What
is the value of In e^4

Answer:

133

Step-by-step explanation:

Given that :

Degree of confidence, α = 0.90 ; The Zcritical vlaue at α = 90% is 1.645

The margin of error, MOE = ±2

Standard deviation, s = 14

Using the relation :

n = (Zcritical * standard deviation) / MOE

n = ((1.645 * 14) / 2)²

n = (23.03 /2)²

n = 11.515²

n = 132.595

n = 133 samples

Step-by-step explanation:

I am not sure I fully understand what your teacher wants from you, but I would say we only need to define the burning rate per hour for both people, and with that normed rate (number / hour) we can answer the main question directly.

Thomas burned 675 cal/ 2 hours.

by dividing to and bottom by 2 (it is important to do the same action on the top and the bottom to keep the value of the ratio unchanged) we get

337.5 cal / hour

and Marvin burned 1035 cal / 3 hours.

so, the same trick, this time dividing to and bottom by 3 to norm the whole ratio to a 1 hour baseline :

345 cal / hour

so, Marvin burned more calories per hour.

Answer:

45 and 23

Step-by-step explanation:

Let x equal the first number and y equal the second number.

We can set the following equations up with our information:

[tex]x+y=68[/tex]

[tex]x-y=22[/tex]

Adding the two equations together, we get:

[tex]2x=90[/tex]

Dividing by two, we receive [tex]x=45[/tex]

We can plug this into our first equation to get [tex]45+y=68[/tex].

Subtracting 45 from both sides, we get [tex]y=23[/tex].

The two numbers are 45 and 23, solved using system of equations.

A system of equations is a set of equations, involving similar variables used to solve for the variables simultaneously.

In the question, we are asked to find the two numbers, whose sum is 68 and the difference is 22.

We assume the two numbers to be x and y.

The sum of the two numbers is given to be 68.

This can be shown as an equation, x + y = 68 ... (i).

The difference of the two numbers is given to be 22.

This can be shown as an equation, x - y = 22 ... (ii).

Equations (i) and (ii) together makes a system of equation in the variables x and y.

To solve for the system of equation, we add (i) and (ii), to get:

x + y = 68

x - y = 22

_________

2x  = 90,

or, x = 45.

Substituting x = 45 in (i), we get:

x + y = 68,

or, 45 + y = 68,

or, y = 23.

Thus, the two numbers are 45 and 23, solved using system of equations.

Learn more about system of equations at

https://brainly.com/question/13729904

#SPJ2

So you pretty much have all you need. 1/3 represents slope, and slope is m. Initial value would be your y intercept which is b.

y=1/3x-3

Answer:

y = x/3 - 3

Step-by-step explanation:

x/3 is the equivalent of 1/3(x)

Answer:

The answer is 18 feet...

Step-by-step explanation:

C. 18ft is the answer

Answer:

this is a 60 60 60 triangle, so one exterior angle is 120 degrees.

Step-by-step explanation:

hope it helps!

Answer:

-5, - 2, 3

Step-by-step explanation:

y=2x+3, y=-7, x=-5; y=-1, x=-2, y=9, x=3

Multiply the numerator and denominator by the conjugate of the denominator:

[tex]\dfrac{6+9i}{-1+4i} \times \dfrac{-1-4i}{-1-4i} = \dfrac{(6+9i)(-1-4i)}{(-1)^2-(4i)^2}[/tex]

Simplify:

[tex]\dfrac{(6+9i)(-1-4i)}{(-1)^2-(4i)^2} = \dfrac{-6-9i-24i-36i^2}{1-16i^2} = \dfrac{-6-33i-36i^2}{1-16i^2} = \dfrac{-6-33i+36}{1+16} = \boxed{\dfrac{30-33i}{17}}[/tex]

Answer:

A is the answer to your question because it's the only answer in exponential form.

B and C are in slope forms.

D is in quadratic form.

Answer:

x = 35.0

Step-by-step explanation:

the height is 26√3 since the left one is a 30-60-90 triangle

so to find x

cos(39) = x/26√3

or, x = 26√3×cos(39)

or, x = 35.0

Answered by GAUTHMATH

Step-by-step explanation:

according to question let 2a and 5a be the given rations

2a/ 5a given fraction

2a-2/5a-2

Answer:

$962.00

Step-by-step explanation:

We can start from the first sentence of the word problem and work from there.

First, the employee is working for 40 hours at $18.50 per hour. This means that for each hour, the employee is gaining $18.50 . This can be represented as $18.50 * 40 = $740 for their base pay.

Next, the employee works 8 hours of overtime at 1.5 * base pay (18.50). For each hour of overtime they work, they earn 1.5 * 18.50 = $27.75 dollars. Their earnings from overtime work for the week can be represented as

8 * 27.75 = $222

Because all the employee's hours are encompassed in overtime and base pay, we can add the two together to get

740 + 222 = $962.00 for their total pay for the week

Answer:

A = 16.625

Step-by-step explanation:

Given :-

To rewrite in :-

Answer :-

Hence :-

Answer:

65.3%

Step-by-step explanation:

what we want: p(2)+p(3)+p(4)

[tex]P(2)={5\choose2}*.4^2*.6^3\\P(3)={5\choose3}*.4^3*.6^2\\P(4)={5\choose4}*.4^4*.6\\P(2)+P(3)+P(4)= .6528[/tex]

which equal 65.28%

which rounds to

65.3%

Step-by-step explanation:

c. The slope is positive.

hope this helps you

have a nice day

Answer:

D) 20°

Step-by-step explanation:

Using the triangle sum theorem, you know that every triangle's interior angles add up to 180°. Therefore the bottom triangle's missing angle can be found by giving it the variable x.

57° + 30° + x = 180°

Simplify: 87° + x =180°

x=93°

By the vertical angles theorem, the vertical angle directly across this angle is congruent to this one. Meaning that the top triangle's angle are 67°, 93°, and unknown, which we can assign y. We can use the same method from above here.

67° + 93° + y = 180°

Simplify: 160° + y = 180°

y=20°

Answer:

(C). 26°

Step-by-step explanation:

Answer:

you can put the number on one side of the equation then the "x" part on the other side.

with c) 4x = 6-10

           4x = -4

            x = -4/4

            x = -1

with d) 7x - 1 = 4x + 8

           7x - 4x = 8 + 1

           3x  = 9

           x = 9/3

           x = 3

Answer:

c) x = -1.  d) x = 3

Step-by-step explanation:

c) move like terms together. then get x by itself

10 + 4x = 6

-10

4x = -4

4x/4 = -4/4

x = -1

d) move like terms together.  then get x by itself

7x-1 = 4x+8

+1          -4x

3x = 9

3x/3 =9/3

x = 3

Answer:

5

Step-by-step explanation:

Answer:

u =√6

v =√5

Step-by-step explanation:

u = √(1²+2²+1²) =√(1+4+1) = √6

v = √(1²+2²) =√(1+4) = √5

Answer:

210

Step-by-step explanation:

In a normal distribtuion mean=mode=median

so 210=median

Answer:

Step-by-step explanation:

Prime numbers are basically numbers that don't have any factors that multiply to get that number except for 1 and the number itself. (For example: 2, 3, 5, 7, 11, 13 and so on are all prime numbers)

The question is asking to express 60 into prime numbers. 60 is 30*2, and since 2 is a prime number, we can circle it. Then we continue on with 30, which can divide into 15*2. Again, since 2 is a prime number, we circle it, while 15 can be factored further because 5*3 is 15. Since 5 and 3 are prime numbers, we circle them too. In the end, we have the prime numbers 5, 3, 2, and 2. There are two 2's in our factorization, so therefore we can simplify that to 2^2 since they ask for your answer in index form. There is only one 5 and one 3, and they ask to write them  in asscending order, and so the answer would be (2^2)*3*5. Hope this helps!

Answer:

4.6

Step-by-step explanation:

tan(75) = 17/x

x = 17/tan(75)

x = 34-17√3

x = 4.6

Answered by GAUTHMATH

Answer:

or,

3/4×2/3=6/8

or, 3/4×3/3=9/12

Answer:

Step-by-step explanation:

1/3×2/8=2/24

1/2×5/12=5/42

5/6×3/4=15/24

Hope it is helpful to you

Answer:

T = 60 degrees

Step-by-step explanation:

The dotted line is the height so it is a right angle

We are able to use trig functions since this is a right triangle

cos T = adj side / hyp

cos T = a/b

cos T = 8 sqrt(2) / 16 sqrt(2)

cos T = 1/2

Taking the inverse of each side

cos^-1 ( cosT) = cos^-1 ( 1/2)

T = 60 degrees

Answer:

[tex]\angle T=60^{\circ}[/tex]

Step-by-step explanation:

In all 30-60-90 triangles, the sides are in ratio [tex]x:x\sqrt{3}:2x[/tex], where [tex]x[/tex] is the side opposite to the 30 degree angle and [tex]2x[/tex] is the hypotenuse of the triangle. We know that two right triangles are created on both sides of the rectangle in the center. Notice that [tex]8\sqrt{2}\cdot 2=16\sqrt{2}[/tex] and since [tex]16\sqrt{2}[/tex] is the hypotenuse of the right triangle on the left, [tex]8\sqrt{2}[/tex] must be facing the 30 degree angle. Therefore, angle T must be 60 degrees.

Alternatively, the cosine of any angle in a right triangle is equal to its adjacent side divided by the hypotenuse.

Therefore, we have:

[tex]\cos \angle T=\frac{8\sqrt{2}}{16\sqrt{2}},\\\cos \angle T=\frac{1}{2},\\\angle T=\arccos(\frac{1}{2}),\\\angle T=\boxed{60^{\circ}}[/tex]

Answer:

-w²+49x²-8wx

Step-by-step explanation:

if you want how I did this it's quite lengthy so let me know if you want the process

Answer:

-w^2 + 21xw - 64x ^2

Step-by-step explanation:

Answer:

[tex]x=-21y+5[/tex]

Step-by-step explanation:

Hi there!

[tex]7y=\frac{5-x}{3}[/tex]

We can isolate x by performing inverse operations on both sides of the equation and canceling values out.

First, multiply both sides by 3 to cancel 3 out on the right side and isolate 5-x:

[tex]7y*3=\frac{5-x}{3}*3\\21y=5-x[/tex]

Now, subtract 5 from both sides to isolate -x:

[tex]21y-5=5-x-5\\21y-5=-x[/tex]

Finally, multiply both sides by -1 to change -x to x:

[tex]-21y+5=x\\x=-21y+5[/tex]

I hope this helps!

Answer:

Solution given:

Sin[tex]\theta_{1}=\frac{-24}{25}[/tex]

[tex]\frac{opposite}{hypotenuse}=\frac{-24}{25}[/tex]

equating corresponding value

opposite=-24

hypoyenuse=25

adjacent=x

By using Pythagoras law

hypotenuse²=opposite²+adjacent²

25²=(-24)²+x²

625=576+x²

x²=625-576

x=49

x=[tex]\sqrt{49}=7[/tex]

In IV quadrant

Cos angle is positive

Cos[tex]\theta_{1}=\frac{adjacent}{hypotenuse}[/tex]

Answer:

cos theta = 7/25

Step-by-step explanation:

sin theta = opp / hyp

We can find the adj side by using the pythagorean theorem

adj ^2 + opp ^2 = hyp^2

adj^2 + (-24)^2 = 25^2

adj^2 +576 = 625

adj^2 =625 -576

adj^2 = 49

Taking the square root of each side

adj = 7

Since we are in the 4th quadrant, adj is positive

cos theta = adj / hyp

cos theta = 7/25

Answer:

Step-by-step explanation:

Given,

[tex] \frac{7}{3} = \frac{x}{49} [/tex]

[tex] = > x = \frac{7}{3} \times 49[/tex]

[tex] = > x = \frac{343}{3} (ans)[/tex]

Answer:

343/3 or 114 1/3

Step-by-step explanation:

7/3 = x/49

Using cross products

3x = 7*49

3x =343

Divide by 3

3x/3 = 343/3

x =343/3

x =114 1/3