What is the derivative of this function?

Answers

Answer 1

[tex]\bf y=\sqrt{x}-\left( \frac{1}{2} \right)^x\implies y=x^{\frac{1}{2}}-\left( \frac{1}{2} \right)^x\implies \cfrac{dy}{dx}=\frac{1}{2}x^{\frac{1}{2}-1}-\left( \frac{1}{2} \right)^xln\left( \frac{1}{2} \right) \\\\\\ \cfrac{dy}{dx}=\frac{1}{2}x^{-\frac{1}{2}}-\left( \frac{1}{2} \right)^xln\left( \frac{1}{2} \right)\implies \cfrac{dy}{dx}=\cfrac{1}{2\sqrt{x}}-\left( \frac{1}{2} \right)^xln\left( \frac{1}{2} \right)[/tex]

Related Questions

Can you help me solve this 2/3 (5 x 4) ÷ 3 + 6/7 =

Answers

[tex]\frac{2}{3}(5 *4)/3+\frac{6}{7}\\\\\frac{2*5*4}{3}*\frac{1}{3}+\frac{6}{7}\\\\\frac{2*5*4}{3*3}+\frac{6}{7}\\\\\frac{40}{9}+\frac{6}{7}\\\\\frac{40}{9}*1+\frac{6}{7}*1\\\\\frac{40}{9}(\frac{7}{7})+\frac{6}{7}(\frac{9}{9})\\\\\frac{280}{63}+\frac{54}{63}\\\\\frac{334}{63}=5\ \frac{19}{63}[/tex]

(pemdas)
this is the order you do the math
parenthesis
exponents
multiplication or division which ever is first
Addition or subtraction which ever is first

2/3 (5 x 4) ÷ 3 + 6/7
2/3 (20)÷3+6/7
40/3÷3+6/7
40/9+6/7
find common denominator
280/63+54/63
334/63 or 5.301

Linear regression describes the extent to which _______ predicts ________.

Answers

Linear regression describes the extent to which the known variable predicts the to-be-predicted variable.

Final answer:

Linear regression describes the extent to which an independent variable predicts a dependent variable through a linear relationship.

Explanation:

Linear regression describes the extent to which an independent variable (x) predicts a dependent variable (y) through a linear relationship.

For example, if we have data that shows the number of hours studied (x) and the test score (y) of students, linear regression can help us determine how well the number of hours studied predicts the test score.

The regression line is used to model the linear relationship between the independent and dependent variables in the population.

Learn more about Linear regression here:

https://brainly.com/question/36829492

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How many license plates can be made using 3 digits and 3 letters of repeated digits and letters are not allowed?statistics?

Answers

[tex]10\cdot9\cdot8\cdot26\cdot25\cdot24=11,232,000[/tex]

An employer interviews 10 people for 6 technical support positions in a company, and 5 of the 10 people are women. If all 10 are qualified, in how many ways can the employer fill the technical support positions if exactly 3 are women?

Answers

Let the people be {M1, M2, M3, M4, M5, W1, W2, W3, W4, W5}

where M1 is Man 1, W1 woman 1 and so on...

The formula [tex]C(n, r)= \frac{n!}{r!(n-r)!} [/tex], gives the total numbers of ways of creating groups of r out of n.

r! means 1*2*3*...(r-1)*r.

The technical support group is going to have exactly 3 women, which will be chosen from 5 women, and 3 men which will be chosen from 5 men.

Each of the selections can be done in C(5, 3) many ways, and since the any selection of the men and women can be combined, in total there are:

C(5,3) *C(5, 3) many ways of creating the technical support group.

[tex]C(5,3) = \frac{5!}{3!2!}= \frac{5*4*3*2*1}{3*2*1*2*1}=10 [/tex]

10*10=100 many ways of forming the group.

Answer: 100

Estimate then find the product 7×7956

Answers

Final answer:

To estimate the product of 7 and 7956, round 7956 to 8000 and then multiply by 7 to get 56,000. The exact product, calculated using the multiplication algorithm, is 55,692.

Explanation:

To estimate the product of 7×7956, we can round 7956 to the nearest thousand which gives us 8000. Then, we multiply 7×8000 to get an estimated product of 56,000. To find the exact product, we multiply 7 by 7956 to get 55,692.

When calculating such a product, we use the multiplication algorithm where we multiply each digit of the second number by the first number and then add up the resulting values.

Here's how you would perform the multiplication step by step:

7×7 = 49, add the carried over 6 to get 55, write down 5 and carry over the 5.

After placing the digits in their correct positions, we get the final answer: 55,692. Therefore, the exact product of 7×7956 is 55,692.

There is a value of a such that subtracting a-4 from 4a+16 gives an answer of -25. What is that value of a?

Answers

Let's see what happens:

4a+16 - (a-4) = 3a + 20 = 25 => 3a = 5 => a = 5/3

If you subtract (a-4) from (4a+16), the new equation to work with would be 3a + 12. And if the difference of these two equations is 3a + 12, which would give an answer of -25, (pictured 3a + 12 = -25), by using algebra we could try a = -13/3 or a equals negative 13 over three. I hope this helps

How can you use place value and period names to read and write 324,904 in word form.

Answers

three hundred twenty-four thousand, nine hundred and four

yes you can. you would read that as:
three hundred twenty four thousand, nine hundred four.

no ands were in between the numbers because there are no decimals.
hope this helped, xx

box contains 15 items,4 of which are defective and 11 are good. Two items are selected. What is probability that the first is good and the second defective?

Answers

The probability of the first item being good is 11/15.
Since we have taken 1 item out the remaining total is now 14, so the probability of getting a defective item is now 4/14.
Now you multiply the probabilities together to get (11/15)(2/7)=22/105

Final answer:

The probability that the first item selected is good and the second item is defective is 22/105.

Explanation:

To find the probability that the first item selected is good and the second item is defective, we need to consider the total number of items, the number of good items, and the number of defective items.

The total number of items is 15, with 11 being good and 4 being defective. When we select the first item, there are 15 options, out of which 11 are good. Therefore, the probability of selecting a good item first is 11/15.

After selecting the first item, there are now 14 items left in the box, with 10 being good and 4 being defective. When we select the second item, there are 14 options, out of which 4 are defective. Therefore, the probability of selecting a defective item second is 4/14, which simplifies to 2/7.

To find the probability that both events occur, we multiply the probabilities: (11/15) * (2/7) = 22/105.

Find the measure of the angle and please explain step by step

Answers

angle 4 is the same as angle 8

angle 7 & angle 8 has to equal 180 degree

so angle 7 and angle 4 also have to equal 180

angle 4 is 3 times the size of 7

lets call 7 (x)

so 4(x) = 180

180/4 =45

x=45

angle 7 is 45 degrees

What is 6 increased by a number?

Answers

6 increased by a number in algebraic terms would be 6+x.

Suppose there is a test for esophageal cancer that is 95% accurate both on those that do and those that do not have esophageal cancer. if 0.7 percent of the population has esophageal cancer, compute the probability that a person has this cancer, given that his or her test results indicates so.

Answers

It was already stated that the probability that the population may have esophageal cancer is 0.7 percent. However, the additional statement that the accuracy is 95% will affect the probability as follows:

Probability = (0.007)(0.95) = 0.00665 or 0.665%

So instead of 0.7%, the probability will decreased to 0.665% because of the accuracy.

To put up several tents for a camping trip, you need several pieces of rope each 6 2/3 feet long. If you have a rope that is 43 feet, how many pieces can you cut for the tents?

Answers

[tex]\bf 43\div 6\frac{2}{3}\implies \cfrac{46}{6\frac{2}{3}}\implies \cfrac{\frac{46}{1}}{\frac{6\cdot 3+2}{3}}\implies \cfrac{\frac{46}{1}}{\frac{20}{3}} \implies \cfrac{46}{1}\cdot \cfrac{3}{20}\implies \cfrac{69}{10} \\\\\\ \boxed{6\frac{9}{10}}\qquad \qquad \cfrac{6\cdot 10+9}{10}\implies \cfrac{69}{10}[/tex]

The equation of the line of best fit of a scatter plot is y = −4x − 6. What is the slope of the equation?

−6
−4
4
6

Answers

The slope-intercept form of a line is:

y=mx+b, where m=slope and b=y-intecept

So if y=-4x-6 the slope is -4.

y = -4x -6

the equation is written in slope intercept form ( y = mx +b ) where b is the y intercept
therefore the y intercept is -6

For each function, use the slope formula to calculate the rate of change between the points. In your final answer, include all of your calculations.

f(x):

(a, f(a) and (b,f(b)

1.) f(x)=x - 3 (0,f(0)) and (6,f(6))
2.) f(x) = -x (-4,f(-4)) and(2,f(2))
3.) f(x)=x2 (-2,f(-2)) and (0,f(0))
4.) f(x)=x3 (-1,f(-1)) and (1,f(1))
5.) f(x)=2x (0,f(0)) and (4,f(4))

Answers

Function 1:

f(x) = x - 3
f(0) = 0 - 3 = -3
f(6) = 6 - 3 = 3

Slope = [tex] \frac{-3-3}{6-0} = \frac{-6}{6} =-1[/tex]

Function 2:

f(x) = -x
f(-4) = 4
f(2) = -2

Slope = [tex] \frac{4--2}{-4-2}= \frac{6}{-6}=-1 [/tex]

Function 3:

f(x) = x²
f(-2) = (-2)² = 4
f(0) = (0)² = 0

Slope = [tex] \frac{4-0}{-2-0}= \frac{4}{-2}=-2 [/tex]

Function 4:

f(x) = x³
f(-1) = (-1)³ = -1
f(1) = (1)³ = 1

Slope = [tex] \frac{-1-1}{-1-1}= \frac{-2}{-2}=1 [/tex]

Function 5:

f(x) = 2ˣ
f(0) = 2⁰ = 1
f(4) = 2⁴ = 16

Slope = [tex] \frac{1-16}{0-4}= \frac{-15}{-4}=3.75 [/tex]

For a standard normal distribution, the probability of obtaining a z value between -1.9 to 1.7 is

Answers

P(X≤−1.9)=0.0287165598160018P(X≤−1.9)=0.0287165598160018

P(X≥1.7)=0.044565462758543P(X≥1.7)=0.044565462758543

P(−1.95996398454005≤X≤1.95996398454005)=0.95

Answer:

92.67% probability of obtaining a z value between -1.9 to 1.7.

Step-by-step explanation:

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

For a standard normal distribution, the probability of obtaining a z value between -1.9 to 1.7 is

This probability is the pvalue of z = 1.7 subtracted by the pvalue of z = -1.9.

z = 1.7 has a pvalue of 0.9554.

z = -1.9 has a pvalue of 0.0287.

So there is a 0.9554-0.0287 = 0.9267 = 92.67% probability of obtaining a z value between -1.9 to 1.7.

Question part points submissions used use a power series to approximate the definite integral, i, to six decimal places. 0.3 ln(1 + x4) dx 0

Answers

[tex]\ln(1+x)=\displaystyle-\sum_{n=1}^\infty\frac{(-x)^n}n[/tex]

[tex]\implies\ln(1+x^4)=\displaystyle-\sum_{n=1}^\infty\frac{(-x^4)^n}n[/tex]

[tex]\displaystyle-\int_0^{0.3}\sum_{n=1}^\infty\frac{(-x^4)^n}n\,\mathrm dx[/tex]
[tex]=\displaystyle\sum_{n=1}^\infty\frac{(-1)^{n+1}}n\int_0^{0.3}x^{4n}\,\mathrm dx[/tex]
[tex]=\displaystyle\sum_{n=1}^\infty\frac{(-1)^{n+1}}n\dfrac{x^{4n+1}}{4n+1}\bigg|_0^{0.3}[/tex]
[tex]=\displaystyle\sum_{n=1}^\infty\frac{(-1)^{n+1}(0.3)^{4n+1}}{n(4n+1)}[/tex]
[tex]\approx0.000485[/tex]

What is the length of a diagonal of a square with a side length of 6?

Answers

By the Pythagorean Theorem:

d^2=x^2+y^2, where x and y are the dimensions of the rectangle, however this is just a square, so x=y=s so

d^2=s^2+s^2

d^2=2s^2, and we are told that s=6 so

d^2=2(6^2)

d^2=2(36)

d=√(2(36))

d=6√2 units

d≈8.49 units (to nearest hundredth of a unit)

d = 8.49

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Jane is making a suit which requires 2 5/8 yards for the jacket and 1 3/4 yards for the skirt. What is the total amount of material she needs? A. 3 1/2 yards B. 3 2/3 yards C. 4 yards D. 4 3/8 yards Mark for review (Will be highlighted on the review page)

Answers

In order to calculate this, We need to make sure that both measurements have the same denominator, so we need to transform 3/4 into a fraction with denominator of 8

1 3/4 >>> 1 6/8 ( the 6 comes from 8/4 x 3)

The total material that jane need would be:

2 5/8 + 1 6/8

= 3 11/8

= 4 3/8

The answer is option D,

From September 1981 to September 1984 the enrollment at a particular school declined to 11%. If the number of students enrolled at that school in September 1984 was 712 what was the enrollment in September 1981?

a) 78 b) 634 c) 701
d) 790 e)800

Answers

634, you have to multiply it by 89% of the original number, 712, to deduct 11%

If 3/2 divided by 1/4 =n, then n is between

Answers

3/2 / 1/4 = 3/2 * 4/1
3*4= 12
2*1= 1
n= 12/1 or 12

Hope this helps!

3. Solve z2 – 15z + 56 = 0 using the zero product property. A. z = 8, 7 B. z = –5, –2 C. z = 8, –4 D. z = –4, 7

Answers

We are tasked to solve for the values of z using and applying the zero product property which means that we need to get the factors and equate it to be equal to zero. Such that the given expression z² - 15z + 56 = 0 will have a solution shown below:
z² - 15z + 56 = 0
The expression will have a and b values such as a = - 7 and b = -8.
z² - 15z + 56 = 0
(z -7) (z-8) = 0
solving for the first value of z, we have it:
z - 7 = 0
z = 7
Solving for the second value of z, we have it:
z - 8 = 0
z = 8

Therefore, the answer to this problem is the letter "A" which is 7 and 8.

Will someone please answer this question?

Answers

surface area = 5ab +5bh

a = 4

b=7

h=18

5*4*7 = 140

5*7*18 = 630

630+140 = 770 square meters

Txt me quicky i need help

Answers

your chances of getting a even number is

P(even) = 4/8

simplified is 1/2

hope this helps

There are 12 more toy cars than toy trucks in a toy box. With a total of 38 toy cars and trucks.How many toy trucks are in the toy box?

Answers

based on my calculation its 31 toy trucks.
i just simply do like this

38÷2
=19-12
=7

38-7
=31#

Answer:

Hui

Step-by-step explanation:

Write the event as a set of outcomes. We flip three coins and obtain more tails than heads.

Answers

We start by listing the outcome of flipping two coins. The first table shows the outcomes HH, HT, TH, and TT. These outcomes then become the input combined with the third coins, as shown in the second table.

We have 8 outcomes in total: HHH, HHT, HHT, TTH, HHT, HTT, TTH, and TTT

The probability that we obtain more tails than heads is 4/8

Susie is paying $502.33 every month for her $150,000 mortgage payment. If this is a 4.5% 30 year mortgage, how much interest will she pay over the 30 years of payments?

Answers

You could find the interest paid by simply realizing that:

502.33(12)30-150000=total interest paid

i=502.33(12)30-150000

i=$30838.80

Answer:

$30838.80

:3 simply it pls

Fill in the blank. In the triangle below x = ______. Round your answer to two decimal places.

Answers

tan42°=x/35

x=35tan42° units

x≈31.51 units (to nearest hundredth of a unit)

Answer:

[tex]x=31.51\ units[/tex]

Step-by-step explanation:

we know that

In the right triangle

[tex]tan(42\°)=x/35[/tex]

isolate the variable x

[tex]x=35tan(42\°)=31.51\ units[/tex]

Look at the radian measure for every 30 degrees and 45 degrees in the Unit Circle. Explain how finding the exact measure in quadrant one can help you determine the remaining exact radian measures.

Answers

Google radian measures on the unit circle for lots of images of completed unit circles with these radian measurements. But the core idea is that if you can find the 30° and 45° radian measures (π/6 and π/4 respectively) to move to the corresponding angle in quadrant 2, you'd just need to add π/2 (90°) to that value, to find the values in quadrant 3 add π (180°), quadrant 4 add 3π/4 or you could also just minus π/2 to move 90° in the opposite direction. Say I wanted to find the 45° angle in quadrant 3, measured from the 0° line on the unit circle, in radians. I could say I know 45° is π/4 in quadrant 1, so to move it to quadrant 3, I need to add π or 180° to it. π/4 + π = π/4 + 4π/4 = 5π/4 which is the angle we need in radians.

EASY 5 POINTS REALLY NEED HELP RN!!!! Which expression finds the length of side x in this right triangle?

Answers

Use Pythagoras:

x² = (8.5)² + (5)²

x = √[(8.5)² + (5)²]

Answer:

Top right one

Step-by-step explanation:

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If cba represents three numbers multiplied together, what property allows you to rearrange the factors to read abc?

Answers

Final answer:

The commutative property allows you to rearrange the factors of a multiplication problem.

Explanation:

The property that allows you to rearrange the factors of a multiplication problem is the commutative property. This property states that the order of the factors can be changed without changing the product. In this case, if cba represents three numbers multiplied together, you can rearrange the factors to read abc because multiplying in any order will give you the same product.

For example, if c = 2, b = 3, and a = 4, then cba = 2 * 3 * 4 = 24. Rearranging the factors to abc gives abc = 4 * 3 * 2 = 24, which is the same product.

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Increased secretion of aldosterone would result in a(n) ______________ of blood ____________? increase, potassium decrease, volume increase, calcium levels decrease, ph increase, sodium Write out a short conversation in Spanish between two people who are meeting each other for the first time. Each person needs to say at least three lines. Greg is trying to solve a puzzle where he has to figure out two numbers, x and y. Three less than two-third of x is greater than or equal to y. Also, the sum of y and two-third of x is less than 4. Which graph represents the possible solutions? in the figure below, angle y and angle x form vertical angles. Angle y forms a straight line with 80 degrees angle and the 60 degree angle. write and solve the equation to determine the measure of angle x Given how the process of evolution appears to occur, how might concepts presented in this unit be used to help predict how any given organism might evolve in the future? How might this knowledge lead to human intervention, positive or negative, in that organisms natural evolutionary process? A cluster of symptoms that regularly occur together is known as a: What conclusion would be most appropriate about the genetic variation between humans and the 3 apes as illustrated by the phylogenetic tree Nicotine, a substance found in cigarettes, causes blood vessels to constrict. What effect might prolonged smoking have on the body? A. Decreased heart rate B.Decreased heart strength C.High blood pressure D. High blood volume Who was Phillis WheatleyA) an African American slaveB) one of the first women to own slavesC) one of the first female puritans preachersD) a leader of the Massachusetts bay colony What is the length of CF? look at image attached The ________ approach to the study of personality came about in reaction to the dominance of western approaches to the study of personality in non-western settings. A website has 826,140 hits what is the value of the 8 in 826,140 Which of the following lists accurately describes the major motivations for European exploration during the 15th and 16th centuries Jeremiah is asked to write the equation of an ellipse. He is given one vertex along the major axis and the location of the center. He realizes he does not have enough information to write the equation. He asks his teacher for one additional piece of information. What information could Jeremiah ask for to help him write the equation? Check all that apply.-the location of the focus nearest the given vertex-the location of the focus nearest the other vertex-the location of the other vertex along the major axis-the location of one covertex along the minor axis-the location of the directrix nearest the given vertex-the location of the directrix nearest the other vertex-the length of the minor axis which protest against the tea act of 1773 was most common Write the equation y=-3/5x+3 in standard form using integer coefficients Identify the sentence with parallel structure.A.Last year, she had the mumps, the measles, and the flu.B.Last year, she had the mumps, the measles, and caught the flu.C.Last year, she had the mumps, has the measles, and caught the flu.D.Last year, she has the mumps, measles, and the flu. You are given solutions of hcl and naoh and must determine their concentrations. you use 27.5 ml of naoh to titrate 100.0 ml of hcl and 18.4 ml of naoh to titrate 50.0 ml of 0.0782 m h2so4. based on this data, what were the concentrations (molarities) of the hcl and naoh solutions, respectively (04.01 LC)Which of the sets of ordered pairs represents a function?A = {(2, 2), (5, 5), (2, 2), (5, 5)}B = {(4, 2), (4, 2), (9, 3), (9, 3)} Only A Only B Both A and B Neither A nor B ugh yuck biology .....help if you can .-. Steam Workshop Downloader