Which fraction is equal to k in the equation below?
1\3 / 2= k

Answer:

32°

Step-by-step explanation:

90 - 58 = 32

The angle of depression from point A to point C is 32°.

The angle of depression is the angle formed by the horizontal line of sight intersecting with the line of sight down to an object. You might estimate the angle of depression if you were standing on top of a hill or a structure, gazing down at an item.

We are asked to find the angle of depression from point A to point C.

We can see the horizontal line of sight by the dotted line. We let this line be AD.

We know that AD ⊥ AB, as AD is the horizontal line of sight, and AB is also perpendicular to B (given).

∴ ∠DAB = 90°.

We can write ∠DAB = ∠DAC + ∠BAC.

or, 90° = ∠DAC + 58°

or, ∠DAC = 90° - 58° = 32°.

We know ∠DAC represents the angle of depression from point A to point C, as DA is the horizontal line of sight and AC is the line of sight to the object, and ∠DAC is between the lines DA and AC.

∴ The angle of depression from point A to point C is 32°.

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Answer: Quadrant 1 (northeast quadrant)

=================================================

Explanation:

Add on 360 degrees to do a full rotation

-302+360 = 58

So angles -302 degrees and 58 degrees are pointing in the same direction. These angles are in quadrant 1, which is the northeast quadrant

Note: because the angles -302 and 58 point in the same direction, we consider these angles to be coterminal.

Answer:

The  probability is  [tex]P(I | \ L ) =0.4[/tex]

Yes with the additional information that the person logs on everyday the probability increased from  [tex]P(I) = 0.3[/tex]  to [tex]P(I | L ) = 0.4[/tex]

Step-by-step explanation:

From the question we are told that

   The probability that the user is from outside the country is  [tex]P(O) = 0.7[/tex]

    The probability that the user log on everyday is  [tex]P(L) = 0.6[/tex]

    The  probability that the user log on everyday and he/she is from inside the country  is  [tex]P(L| I) = 0.80[/tex]

Generally using Bayes theorem the the probability that a person is from the country given that he logs on the website every day is mathematically represented as

        [tex]P(I | \ L ) = \frac{ P(L|I) * P(I)}{ P(L)}[/tex]

Here [tex]P(I)[/tex] is the probability that the person log on every day and it is mathematically evaluated as

        [tex]P(I) = 1 - P(O)[/tex]

          [tex]P(I) = 1 - 0.7[/tex]

         [tex]P(I) = 0.3[/tex]

So

      [tex]P(I | \ L ) = \frac{ 0,8 * 0.3}{ 0.6}[/tex]

      [tex]P(I | \ L ) =0.4[/tex]

Answer:

-1

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]Mass = 50kg\\Acceleration = 5m/sec\\Force = ?\\\\Force = Mass\times acceleration\\\\Force = 50\times 5\\\\ Force = 250\: joules \: or \:250kgm/s[/tex]

Answer:

y = 1

Step-by-step explanation:

y - 3 = 7 (y - 9/7)

y - 3 = 7*y + 7*-9/7

y - 3 = 7y - 9

y - 7y = 3 - 9

-6y = -6

y = -6/-6

y = 1

probe:

1 - 3 = 7(1 - 9/7)

-2 = 7*-2/7

Answer:

[tex]\huge \boxed{\mathrm{4}} \\ \huge \boxed{\mathrm{2}}[/tex]

Step-by-step explanation:

Rate of change is another term for the slope.

rate of change = slope = (change in y)/(change in x)

Function A:

y = mx + b (m = slope)

y = 4x - 3

Function A has a slope of 4.

The rate of change for function A is 4.

Function B:

Take two points.

(-1, 0) and (1, 4)

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

slope = (4 -0)/(1 - -1)

slope = 4/2 = 2

The rate of change for function B is 2.

Answer:

(4 + 7i)(4 - 7i)

Step-by-step explanation:

Factors of the form of a conjugate pair always produce a real number

(a + bi)(a - bi) ← produce a real number product ( a and b are real ), that is

(a + bi)(a - bi) ← expand using FOIL

= a² - bi² ( i² = - 1)

= a² + b² ← a real number

Thus

(4 + 7i)(4 - 7i)

= 16 - 49i²

= 16 + 49 = 65

Answer:

the correct answer is the last one, (4+7i)(4-7i)

Step-by-step explanation:

Answer:

x = 5

Step-by-step explanation:

First, we move all variables to one side of the equation. (Don't forget to change signs.)    

9x - 8x + x = 7 + 3

Then, we simplify

x + x = 10

2x = 10

10 divided by 2 is equal to 5.

Therefore, x = 5

Hope this helps!

The solution of the given equation  9x-3-8x=7-x for x will be 5.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

The equation must be constrained with some constraints.

As per the given equation,

9x - 3 - 8x = 7 - x

x - 3 = 7 - x

x + x = 7 + 3

2x = 10

x = 5

Hence "The solution of the given equation  9x-3-8x=7-x for x will be 5.".

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Answer:

Step-by-step explanation:

Hello, let's compute the first lines of the Pascal's triangle.

1

1 1

1 2 1

1 3 3 1

So for this question,

[tex](a+b)^3=a^3+3a^2b+3ab^2+b^3[/tex]

And then, the correct answer is A.

Thank you

Using pascals triangle coefficients of the expanded polynomial (a + b )³ is  1  3  3  1. Option A is correct

it is the array(in triangle form) of numbers, starting with 1 on the uvertexvetex and with 1's tending down to the two sides of a triangle. Each number lies between two numbers and down to them, and every value is the addition of the two numbers present at the above adjacent.

( a + b )³ = a³ + 3 a² b + 3 b² a + b³

Pascal's triangle =
              1
       1     2     1
  1       3     3      1  
1      4      6      4    1  
and so on
From the above triangle, it represents ( a + b )^n  where every number represents the coefficient. As for the given question the n = 3 so the third row in the pascal triangle i.e. coefficients of the expanded polynomial ( a + b )³ is  1  3  3  1.

Thus, the coefficients of the expanded polynomial ( a + b )³ is  1  3  3  1.

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Answer:

-3x-3=-3(x+1)

opening the bracket and collecting like terms, we have

-3x+3x=-1+3

thus, no solution

Answer:

y = 0.019x - 7

32.9 therms

0.019 therms

1.9 therms

Step-by-step explanation:

Given the following :

X =size of house (sq ft)

Y = Amount of natural gas used

The general form of a some linear regression model :

y = ßx + a

Where ;

ß = slope or gradient

x = independent variable

y = predicted value

a = y- intercept value

(A)

If ß = slope of population regression line = 0.019

a = y intercept of population regression line = -7

The regression model could be expressed as :

y = 0.019x + (-7)

y = 0.019x - 7

(B)What is the mean value of gas usage for houses with 2100 sq ft of space?

Here x = 2100 sq ft ; Inputting the value of x into the regression equation:

y = 0.019x - 7

y = 0.019(2100) - 7

y = 39.9 - 7

y = 32.9 therms

C) What is the average change in usage associated with a 1 square foot increase in size?

Change in usage associated with change in size can be gotten from :

ßx, where, ß change in y with respect to x ;

x = 1 square foot

ß = 0.019

Change = 0.019*(1) = 0.019 therms

(d) What is the average change in usage associated with a 100 square feet increase in size?

ßx, where, ß change in y with respect to x ;

x = 100 square feet

ß = 0.019

Change = 0.019*(100) = 1.9 therms

Answer:

-3

Step-by-step explanation:

(y2-y1)/(x2-x1)  =  (2-(-1))/(-4-(-3))

= (2+1)/(-4+3)

= 3/-1

= -3

Answer:

-3

Step-by-step explanation:

To get the slope we do (-1-2)/(-3+4)

so the slope is -3

Answer:

The goodness of fitness test χ²with significance of level ∝= 0.05 and 5 degrees of freedom is 11.07  (One tailed test )

Step-by-step explanation:

For n=6  the degrees of freedom will be n-1 = 5 .

The goodness of fitness test χ²with significance of level ∝= 0.05 and 5 degrees of freedom is 11.07  (One tailed test )

The critical region depends on ∝ and the alternative hypothesis

a) When Ha is σ²≠σ² the critical region is

χ²  < χ²(1-∝/2)(n-1) and  χ² > χ²(1-∝/2)(n-1)   Two tailed test

( χ²  < 0.83) and ( χ²  > 0.83)

b) When Ha is σ²> σ² the critical region falls in the right tail and its value is

 χ² > χ²(∝)(n-1)   One tailed test  {11.07  (One tailed test )}

c) When Ha is σ² <σ² the critical region will be entirely in the left tail with critical value  

χ²(1-∝)(n-1)  One tailed test  (1.145)

Answer:

the newsar si evsenyt esventy

Step-by-step explanation:

Answer:

w = -20

Step-by-step explanation:

Solve for w:

4 - 2 (1 - w) = -38

Hint: | Distribute -2 over 1 - w.

-2 (1 - w) = 2 w - 2:

2 w - 2 + 4 = -38

Hint: | Group like terms in 2 w - 2 + 4.

Grouping like terms, 2 w - 2 + 4 = 2 w + (4 - 2):

2 w + (4 - 2) = -38

Hint: | Evaluate 4 - 2.

4 - 2 = 2:

2 w + 2 = -38

Hint: | Isolate terms with w to the left hand side.

Subtract 2 from both sides:

2 w + (2 - 2) = -2 - 38

Hint: | Look for the difference of two identical terms.

2 - 2 = 0:

2 w = -2 - 38

Hint: | Evaluate -2 - 38.

-2 - 38 = -40:

2 w = -40

Hint: | Divide both sides by a constant to simplify the equation.

Divide both sides of 2 w = -40 by 2:

(2 w)/2 = (-40)/2

Hint: | Any nonzero number divided by itself is one.

2/2 = 1:

w = (-40)/2

Hint: | Reduce (-40)/2 to lowest terms. Start by finding the GCD of -40 and 2.

The gcd of -40 and 2 is 2, so (-40)/2 = (2 (-20))/(2×1) = 2/2×-20 = -20:

Answer: w = -20

Answer:

Hi! The answer would be 21.

Step-by-step explanation:

First, we must add.

[tex]15 + 14 = 29[/tex]

29 is our first number. Bailey cannot evenly split the cookies into each bag with that amount of cookies, so we must move on to the next number.

[tex]10 + 9 + 2 = 21 [/tex]

21 can be divided 3 times by 7. Now we know the least amount of cookies total, is 21.

Hope this helped!

Full question attached

Answer:

D. With 99​% ​confidence, it can be said that the population mean driving distance to work​ (in miles) is between the​ interval's endpoints

Step-by-step explanation:

The new confidence interval is narrower than the confidence interval for the t-distribution and the center is 21.7

please note that the options chosen are different for the attachment and the question here but are same answer

Answer:

15

Step-by-step explanation:

6/10=9/x

cross multiply

6x=9*10

6x=90

x=90/6x=15

Answer:

dollars per hour rate = $10

hours per dollar = 6 minutes 15 seconds

Step-by-step explanation:

Take note that one is singular (dollar) without an 's', and the other is plural (dollars). Thus, since her dollars per hour rate tells us how much she will earn for each hour of work, we would expect her hours per dollar rate to tell us how much she has to work in minutes to earn a single dollar ($1).

If we divide [tex]\frac{10}{60 minutes}[/tex] = $0.16 which indicates how much she earns for every minute she works at the theater. Further dividing this value into 1 minute we find the hour per dollar rate 1/0.16 = 6.25. minutes.

Answer:This was my answer.

If she were to earn dollars per hour, then she would get 16 cents for every minute she worked. If she were to work hours per dollar, then for every dollar, she would work 10 minutes for that dollar. If we divide 10 dollars by 60 minutes, then we would get 16 cents per minute. If we divide 60 minutes by 10 dollars, then we would get 6 minutes for each dollar.

Step-by-step explanation: This is the criteria.

Sample Response

10 dollars/hour describes how much money Mariah earns for each hour she works.

1/10  hour/dollar describes how much time Mariah has to work for each dollar she earns.

Evaluate Your Response

Your response should state and describe the two unit rates. To find hours per dollar, write the rate as 1 hour/ $10 and divide the numerator and denominator by 10.

Complete Question

The quality control manager at a light bulb factory needs to estimate the mean life of a large shipment of light bulbs. The standard deviation is 100 hours. A random sample of 64 light bulbs indicated a sample mean life of 350 hours

A. Construct a 95% confidence interval estimate for the population mean life of light bulbs in this shipment.

B. Do you think that the manufacturer has the right to state that the light bulbs have a mean life of 400

a. No.

b. Yes.

c. Maybe.

d. Do not know

Answer:

A

   [tex]325.5 < \mu < 374.5[/tex]

B

  correct option is  a

Step-by-step explanation:

From the question we are told that

   The  standard deviation is  [tex]\sigma = 100[/tex]

    The  sample mean is  [tex]\= x = 350 \ hours[/tex]

      The sample  size is  [tex]n = 64[/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} } * \frac{\sigma }{\sqrt{n} }[/tex]

=>     [tex]E = 1.96 * \frac{100 }{\sqrt{64} }[/tex]

=>    [tex]E = 24 .5[/tex]

Generally the 95% confidence interval is mathematically represented as

     [tex]\= x - E < \mu < \= x + E[/tex]

     [tex]350 - 24.5 < \mu < 350 + 24.5[/tex]

     [tex]325.5 < \mu < 374.5[/tex]

This 95% confidence interval  can be interpreted as follows

   There is 95 confidence that the true population mean lies in this interval

 Now  looking at the interval we see that it dose not contain 400 hence

the correct answer is  No the   manufacturer do not  have  the right to state that the light bulbs last on average 400 hours

Question options:

There is not sufficient evidence to reject the claim μ ≤ 3.6.

There is sufficient evidence to reject the claim μ ≤ 3.6.

There is sufficient evidence to support the claim μ ≤ 3.6.

There is not sufficient evidence to support the claim μ ≤ 3.6.

Answer:

There is sufficient evidence to reject the claim μ ≤ 3.6.

Step-by-step explanation:

The null and alternative hypotheses denoted H0 and Ha respectively are used in inferential statistics to test relationship between two variables.

the null hypothesis holds the default position and is the one tested while the alternative hypothesis is everything else. The alternative hypothesis can not be proven. From the above example if we wish to reject the null hypothesis which holds the default position that students study a most 3.6 hours, we reject H0, the null hypothesis which holds that position . In other words the null hypothesis is innocent until proven guilty

Answer:

Parallel Lines

Step-by-step explanation:

This drawing below represent parallel lines. We know these are parallel because they are marked with "feathers": those triangle looking things. They have to have the same amount of feathers to be parallel.

Hope this helped!

Answer:

(m-1)(m+1)(m+10)

Step-by-step explanation:

Factors of each expression:

m² + 11m + 10 = (m+1)(m+10)

m² + 9m – 10 = (m-1)(m+10)

LCM of the two expressions is:

Answer:

Sample Answer

Step-by-step explanation:

Answer: Hey There!!

The answer to this is: Option D. If two triangles ΔABC and ΔA'B'C' are similar then we take point C of ΔABC to find the transformation performed form C to C'.

Coordinates of C are (0, 3) and the coordinates of C' are (0, -1).

This shows that C is rotated 180° about origin to get the new coordinates as (0, -3) and then new coordinates were dilated by 1/3 which forms C' as (0, -1)

Therefore option D is the correct option.

Hope It Helped!~ ☆

ItsNobody~ ♡

Triangle ABC was rotated 180° about the origin, then a by a scale factor of 1/3 was done to form triangle A'B'C'.

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.

Given that;

Triangle ABC is similar to A"B"C".

Now, If a point A(x, y) is rotated clockwise by 180 degrees, the new point is at A'(y, -x)

Hence, Triangle ABC was rotated 180° about the origin, then a by a scale factor of 1/3 was done to form triangle A'B'C'.

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Answer:

The number of duck is 32.

Step-by-step explanation:

Let x represent the number of rabbits.

Let y represent the number of ducks

From the question given:

The sum of rabbit and duck is 36 i.e

x + y = 36 .... (1)

The sum of the feets of the rabbit and duck is 80.

Rabbits has 4 legs

Duck has 2 legs

Therefore, the sum their feets (i.e 80) can be written as:

4x + 2y = 80 .... (2)

The equations are:

x + y = 36 .... (1)

4x + 2y = 80 .... (2)

Solving by substitution method:

From equation (1)

x + y = 36

Make x the subject

x + y = 36

x = 36 - y

Substitute the value of x into equation (2)

4x + 2y = 80

x = 36 - y

4(36 - y) + 2y = 80

Clear bracket

144 - 4y + 2y = 80

144 - 2y = 80

Collect like terms

- 2y = 80 - 144

- 2y = - 64

Divide both side by - 2

y = - 64/ - 2

y = 32

Therefore, the number of duck is 32.

Answer:

244.8

Step-by-step explanation:

If we divide a number by 10, we are moving the decimal place on value to the left.

The decimal place is currently here:

2448.000

So moving it left one gets us:

244.8000

Hope this helped!