Solve 4^(x+2) = 12 for x using the change of base formula log base b of y equals log y over log b.

Answer:

75 + 40i

Step-by-step explanation:

Answer:

xy = 1

Step-by-step explanation:

Given

[tex]x+y=\dfrac{1}{x}+\dfrac{1}{y}\\ \\x+y\neq 0[/tex]

Simplify the first expression:

[tex]x+y=\dfrac{1}{x}+\dfrac{1}{y}\\ \\x+y=\dfrac{y+x}{xy}\ [\text{Add fractions in the left side}]\\ \\1=\dfrac{1}{xy}\ [\text{Divide by }x+y \ (\text{it can be done since})\ x+y\neq 0]\\ \\xy=1\ [\text{Cross multiply}][/tex]

Answer:

Step-by-step explanation:

Given that the percentage of physicians who are women is 27.9%. In a survey of physicians employed by a large  university health system,

45 of 120 randomly selected physicians were women.

Sample size n = 120

Sample proportion p = [tex]\frac{45}{120} \\=0.375[/tex]

H0: p = 0.279

Ha: p >0.279

(Two tailed test at 5% significance level)

p difference = 0.096

STd error of p assuming H0 true

= [tex]\sqrt{\frac{pq}{n} } \\=\sqrt{\frac{0.279(0.721}{120} } \\=0.041[/tex]

Test statistic Z = [tex]\frac{0.096}{0.041} \\=2.345[/tex]

Z critical value one tailed is 1.645

Since Z statistic > 1.645 we reject H0

There is evidence to conclude that the proportion of women physicians at the university health system exceeds

27.9%

Hey there!

First, set up an exponential equation that represents the rate at which your original amount, 1000, gains interest:

y = 1000(1.24)^x

Y represents the value after X years. 1.24 represents the rate at which the money gains interest, 1 + 0.24 (your 24% interest rate in decimal form). 1000 is your original amount.

Now, set this equation equal to 64000, graph y = 64000 and y = 1000(1.24)^x on a graphing calculator, and see where the two equations intersect in order to solve for x.

They intersect when x is about 19.334, as seen in the graph below (it is very zoomed in so that you can see where the two functions intersect). Therefore, it will be about 19 years after the year in which you deposited the 1000 dollars before the money is worth 64000 dollars.

Answer:

AB = 5 units

Step-by-step explanation:

Given that:

So the the length in units of the line segment that connects vertex A and vertex B is the length of line AB. So we have the following formula:

AB = [tex]\sqrt{(x2-x1)^{2} + (y2-y1)^{2} }[/tex]

<=> AB = [tex]\sqrt{(1-1)^{2} +(4-(-1))^{2} }[/tex]

<=> AB = 5 units

Hope it will find you well.

The question relates to finding the distance between two points in a coordinate system. The length of the line segment connecting vertex A (1,-1) and vertex B (1,4) of the triangle ABC can be calculated using the distance formula, which yields a result of 5 units.

The subject of your question is geometry, specifically the concept of distance between two points in a coordinate system. In finding the length of the line segment that connects vertex A (1,-1) and vertex B (1,4), you can use the distance formula based on Pythagorean theorem.

The distance formula is d = sqrt [(x2 - x1)² + (y2 - y1)²]. In this case, x1 = 1, x2 = 1, y1 = -1 and y2 = 4.

Substituting these values, we have d = sqrt [(1 - 1)² + (4 - (-1))²] = sqrt [0 + 25], hence d = sqrt [25] = 5 units.

Therefore, the length of the line segment connecting vertex A (1, -1) and vertex B (1, 4) is 5 units.

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We have

[tex]

\begin{cases}

2x+4y=20\Longrightarrow x+2y=10\\

3x+2y=26\\

\end{cases}

[/tex]

Then multiply the second equation by -1 to get

[tex]

\begin{cases}

x+2y=10\\

-3x-2y=-26\\

\end{cases}

[/tex]

Now add the equations that way you eliminate y-terms. You find that

[tex]-2x=-16\Longrightarrow x=8[/tex]

Now plug in the x to either of the original equations and solve for y.

[tex]

x+2y=10\\

8+2y=10\\

2y=2\Longrightarrow y=1

[/tex]

The solution is the intersection of two lines at [tex]P(8,1)[/tex].

Hope this helps.

Answer:

4x+3=5x-12    8x-3=3x+5

Step-by-step explanation:

Answer:

∠A =  47 deg

∠B = 43 deg

∠C =  124.82 deg

∠D =  55.18 deg

Step-by-step explanation:

recall that by definition:

Complementary angles : add up to 90 deg

Supplementary angles: add up to 180 deg

for ∠A and ∠B, they are complementary, i.e.

∠A + ∠B = 90

(4x+3) + (5x-12) = 90

4x + 3 + 5x - 12 = 90

9x - 9 = 90

9x = 90 + 9

9x = 99

x = 11

hence

∠A = 4x + 3 = 4(11) + 3 = 44+3 = 47 deg

∠B = 90 - 47 = 43 deg

for ∠A and ∠B, they are Supplementary, i.e.

∠C + ∠D = 180

8x-9+3x+5 = 180

x = 16.727 degrees

∠C = 8x - 9 = 8(16.727) - 9 = 124.82

∠D = 180 - 124.82 = 55.18

Answer:

0.800 is the answer. If you want an explanation let me know.

Step-by-step explanation:

Answer:

1 hour later , 21 pages read

Step-by-step explanation:

x hour later they will read the same number of pages

Tori: 16 + 5x

cora: 13 + 8x

16 + 5x = 13 + 8x

minus 5x each sides: 16 = 13 + 3x

minus 13 each sides: 3 = 3x

divide 3 each sides: x = 1

1 hour later both of them will read 16 + 5 x 1 = 21 pages

check cora: 13 + 8 x 1 = 21

Answer:

1 hour later , 21 pages read

Step-by-step explanation:

After 1 hour, Tori and Cora will have each completed 21 pages in their workbooks.

Quite an interesting question, let us see.

60 x 60 x 24 x 250 = 21,600,000

answer: 21,600,000

Step-by-step explanation: First, let's convert days to hours by multiplying 250 by the conversion factor of 24 to get 6,000 hours. Next we can convert hours to minutes by multiplying 6,000 by the conversion factor 60 to get 360,000 minutes. Finally, we convert minutes to seconds by multiplying 360,000 by the conversion factor 60 to get 21,600,000.

So, there are 21,600,000 seconds in 250 days.

Answer:D

Step-by-step explanation:

Answer:

The answer is B.

Step-by-step explanation:

You have to have a straight line and it has to go through the origin or else its not proportional

Answer:

A.) A straight line can be drawn through all the points and the line passes through the point (0, 0)

Step-by-step explanation:

When a line is straight, drawn through all points, and passes through the origin, that is how you know it's proportional.

B. would be incorrect because a line would have to be drawn through tall points to show that it is proportional

C. the first part of c would be correct but a line doesn't have to pass through (0,3) it has to pass through (0,0) also known as the origin

D. This answer is also incorrect. A line always has to pass through (0,0) to be proportional

Hope this helps :D

Answer:

Therefore the value of [tex]x=31\°[/tex]

Step-by-step explanation:

Given:

m∠ A = 56°

m∠ B = 75°

m∠ ACD = x°

To Find:

x = ?

Solution:

In Δ ABC

An exterior angle of a triangle is equal to the sum of the opposite interior angles.

Here,

The opposite interior angles are angle A and angle B.

An exterior angle of a triangle is angle ACD which is x°

∴ [tex]m\angle A +m\angle B=m\angle ACD\\[/tex]...Exterior angle property of Δ

Substituting the values we get

[tex]56+75=x\\\\\therefore x=131\°[/tex]

Therefore the value of [tex]x=31\°[/tex]

Answer:

The salesperson will earn total commission of $ 445 .

Step-by-step explanation:

The salesperson gets 5% commission for first $2500, and 8% for above that.

So, for sale of $ 6500, the salesperson will earn commission,

$ [tex](2500 \times \frac {5}{100} + (6500 - 2500) \times \frac {8}{100})[/tex]

= $ [tex](125 + (4000) \times \frac {8}{100})[/tex]

= $ (125 + 320)

= $ 445

Answer:

420 miles in 2 hours.

If it where to fly for 13 hours then you divide 420 by 2 which is 210. Multiply 210 by 13.

=2730 miles.

The rate of speed would be 420 divided by 2. This would equal 210 miles per hour.

Answer:

The jet could fly 2730 miles in 13 hours. The rate of speed of the jet is 210 miles per hour.

Step-by-step explanation:

420/2=x/13

simplify 420/2 into 210

x/13=210

x=210*13

x=2730

Answer:

[tex]\frac{1}{2}\sqrt{2+\sqrt{3}}[/tex]

Step-by-step explanation:

we know that

An half-angle identity is equal to

[tex]sin(\frac{\theta}{2})=(+/-)\sqrt{\frac{1-cos(\theta)}{2}}[/tex]

we have

[tex]sin(\frac{5\pi}{12})[/tex]

The angle [tex]\frac{5\pi}{12}=75^o[/tex]  ----> belong to the First Quadrant, so the value of the sine is positive

Let

[tex]\frac{\theta}{2}=\frac{5\pi}{12}[/tex]

so

[tex]{\theta=\frac{5\pi}{6}[/tex]

[tex]sin(\frac{5\pi}{12})=\sqrt{\frac{1-cos(\theta)}{2}}[/tex]

[tex]cos(\theta)=cos(\frac{5\pi}{6})=cos(150^o)=-\frac{\sqrt{3}}{2}[/tex]

substitute

[tex]sin(\frac{5\pi}{12})=\sqrt{\frac{1-(-\frac{\sqrt{3}}{2})}{2}}[/tex]

[tex]sin(\frac{5\pi}{12})=\sqrt{\frac{1+\frac{\sqrt{3}}{2}}{2}}[/tex]

[tex]sin(\frac{5\pi}{12})=\sqrt{\frac{2+\sqrt{3}}{4}[/tex]

[tex]sin(\frac{5\pi}{12})=\frac{1}{2}\sqrt{2+\sqrt{3}}[/tex]

Answer:

18:1

Step-by-step explanation:

To convert inches to feet, we divide the value of inches by 12

Therefore, 6 inches=66/12=0.5 ft

The length of model = 0.5 ft

Length of actual car=9 ft

Ratio of actual car to model= 9:0.5=18:1

Therefore, the ratio is 18:1

Answer:

d) $498.75

Step-by-step explanation:

Given:

Fixed expenses = $475

Expense raised by = 5%

We need to find updated Total Fixed Expenses.

Amount of expense raised is equal to Percentile expense raised multiply by Fixed expenses and then Divided by 100.

framing in equation form we get;

Amount of expense = [tex]\frac{5}{100}\times 475 = \$23.75[/tex]

Now Updated Total Fixed expense will be equal to sum of Fixed expenses and Amount of expense raised.

framing in equation form we get;

Updated Total Fixed expense = $475 + $23.75 = $498.75

Hence The updated Total fixed expenses will be $498.75.

Answer:498.75

Step-by-step explanation:

Hope it helped

Answer:

[tex]a=3.36 +0.816*0.18=3.507[/tex]

The value of height that separates the bottom 90% of data from the top 10% is 3.507.  

Step-by-step explanation:

1) Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

2) Solution to the problem

Let X the random variable that represent the grades of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(3.36,0.18)[/tex]  

Where [tex]\mu=3.36[/tex] and [tex]\sigma=0.18[/tex]

And the best way to solve this problem is using the normal standard distribution and the z score given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

For this part we want to find a value a, such that we satisfy this condition:

[tex]P(X>a)=0.10[/tex]   (a)

[tex]P(X<a)=0.90[/tex]   (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.90 of the area on the left and 0.10 of the area on the right it's z=0.816. On this case P(Z<0.816)=0.90 and P(Z>0.816)=0.1

If we use condition (b) from previous we have this:

[tex]P(X<a)=P(\frac{X-\mu}{\sigma}<\frac{a-\mu}{\sigma})=0.90[/tex]  

[tex]P(z<\frac{a-\mu}{\sigma})=0.90[/tex]

But we know which value of z satisfy the previous equation so then we can do this:

[tex]z=0.816=\frac{a-3.36}{0.18}[/tex]

And if we solve for a we got

[tex]a=3.36 +0.816*0.18=3.507[/tex]

So the value of height that separates the bottom 90% of data from the top 10% is 3.507.  

To find the minimum Undergraduate grade point average (UGPA) that would place a student in the top 10%, we use the Z-score corresponding to the top 10% (which is about 1.28) and apply it within the normal distribution parameters, mean (3.36) and standard deviation (.18). The result is a UGPA of approximately 3.59.

This question pertains to the concept of normal distribution in statistics. Given a mean of 3.36 and a standard deviation of .18, we're asked to find the minimum Undergraduate grade point average (UGPA) that would place a student in the top 10%. This requires the understanding of Z-scores (standard deviations away from the mean).

The Z-score that corresponds to the top 10% in a standard normal distribution is about 1.28 (this value comes from a standard Z-table or can be calculated using a statistical calculator). Remember that the Z-score formula is Z = (X - μ) / σ, where X is the value we're looking for, μ is the mean, and σ is the standard deviation.

So, rearranging the formula to solve for X gives X = Z*σ + μ. Substituting the known values into the equation gives: X = (1.28*.18) + 3.36, which gives X approximately equal to 3.59. Therefore, the minimum UGPA that will place a student in the top 10% is approximately 3.59.

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Answer:

Area = 26(10) + 5(3) + 5(4)

= 260 + 15 + 20

= 295 ft²

The value of f(5) is 49.1

Step-by-step explanation:

To find f(x) from f'(x) use the integration

f(x) = ∫ f'(x)

1. Find The integration of f'(x) with the constant term

2. Substitute x by 1 and f(x) by π to find the constant term

3. Write the differential function f(x) and substitute x by 5 to find f(5)

∵ f'(x) =  + 6

- Change the root to fraction power

∵  =

∴ f'(x) =  + 6

∴ f(x) = ∫  + 6

- In integration add the power by 1 and divide the coefficient by the

 new power and insert x with the constant term

∴ f(x) =  + 6x + c

- c is the constant of integration

∵

∴ f(x) =   + 6x + c

- To find c substitute x by 1 and f(x) by π

∴ π =   + 6(1) + c

∴ π =  + 6 + c

∴ π = 6.4 + c

- Subtract 6.4 from both sides

∴ c = - 3.2584

∴ f(x) =   + 6x - 3.2584

To find f(5) Substitute x by 5

∵ x = 5

∴ f(5) =   + 6(5) - 3.2584

∴ f(5) = 49.1

Answer:

[tex]\sqrt{61}[/tex] (= 7.81 )

The distance between (-2,-3) and (3,3) is 7.81

Step-by-step explanation:

The distance between two points can be calculated using :

[tex]\sqrt{(X_{2}-X_{1})^{2} + (Y_{2}-Y_{1})^{2}}[/tex]

First point A = (-2,-3)

[tex]X_{1}[/tex] = -2

[tex]Y_{1}[/tex] = -3

Second Point B = (3,3)

[tex]X_{2}[/tex] = 3

[tex]Y_{2}[/tex] = 3

Insert the value of X and Y coordinates in the formula:

[tex]\sqrt{(X_{2}-X_{1})^{2} + (Y_{2}-Y_{1})^{2}}[/tex]

[tex]\sqrt{(3- (-2))^{2} + (3- (-3))^{2}}[/tex]

[tex]\sqrt{(3 + 2)^{2} + (3 + 3)^{2}}[/tex]

[tex]\sqrt{(5)^{2} + (6)^{2}}[/tex]

[tex]\sqrt{25 + 36}[/tex]

[tex]\sqrt{61}[/tex]

= 7.86

Distance between A and B is 7.81

Let...

1st number=x

2nd number=x+2

3rd number=x+4

4th number=x+6

x+x+2+x+4+x+6=200

4x=188

x=47

x+6=53

answer: 53

Answer:

Step-by-step explanation:

Dilation can be compared with zooming some image according to the given scale.

The vertices of VWXY is given by (-1, -1), (-1, 2), (2, -1), (2, 2) respectively.

Since the given scale is 4, to get the vertices of V'W'X'Y' we need to multiply the co-ordinates by 4.

The desired co-ordinates will be (-4, -4), (-4, 8), (8, -4), (8, 8) respectively.

Answer:

(3,-8)

(2,-10)

Step-by-step explanation:

we have

[tex]10x + 4y < 12[/tex] ----> inequality A

[tex]8x- 3y > 20[/tex] ----> inequality B

we know that

If a point is a solution of the system of inequalities, then the point must satisfy both inequalities (makes true both inequalities)

Verify  all the points

Substitute the value of x and the value of y of each point in both inequalities  

Case 1) point (3,-8)    

For x=3, y=-8

inequality A

[tex]10(3) + 4(-8) < 12[/tex]

[tex]-2 < 12[/tex] ----> is true

inequality B

[tex]8(3)- 3(-8) > 20[/tex]

[tex]48 > 20[/tex] ---> is true

therefore

The point is a solution of the system of linear inequalities

Case 2) point (2,5)    

For x=2, y=5

inequality A

[tex]10(2) + 4(5) < 12[/tex]

[tex]40 < 12[/tex] ----> is not true

therefore

The point is not a solution of the system of linear inequalities

Case 3) point (-5,1)    

For x=-5, y=1

inequality A

[tex]10(-5) + 4(1) < 12[/tex]

[tex]-46 < 12[/tex] ----> is true

inequality B

[tex]8(-5)- 3(1) > 20[/tex]

[tex]-43 > 20[/tex] ---> is not true

therefore

The point is not a solution of the system of linear inequalities

Case 4) point (10,3)    

For x=10, y=3

inequality A

[tex]10(10) + 4(3) < 12[/tex]

[tex]112 < 12[/tex] ----> is not true

therefore

The point is not a solution of the system of linear inequalities

Case 5) point (2,-10)    

For x=2, y=-10

inequality A

[tex]10(2) + 4(-10) < 12[/tex]

[tex]-20 < 12[/tex] ----> is true

inequality B

[tex]8(2)- 3(-10) > 20[/tex]

[tex]46 > 20[/tex] ---> is true

therefore

The point is a solution of the system of linear inequalities

see the attached figure to better understand the problem

If a ordered pair is a solution of the system , then the ordered pair must lie in the shaded area of the solution set

Answer:

(3,-8)(2,-10)

Step-by-step explanation:

Answer:

A) 0.15

Step-by-step explanation:

Because 15/20=75/100=75%=0.75.

1520 is the value that is not equivalent to the other three options.

Option B is the correct answer.

We have,

To determine which option is not equivalent to the other three, we can analyze the given values.

A: 0.15

B: 1520

C: 75%

D: 0.75

Option B (1520) stands out as it does not share the same numerical pattern or representation as the other options.

Options A, C, and D are all related to each other as they represent the same value, albeit in different formats.

Option A (0.15) can be converted to a percentage as 15%.

0.15 x 100 = 15%.

Option C (75%) represents 75 out of 100, which is equivalent to 0.75 as a decimal or 75% as a percentage.

Option D (0.75) is the decimal representation of 75%, or 75 out of 100.

Therefore,

1520 is the value that is not equivalent to the other three options.

Learn more about expressions here:

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Answer:

Step-by-step explanation:

21% more then 5/11...

5/11 + 21% of 5/11 = 5/11 + 0.21(5/11) = 5/11 + (21/100 * 5/11) =

5/11 + 21/220 = 11/20 <===

Firstly, we converted the fraction 5/11 to its decimal equivalent, which is approximately 0.4545. Then, we calculated a number that is 121% of 0.4545 (because 21% more than the original number means we have to count the original number plus the additional 21%). The calculation gave us approximately 0.5499.

To answer this question, we can firstly calculate the equivalent decimal of 5/11. This can be done either by manual calculation or using a calculator. Dividing 5 by 11, we get approximately 0.4545.

Next, it's important to understand what the question is asking. When it asks what number is 21% more than a given number, it's essentially asking you to calculate a number that is 121% of the given number. Why? Because the original number (100%) plus the additional 21% gives you a total of 121%.

Once you know this, you simply multiply the given number (0.4545) by 1.21 (the decimal equivalent of 121%). And finally, multiplying 0.4545 by 1.21, we get approximately 0.5499. That is your final answer: The number that is 21% more than 5/11 is approximately 0.5499.

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Answer:

The width of the conference room = 18 feet

Step-by-step explanation:

Given:

Scale drawing of a planned office space is represented as

1 in : 6 feet

To find the width of the conference room if the width in the drawing is 3 inches.

Solution:

Scale is the representation of ratio of lengths in the drawing to the actual length.

The scale given here means that 1 inch length in the drawing corresponds to 6 feet length actually.

Thus, in order to find the actual length of 3 inches, we can use unitary method

If 1 inch in drawing corresponds to  = 6 feet

∴ 3 inches in drawing corresponds to = [tex]3\times 6 \ft[/tex] = 18 feet

Thus, width of the conference room = 18 feet

Answer:

(0,0)

Step-by-step explanation:

(0, 3) + 4 = (0,7)

(0, 7) - 7 = (0,0)

To determine if the speeds of the runners are in a proportional relationship, compare the ratios of their distances to their times.

In order for the speeds of the runners to be in a proportional relationship, their rates of covering distance should be consistent. In other words, the ratios of their distances to their times should be the same or equal.

For example, if Runner A ran 5 miles in 1 hour, and Runner B ran 10 miles in 2 hours, their speeds would be proportional because the ratio of distance to time is the same (5/1 = 10/2 = 5).

So, to determine which runners have proportional speeds, compare the ratios of their distances to their times and see if they are equal.

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Final answer:

Runners whose speeds are in a proportional relationship with each other are those who have the same average speed when the distance they run is divided by the time it took them. To find this, we use the average speed formula, which helps compare runners not only on an individual level but also in terms of speed fractions and distributions.

Explanation:

To determine which runners have speeds in a proportional relationship with each other, we need to use the concept of proportional relationships and the formula for average speed, which is calculated by dividing the distance by the time. If the ratio of distances to times for two runners is the same, then their speeds are proportional. For example, Runner A covering a distance of 10 miles in 2 hours and Runner B covering 5 miles in 1 hour both have an average speed of 5 miles per hour, which shows a proportional relationship.

Relating this to the details provided about the runners, for any pair of runners to have speeds that are in a proportional relationship, their speeds must be consistent or equivalent when calculated. The speed in miles per hour can be found by dividing the recorded distances by the recorded times. If multiple runners have the same result when distance is divided by the time, they are in a proportional relationship with each other in terms of speed.