Krista spent 6 hours on her homework this weekend. She spent 24 hours
studying for her social studies test and 1 hours on her math homework. The
rest of her time she spent writing a book report. How much time did Krista spend
on her book report?

Pls help

the required indefinite integral is x³/3 - x²/6 + C.

Given: x − 1/3x dx We need to find the indefinite integral. To integrate the above function, we can use the following basic integration formulas.

∫x dx = 1/2x² + C∫k dx

kx + C∫xⁿ dx = xⁿ⁺¹ / (n + 1) + C,

where n ≠ -1The given function is of the form x - 1/3x. We can write it as (3x² - x)/3.Now,

we can integrate (3x² - x)/3 using the basic integration formula.

∫(3x² - x)/3 dx= 3/3 ∫x² dx - 1/3 ∫x dx

∫x² dx - 1/3 ∫x dx= x³/3 - x²/6 + C On substituting the value of x, we get

∫(x - 1/3x) dx= ∫(3x² - x)/3 dx

x³/3 - x²/6 + C

Hence, the required indefinite integral is x³/3 - x²/6 + C.

To know more about indefinite integral Visit:

https://brainly.com/question/31549816

#SPJ11

Answer: 5 dimes 4 nickels 12 quarters

Step-by-step explanation:

i dont think u need one bro

Beth has 7.5 Dimes, 6.5 Nickel, and 14.5 Quarters.

Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.

+ Addition operation: Adds values on either side of the operator.

For example 4 + 2 = 6

- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.

for example 4 -2 = 2

Total value =$3.70

Let

Nickel = x -1

Dimes =  x

Quarters = x + 7

Every

Nickel = 5 cents

Dimes = 10 cents

Quarters = 25 cents

Total cents = $3.70× 100 = $370

⇒ 5n + 10d + 25q = 370

⇒ 5(x-1) + 10(x) + 25(x+7) = 370

⇒ 5x-5 + 10x + 25x+175  = 370

⇒ 40x + 70= 370

⇒ 40x = 370 - 70

⇒ 40x = 300

Divide both sides by 40

⇒ x= 300/40

⇒ x = 7.5

⇒ Dimes =  7.5

⇒ Nickel = 7.5 -1 = 6.5

⇒ Quarters = 7.5 + 7 = 14.5

Hence, Beth has 7.5 Dimes, 6.5 Nickel, and 14.5 Quarters.

Learn more about Arithmetic operations here:

brainly.com/question/25834626

#SPJ2

Answer:

3y+x=40

x=40-3y..........1

2x+1=y........2

subst. 2into1:

x=40-3(2x+1)

x=40-6x-3

7x=37

x=37/7

subst.x into2:

2(37/7)+1=y

y=81/7

Answer:

y=3/2x+1

Step-by-step explanation:

y=mx+b is the slope-intercept form

y=3/2x+b

we are looking for b now

plug in the points you provided

2=x, 4=y

4=3/2(2)+b

4=3+b

b=1 which is the intercept

The expected number of marks that Judge B would award to the sth debater, assuming the same degree of linear relationship exists in their judgement, is (option) b) 78.

In order to calculate the expected number of marks, we need to use the formula for the regression line, which is given by:

Ŷ = a + bX

where Ŷ is the predicted value (number of marks awarded by Judge B), X is the given value (number of marks awarded by Judge A), a is the y-intercept, and b is the slope of the regression line.

From the given information, we can calculate the slope (b) using the formula:

b = zXY / Y2 = 8734 / 3287 ≈ 2.657

Next, we can calculate the y-intercept (a) using the formula:

a = Y - bX = (237 / 7) - (2.657 * (252 / 7)) ≈ -9.03

Now, we can substitute the given value of 35 marks awarded by Judge A into the regression line formula:

Ŷ = -9.03 + (2.657 * (35 / 7)) = 78

Therefore, the expected number of marks that Judge B would award to the sth debater is 78.

To learn more about regression line click here: brainly.com/question/29048116

#SPJ11

The double integral. ∫∫R 2x/1 + xy dA, R = [0, 2] × [0, 1] is: 2*(1/2ln(3) - 1/2ln(1))

To calculate the double integral ∫∫R 2x/1 + xy dA, we need to integrate with respect to x and y over the region R = [0, 2] × [0, 1].

We can solve this by using the order of integration.

First we need to fix the limits of integration with respect to y and then integrate with respect to x.

∫∫R 2x/1 + xy dA = ∫(0 to 1) (∫(0 to 2) 2x/(1+xy) dx) dy

∫(0 to 1) (∫(0 to 2) 2x/(1+xy) dx) dy = ∫(0 to 1) ( 2*ln(1+xy)|x=0 to 2) dy

∫(0 to 1) ( 2ln(1+2y) - 2ln(1+0) ) dy

= 2*∫(0 to 1) ln(1+2y) dy

= 2*[y*ln(1+2y) - ∫(0 to 1) ln(1+2y) dy] |y = 0 to 1

= 2*[yln(1+2y) - (1/2 ln(3) - 1/2* ln(1))] |y = 0 to 1

= 2*(1ln(3) - 0ln(1) - 1/2* ln(3) + 1/2* ln(1))

= 2*(1/2ln(3) - 1/2ln(1))

Learn more about Double integration here:  brainly.com/question/30217024

#SPJ4

We need to  know about margin of error to solve the problem. The factors that influence margin of error are confidence level and sample size.

Margin of error is a statistic expressing the amount of random sampling error in the results of a survey. The larger the margin of error, the less confidence one should have that a poll result will reflect the result of a census of the entire population. Margin of error is influenced by three factors, confidence level, sample size and population standard deviation. In absence of population standard deviation, the margin of error is influenced by confidence level and sample size.

Therefore the margin of error is influenced by confidence level and sample size.

Learn more about margin of error here:

https://brainly.com/question/10218601

#SPJ4

Answer:

6

Step-by-step explanation:

Answer:

a + 7

Step-by-step explanation:

x^2 + 2x - 8. on [5,a]

(f(a)-f(5))/( a - 5 )

(( a^2 + 2a - 8 ) - 27 ) / a - 5

( a^2 + 2a - 35 ) / a - 5

(a - 5)(a + 7) / a - 5

a + 7

Answer:

Step-by-step explanation:

10 miles in 2 hours

10/2 = 5 so Helena runs 5 miles in 1 hour

5 mph

5miles/1hour

I am here my friend!  

Answer:

(3+4)1/2

Step-by-step explanation:

Answer: x=50

Step-by-step explanation:

Use the distributive property to multiply -0.2 by x-20.

-0.2x+4=44-x

Add x to both sides.

-0.2x+4+x=44

Combine -0.2x and x to get 0.8x.

0.8x+4=44

Subtract 4 from both sides.

0.8x=44-4

Subtract 4 from 44 to get 40.

0.8x=40

Divide both sides by 0.8.

x=40/0.8

Expand 40/0.8 approx 50 by multiplying both numerator and the denominator by 10.

X=400/8

Divide 400 by 8 to get 50.

x=50

If f(x, y, z) = xyzi + yj + zk, the divergence of the curl of the vector field f is zero.

To find the divergence of the curl of the vector field f(x,y,z) = xyzi + yj + zk, we first need to compute the curl of f, which is given by:

curl f = (∇ × f) = ∂(zk)/∂y - ∂(yj)/∂z + (∂(yj)/∂x - ∂(xyzi)/∂y)k + (∂(xyzi)/∂z - ∂(zk)/∂x)j + (∂(zk)/∂x - ∂(yj)/∂y) i

Simplifying this expression, we get:

curl f = (-z)i + xj + yk

Next, we need to find the divergence of the curl of f, which is given by:

div(curl f) = ∇ · (∇ × f) = ∂(∂(zk)/∂y - ∂(yj)/∂z)/∂x + ∂(∂(yj)/∂x - ∂(xyzi)/∂y)/∂y + ∂(∂(xyzi)/∂z - ∂(zk)/∂x)/∂z

Substituting the values from the curl f expression, we get:

div(curl f) = ∂(-z)/∂x + ∂(x)/∂y + ∂(y)/∂z

Simplifying this expression, we get:

div(curl f) = 0

To learn more about vector click on,

https://brainly.com/question/30195131

#SPJ4

Step-by-step explanation:

The sum of consecutive squares is

\(1^2+2^2+\dots+n^2=\frac16n(n+1)(2n+1)\)

Therefore

\(1^2+2^2+\dots+30^2=\frac16(30)(31+1)(2\cdot30+1) = 9455\)

In the equation, The possible value of k is,

⇒ k = - 3

We have to given that,

An expression is,

⇒ 25 = (ky - 1)²

And, In the equation above, y = −2 is one solution.

Now, We can plug y = - 2 in above equation, we get;

⇒ 25 = (ky - 1)²

⇒ 25 = (k × - 2 - 1)²

⇒ 25 = (- 2k - 1)²

Take square root both side, we get;

⇒ √25 = (- 2k - 1)

⇒ 5 = - 2k - 1

⇒ 5 + 1  = - 2k

⇒ - 2k = 6

⇒ - k = 6/2

⇒ - k = 3

⇒ k = - 3

Therefore, The possible value of k is,

⇒ k = - 3

Learn more about the equation visit:

brainly.com/question/28871326

#SPJ2

The right response is B. According to Option B, a data value X is regarded as an outlier if it deviates from the range Q1 - 1.5(IQR) to Q3 + 1.5. (IQR).

The right response is B.

The distance between the first quartile (Q1) and the third quartile in a box plot is known as the interquartile range (IQR) (Q3).

According to Option B, a data value X is regarded as an outlier if it deviates from the range Q1 - 1.5(IQR) to Q3 + 1.5. (IQR).

Although the range given in Option A is erroneous, the idea of an outlier being outside of a specific range based on the IQR is correct.

Option C's range, which is Q2 - 1.5(IQR) to Q2 + 1.5(IQR), is incorrect for locating outliers.

The phrase "TQR," which is uncommon in box plots, is mentioned in Option D. The range of Q2 -1.0(IQR) to Q2 +1.0(IQR) provided is incorrect for either locating outliers.

Learn more about  "outlier." here:

https://brainly.com/question/3779855

#SPJ4

The interest is %2 of 520 which, if you do the math, is 10.4 cents. You want to find out how much interest it is for 6 years so you have to multiply them.

10.4 x 6 = 62.4

The total interest for 6 years is $62.4

your welcome

All humans are considered to be consumers. A consumer is an organism that obtains its energy and nutrients by feeding on other organisms.

As humans, we consume food to provide our bodies with the energy and nutrients necessary for survival. Whether we eat meat, plants, or a combination of both, we are still consumers. In the case of herbivores, they consume only plant matter, but they are still considered consumers because they are obtaining their energy and nutrients from other living organisms (plants). Therefore, regardless of our dietary choices, all humans are classified as consumers in ecological terms.

Learn more about omnivores :

https://brainly.com/question/1970170

#SPJ4

Answer:

9 is c

10 is b

i think the last one is a but not too sure

Step-by-step explanation:

Answer:

Step-by-step explanation:

(a) To find the probability that it is raining when you arrive in Oneirabad on a random day, we need to use the law of total probability.

Let A be the event that it is raining, and B be the event that it is the Wet season.

P(A) = P(A|B)P(B) + P(A|B')P(B')

Given that the Wet season lasts for 1/3 of the year, we have P(B) = 1/3. The probability that it is raining during the Wet season is 3/4, so P(A|B) = 3/4.

The Dry season lasts for 2/3 of the year, so P(B') = 2/3. The probability that it is raining during the Dry season is 1/6, so P(A|B') = 1/6.

Now we can calculate the probability that it is raining when you arrive:

P(A) = (3/4)(1/3) + (1/6)(2/3)

= 1/4 + 1/9

= 9/36 + 4/36

= 13/36

Therefore, the probability that it is raining when you arrive in Oneirabad on a random day is 13/36.

(b) Given that it is raining when you arrive, we can use Bayes' theorem to calculate the probability that your visit is during the Wet season.

Let C be the event that your visit is during the Wet season.

P(C|A) = (P(A|C)P(C)) / P(A)

We already know that P(A) = 13/36. The probability that it is raining during the Wet season is 3/4, so P(A|C) = 3/4. The Wet season lasts for 1/3 of the year, so P(C) = 1/3.

Now we can calculate the probability that your visit is during the Wet season:

P(C|A) = (3/4)(1/3) / (13/36)

= 1/4 / (13/36)

= 9/52

Therefore, given that it is raining when you arrive, the probability that your visit is during the Wet season is 9/52.

(c) Given that it is raining when you arrive, the probability that it will be raining when you return to Oneirabad in a year's time depends on the season. If you arrived during the Wet season, the probability of rain will be different from if you arrived during the Dry season.

Let D be the event that it is raining when you return.

If you arrived during the Wet season, the probability of rain when you return is the same as the probability of rain during the Wet season, which is 3/4.

If you arrived during the Dry season, the probability of rain when you return is the same as the probability of rain during the Dry season, which is 1/6.

Since the season you arrived in is independent of the weather when you return, we need to consider the probabilities based on the season you arrived.

Let C' be the event that your visit is during the Dry season.

P(D) = P(D|C)P(C) + P(D|C')P(C')

Since P(C) = 1/3 and P(C') = 2/3, we can calculate:

P(D) = (3/4)(1/3) + (1/6)(2/3)

= 1/4 + 1/9

= 9/36 + 4/36

= 13/36

Therefore, the probability that it will be raining when you return to Oneirabad in a year's time, given that it is raining when you arrive, is 13/36.

To know more about probability refer here:

https://brainly.com/question/32117953

#SPJ11

Answer:

Step-by-step explanation:

tan23=h1/500

h1=500tan23

tan50=h2/500

h2=500tan50

The height of the building is h1+h2 so

H=500(tan23+tan50)ft (exact)

H=808.1 ft (rounded to nearest tenth of a foot)

Step-by-step explanation:

there are 91 2-digit numbers : 10 ..99

and there are 9 2-digit numbers with identical first and second digit : 11, 22, 33, 44, 55, 66, 77, 88, 99

99 has to be excluded, because there are no 2 2- digit numbers that I can subtract from each other and get 99.

so, e are dealing with 8 possibilities.

88 = 99-11

98-10

77 = 99-22

98-21

97-20

...

78-1

66 = 99-33

98-32

...

67-1

...

11 = 99-88

98-87

...

12-1

all the double- digit numbers are 11 apart. so, by picking 12 numbers, I have to have at least one that I can combine with one of the other 11 to get a double-digit number.

The expression for the power delivered to a resistance in terms of csc^2 2 pi ft is P = I^2_0 R (csc^2 2 pi ft).

According to the given information, the power delivered to a resistance R when an alternating current of frequency f and peak current I_0 passes through it is represented by the equation P = I^2_0 R sin^2 2 pi ft.

To express this equation in terms of csc^2 2 pi ft, we can use the trigonometric identity csc^2 x = 1/sin^2 x. Substituting this identity into the equation, we get P = I^2_0 R (1/sin^2 2 pi ft).

Since csc^2 x is the reciprocal of sin^2 x, we can rewrite the equation as P = I^2_0 R (csc^2 2 pi ft). This expression represents the power delivered to the resistance in terms of csc^2 2 pi ft.

Therefore, the correct expression for the power delivered to the resistance in terms of csc^2 2 pi ft is P = I^2_0 R (csc^2 2 pi ft).

Learn more about resistance here:

https://brainly.com/question/33728800

#SPJ11

Answer:

x-4y=36

Step-by-step explanation:

standard form is Ax+By=C

Answer:

15 meters in 1 second

Step-by-step explanation:

Divide 600 by 40 which is 15

so it travels 15 meters in 1 second

hope this helps!

Answer:15 meters per second

Step-by-step explanation:

600/40= 15