , 41.089)

Step-by-step explanation:

To solve the above question, we would be making use of the confidence interval formula:

Confidence Interval = Mean ± z score × σ/√n

In the above question,

Mean = 40

σ = Standard deviation = 5

n = number of samples = 81

Confidence Interval = 95%

The z score for a 95% confidence interval = 1.96

Therefore, the confidence interval =

= 40 ± 1.96 (5/√81)

= 40 ± 1.96(5/9)

= 40 ± 1.0888888889

Confidence Interval

a)40 + 1.0888888889

= 41.0888888889

Approximately = 41.089

b ) 40 - 1.0888888889

= 38.911111111

Approximately = 38.911

Therefore, the 95 percent Confidence Interval is for the population is (38.911 , 41.089)

Answer:

22.57 x 28

Step-by-step explanation:

10.86 + 4x = 101.14

-10.86           -10.86

            4x = 90.28

             /4       /4

              x = 22.57

5.43 + 22.57 = 28

22.57

Answer:

3[x + 3(4x – 5)] = (39x-15)

Step-by-step explanation:

The given expression is : 3[x + 3(4x – 5)]

We need to find the equivalent expression for this given expression. We need to simplify it. Firstly, open the brackets. So,

[tex]3[x + 3(4x -5)]=3[x+12x-15][/tex]

Again open the brackets,

[tex]3[x+12x-15]=3x+36x-45[/tex]

Now adding numbers having variables together. So,

[tex]3[x + 3(4x - 5)]=39x-15[/tex]

So, the equivalent expression of 3[x + 3(4x – 5)] is (39x-15).

Answer:

y - 1 = -2(x - 4).

Step-by-step explanation:

First, we need to find the slope. Two sets of coordinates are (-3, 3), and (-2, 1).

(3 - 1) / (-3 - -2) = 2 / (-3 + 2) = 2 / (-1) = -2.

The line will be parallel to the given line, so the slope is the same.

Now that we have a point and the slope, we can construct an equation in point-slope form.

y1 = 1, x1 = 4, and m = -2.

y - 1 = -2(x - 4).

Hope this helps!

The slope of the line passing  parallel to the given line and passes through the point (4, 1) is y = -2x + 9

The equation of a straight line is given by:

y = mx + b

where y, x are variables, m is the slope of the line and b is the y intercept.

The slope of the line passing through the points (-3,3) and  (-2,1) is:

[tex]m=\frac{y_2-y_1}{x_2-x_1} \\\\m=\frac{1-3}{-2-(-3)} \\\\m=-2[/tex]

Since both lines are parallel, hence they  have the same slope (-2). The line passes through (4,1). The equation is:

[tex]y-y_1=m(x-x_1)\\\\y-1=-2(x-4)\\\\y=-2x+9[/tex]

Find out more at: https://brainly.com/question/18880408

Answer:

Question 1: 40 shirts and 40 magizines

Question 2: $4.4

Question 3: 6 gallons

Answer:

hello

Step-by-step explanation:

Answer:

Perimeter=60.18cm

Area=215.495cm^2

Step-by-step explanation:

Given:

Length of book=18.34cm

Breadth=11.75cm

Solution:

Perimeter=2(l +b)

P=2(18.34+11.75)

P=2 x 30.09

P=60.18cm

Area=l x b

A=18.34 x 11.75

A=215.495 cm^2

Thank you!

Answer: 2361.53

Step-by-step explanation:

Use long division and round.

(The 3 is repeated)

Answer:

4

Step-by-step explanation:

Original coordinates:

A (0, 2)

B (2, 3)

The scale is what number the original coordinates was multiplied by to reach the new coordinates

1. Divide

(0, 8) ÷ (0, 2) = 4

(8, 12) ÷ (2, 3) = 4

AB was dilated by a scale factor of 4.

Answer:

5

Step-by-step explanation:

a^2 + b^2 = c^2

4^2 + 3^2 = c^2

16 + 9 = c^2

25 = c^2

c = 5

Answer:

Step-by-step explanation:

[tex]Hypotenuse = ?\\Opposite = 4\\Adjacent = 3\\\\Pythagoras \: Theorem ;\\\\Hypotenuse^2 =Opposite^2+Adjacent ^2\\\\Hypotenuse^2 = 4^2 +3^2\\\\Hypotenuse^2 = 16+9\\\\Hypotenuse^2 = 25\\\\\sqrt{Hypotenuse^2}=\sqrt{25} \\Hypotenuse = 5[/tex]

Answer:

716.75 m^3

Step-by-step explanation:

Volume of a cylinder:

=> PI x R^2 x H

H = Height

R = Radius

=> PI x 3.9^2 x 15

=> PI x 15.21 x 15

=> PI x 228.15

=> 228.15 PI

           or

=> 228.15 x 3.14159

=> 716.75 m^3

Answer:

[tex]\Large \boxed{\sf 17 \ and \ 18}[/tex]

Step-by-step explanation:

The product means multiplication.

There are two positive consecutive integers.

Let the first positive consecutive integer be x.

Let the second positive consecutive integer be x+1.

[tex](x) \times (x+1) =306[/tex]

Solve for x.

Expand brackets.

[tex]x^2 +x =306[/tex]

Subtract 306 from both sides.

[tex]x^2 +x -306=306-306[/tex]

[tex]x^2 +x -306=0[/tex]

Factor left side of the equation.

[tex](x-17)(x+18)=0[/tex]

Set factors equal to 0.

[tex]x-17=0[/tex]

[tex]x=17[/tex]

[tex]x+18=0[/tex]

[tex]x=-18[/tex]

The value of x cannot be negative.

Substitute x=17 for the second consecutive positive integer.

[tex](17)+1[/tex]

[tex]18[/tex]

The two integers are 17 and 18.

The product of two consecutive positive integers is 306.

We need to find the integers

solution : Let two consecutive numbers are x and (x + 1)

A/C to question,

product of x and (x + 1) = 306

⇒x(x + 1) = 306

⇒x² + x - 306 = 0

⇒ x² + 18x - 17x - 306 = 0

⇒x(x + 18) - 17(x + 18) = 0

⇒(x + 18)(x - 17) = 0⇒ x = 17 and -18

so x = 17 and (x +1) = 18

Therefore the numbers are 17 and 18.

Hope it helped u if yes mark me BRAINLIEST

TYSM!

Answer:

3 years

Step-by-step explanation:

A = P(1 + r)^t

A = I + P

A = 14,000 + 4,634 = 18,634

18,634 = 14,000(1 + 0.1)^t

18,634/14,000 = 1.1^t

log (18,634/14,000) = log 1.1^t

log (18,634/14,000) = t * log 1.1

t = [log (18,634/14000)]/(log 1.1)

t = 3

Answer:

1+5.3=6.3

Step-by-step explanation:

not sure what your asking for with the 2

explain what your looking for with the 2 and maybe we can help you further

(I have to do it the way I did it because the 2 in the question is confusing)

Answer:

For expression 1 + 5.32: 6.32

For expression 1 + 5.3 × 2: 11.6

Step-by-step explanation:

If the expression is 1 + 5.32:

If the expression is 1 + 5.3 × 2:

Answer:

Step-by-step explanation:

The exponential equation for the fraction remaining after x years can be written as ...

  y = (1/2)^(x/30)

A) For x=1, the fraction remaining is ...

  y = (1/2)^(1/30) ≈ 0.97716 = 1 - 0.0228

Of the original amount, 0.0228 decays each year.

__

B) The continuous decay rate is the natural log of the growth factor, so is ...

  ln(0.97716) = -0.0231

The continuous decay rate is 0.0231 of the present amount (per year).

__

C) For y=.10 (1/10 of the original amount) we find x to be ...

  .1 = .5^(x/30)

  ln(.1) = (x/30)ln(.5) . . . . . take the natural log

  30ln(0.1)/ln(0.5) = x ≈ 100 . . . years

It will take 100 years for a 10-gram sample to decay to 1 gram.

__

D) As x goes to infinity, y goes to zero.

_____

The relationship between growth rate and growth factor is ...

  growth factor = 1 + growth rate

When the growth rate is negative, it is called a decay rate.

Answer:

x=3

Step-by-step explanation:

● -3 (-4x+4) = 15 + 3x

Multiply -3 by (-4x+4) first

● (-3) × (-4x) + (-3)×(4) = 15 + 3x

● 12 x - 12 = 15 +3x

Add 12 to both sides

● 12x - 12 + 12 = 15 + 3x +12

● 12 x = 27 + 3x

Substract 3x from both sides

● 12x -3x = 27 + 3x - 3x

● 9x = 27

Dividr both sides by 9

● 9x/9 = 27/9

● x = 3

Answer:

7 square units

Step-by-step explanation:

We can break down this complex shape into smaller shapes.

I've broken it down into a rectangle, a square, and a triangle (See attached picture)

Let's first find the area of the triangle. To do this we use the formula [tex]\frac{bh}{2}[/tex]. The base is 1 (because the top is 2, and 1 is already used on the triangle - 2-1 = 1.) and the height is 2 (because 4 is already used on the left, and 2 was used on the right so 4-2=2).

[tex]\frac{2\cdot1}{2} = \frac{2}{2} = 1[/tex].

Now let's find the area of the top square - we can just square 2 which is 4.

To find the area of the bottom rectangle, we can multiply it's two side lengths of 2 and 1 = 2.

Adding these all together gets us 4+2+1 = 7.

Hope this helped!

Answer:

n = 9 is the answer.

Step-by-step explanation:

Given a Triangle [tex]\triangle KLM[/tex] with its perpendicular bisectors intersecting at a point A.

AK = 25 units and

AM = 3n -2

To find:

Value of n = ?

Solution:

First of all, let us learn about perpendicular bisectors and their intersection points.

Perpendicular bisector of a line PQ is the line which divides the line PQ into two equal halves and is makes an angle of [tex]\bold{90^\circ}[/tex] with the line PQ.

And in a triangle, the perpendicular bisectors of 3 sides meet at one point and that point is called Circumcenter of the triangle.

We can draw a circle from circumcenter so that the circle passes from the three vertices of the triangle.

i.e.

Circumcenter of a triangle is equidistant from all the three vertices of the triangle.

In the given statement, we are given that A is the circumcenter of the [tex]\triangle KLM[/tex].

Please refer to the attached image for the given triangle and sides.

The distance of A from all the three vertices will be same.

i.e. AK = AM

[tex]\Rightarrow 25 = 3n-2\\\Rightarrow 3n =25+2\\\Rightarrow 3n =27\\\Rightarrow \bold{n = 9}[/tex]

Therefore, n = 9 is the answer.

Answer:

A. a line segment

Step-by-step explanation:

Answer:

The probability is 0.31084

Step-by-step explanation:

We can calculate this probability using the z-score route.

Mathematically;

z = (x-mean)/SD/√n

Where the mean = 16, SD = 3 and n = 36

For 15.8, we have;

z = (15.8-16)/3/√36 = -0.2/3/6 = -0.2/0.5 = -0.4

For 16.2, we have

z = (16.2-16)/3/√36 = 0.2/3/6 = 0.2/0.5 = 0.4

So the probability we want to calculate is;

P(-0.4<z<0.4)

We can get this using the standard normal distribution table;

So we have;

P(-0.4 <z<0.4) = P(z<-0.4) - P(z<0.4)

= 0.31084

Answer:

7(n + 4)

Step-by-step explanation:

Represent the number by n.  Then the verbal expression becomes

7(n + 4).

Answer:

I thinksomething is wrong.

I'm getting another proving it's-tan thita.

I hope this is the one you are searching for..

Answer:

Garden: 36 square feet

Path: 64 square feet

Step-by-step explanation:

Let's first find the total area. The total area will be 100 square feet since the side length is 10. Since the path is 2 feet wide and on all sides, that means that the inside square will have a side length of 6. That means that the vegetable garden is 36 square feet. The path will be 100 - (the garden), and the garden is 36 square feet, which means the outer path will be 64.

Answer:

2.952755906 ft

Step-by-step explanation:

We need to convert 90 cm to inches

90 cm * 1 inch / 2.54 cm =35.43307087 inches

Now convert inches to ft

12 inches = 1ft

35.43307087 inches * 1 ft/ 12 inches =2.952755906 ft

Answer:

Step-by-step explanation:

Formula for area of a triangle:

Height x Base /2

Base (b) = h +4

Height = h

h + 4 x h /2 = 30cm

=> h +4 x h = 60

=> h+4h =60

=> 5h = 60

=> h = 12

Height = 12

Base = 12 +4 = 16

Answer:

The probability  is  [tex]P(x < 13) = 0.8732[/tex]

Step-by-step explanation:

From the question we are told that

    The  probability of success is    p = 0.70

     The  sample size is  [tex]n = 15[/tex]

Generally the distribution of U.S. households have vcrs follow a binomial distribution given that there are only two outcome (household having vcrs or household not having vcrs )

The probability of failure is mathematically evaluated as

       [tex]q = 1- p[/tex]

substituting values

      [tex]q = 1- 0.70[/tex]

      [tex]q = 0.30[/tex]

The probability that fewer than 13 have vcrs is mathematically represented as

          [tex]P(x < 13) = 1- [P(13) + P(14) + P(15)][/tex]

=>     [tex]P(x < 13) = 1-[( \left 15 } \atop {}} \right. C_{13} *p^{13}* q^{15-13})+ (\left 15 } \atop {}} \right. C_{14} *p^{14}* q^{15-14}) +( \left 15 } \atop {}} \right. C_{15} *p^{15}* q^{15-15}) ][/tex]

 Here  [tex]\left 15 } \atop {}} \right. C_{13}[/tex] means  15 combination 13 and the value is  105 (obtained from calculator)

 Here  [tex]\left 15 } \atop {}} \right. C_{14}[/tex] means  15 combination 14 and the value is  15 (obtained from calculator)

 Here  [tex]\left 15 } \atop {}} \right. C_{15}[/tex] means  15 combination 15 and the value is  1 (obtained from calculator)

So

 [tex]P(x < 13) = 1-[(105 *p^{13}* q^{2})+ (15 *p^{14}* q^{1}) +(1*p^{15}* q^{0}) ][/tex]

substituting values      

 [tex]P(x < 13) = 1-[(105 *(0.70)^{13}* (0.30)^{2})+ (15 *(0.70)^{14}* (0.30)^{1}) +(1*(0.70)^{15}* (0.30)^{0}) ][/tex]

 [tex]P(x < 13) = 0.8732[/tex]

Answer:

320

Step-by-step explanation:

Total no of employees = 1600

% of employees attended the training = 80%

no. of employee who attended the training = 80/100* 1600 = 1280

No. of employees who are yet to attend the training = Total no of employees - no. of employee who attended the training =  1600-1280 = 320

Thus, 320 employees have yet to attend the training

Answer:

This is a geometric progresion that begins with 1 and each term is 1/3 the preceeding term

   Let Pn represent the nth term in the sequence

   Then Pn = (1/3)^n-1

   From this P14 = (1/3)^13 = 1/1594323

5. The sum of the first n terms of a GP beginning a with ratio r is given by

   Sn = a* (r^n+1 - 1)/(r - 1)

   With n = 10, a = 1 and r = 1/3, S10 = ((1/3)^11 - 1)/(1/3 - 1) = 1.500

Answer:

b. 1

Step-by-step explanation:

All first coordinates are 1/2.

Answer: b. 1

Answer:

Attachment 1 : Option C

Attachment 2 : Option A

Step-by-step explanation:

( 1 ) Expressing the product of z1 and z2 would be as follows,

[tex]14\left[\cos \left(\frac{\pi \:}{5}\right)+i\sin \left(\frac{\pi \:\:}{5}\right)\right]\cdot \:2\sqrt{2}\left[\cos \left(\frac{3\pi \:}{2}\right)+i\sin \left(\frac{3\pi \:\:}{2}\right)\right][/tex]

Now to solve such problems, you will need to know what cos(π / 5) is, sin(π / 5) etc. If you don't know their exact value, I would recommend you use a calculator,

cos(π / 5) = [tex]\frac{\sqrt{5}+1}{4}[/tex],

sin(π / 5) = [tex]\frac{\sqrt{2}\sqrt{5-\sqrt{5}}}{4}[/tex]

cos(3π / 2) = 0,

sin(3π / 2) = - 1

Let's substitute those values in our expression,

[tex]14\left[\frac{\sqrt{5}+1}{4}+i\frac{\sqrt{2}\sqrt{5-\sqrt{5}}}{4}\right]\cdot \:2\sqrt{2}\left[0-i\right][/tex]

And now simplify the expression,

[tex]14\sqrt{5-\sqrt{5}}+i\left(-7\sqrt{10}-7\sqrt{2}\right)[/tex]

The exact value of [tex]14\sqrt{5-\sqrt{5}}[/tex] = [tex]23.27510\dots[/tex] and [tex](-7\sqrt{10}-7\sqrt{2}\right))[/tex] = [tex]-32.03543\dots[/tex] Therefore we have the expression [tex]23.27510 - 32.03543i[/tex], which is close to option c. As you can see they approximated the solution.

( 2 ) Here we will apply the following trivial identities,

cos(π / 3) = [tex]\frac{1}{2}[/tex],

sin(π / 3) = [tex]\frac{\sqrt{3}}{2}[/tex],

cos(- π / 6) = [tex]\frac{\sqrt{3}}{2}[/tex],

sin(- π / 6) = [tex]-\frac{1}{2}[/tex]

Substitute into the following expression, representing the quotient of the given values of z1 and z2,

[tex]15\left[cos\left(\frac{\pi \:}{3}\right)+isin\left(\frac{\pi \:\:}{3}\right)\right] \div \:3\sqrt{2}\left[cos\left(\frac{-\pi \:}{6}\right)+isin\left(\frac{-\pi \:\:}{6}\right)\right][/tex] ⇒

[tex]15\left[\frac{1}{2}+\frac{\sqrt{3}}{2}\right]\div \:3\sqrt{2}\left[\frac{\sqrt{3}}{2}+-\frac{1}{2}\right][/tex]

The simplified expression will be the following,

[tex]i\frac{5\sqrt{2}}{2}[/tex] or in other words [tex]\frac{5\sqrt{2}}{2}i[/tex] or [tex]\frac{5i\sqrt{2}}{2}[/tex]

The solution will be option a, as you can see.