Is the following statement true or false? Integration and differentiation are inverse processes. Group of answer choices

Answer:

[tex]y=3t^9+C[/tex]

Step-by-step explanation:

Given:  [tex]\dfrac{dy}{dt}=27t^8[/tex]

We want to obtain the general solution of the given differential equation.

[tex]dy=27t^8$ dt\\$Take the integral of both sides\\\int dy =\int 27t^8$ dt$\\y=\dfrac{27t^{8+1}}{8+1} +C$, (where C is the constant of integration)$\\y=\dfrac{27t^{9}}{9} +C\\\\y=3t^9+C[/tex]

The general solution of the differential equation is: [tex]y=3t^9+C[/tex]

CHECK:

[tex]\dfrac{d}{dt} y=\dfrac{d}{dt}(3t^9+C)=\dfrac{d}{dt}(3t^9)+\dfrac{d}{dt}(C)\\\\\text{Since derivative of a constant is zero}\\\\\dfrac{dy}{dt}=27t^{9-1}\\\dfrac{dy}{dt}=27t^8[/tex]

Answer:

solution,

[tex]a. \: \: \frac{3x + 4}{2} = 9.5 \\ \: \: or \: 3x + 4 = 9.5 \times 2(cross \: multiplication) \\ \: \: or \: 3x + 4 = 19 \\ \: \: or \: 3x = 19 - 4 \\ \: \: or \: 3x = 15 \\ \: or \: x = \frac{15}{3} \\ \: x = 5[/tex]

[tex]b. \: \: \frac{7 + 2x}{3} = 5 \\ \: \: or \: 7 + 2x = 5 \times 3(cross \: multiplication) \\ \: \: or \: 7 + 2x = 15 \\ \: \: or \: 2x = 15 - 7 \\ \: or \: 2x = 8 \\ \: or \: x = \frac{8}{2} \\ \: \: x = 4[/tex]

Hope this helps..

Good luck on your assignment..

Answer:

a) 0.65 mpg

b) Between 24.99 mpg and 28.01 mpg.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use 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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation, which is also called standard error, [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

[tex]\mu = 26.50, \sigma = 3.25, n = 25, s = \frac{3.25}{\sqrt{25}} = 0.65[/tex]

a. What is the standard error of X and the mean from a random sample of 25 fill-ups by one driver?

s = 0.65 mpg

b. Within what interval would you expect the sample mean to fall, with 98 percent probability?

From the: 50 - (98/2) = 1st percentile

To the: 50 + (98/2) = 99th percentile

1st percentile:

X when Z has a pvalue of 0.01. So X when Z = -2.327.

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

By the Central Limit Theorem

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

[tex]-2.327 = \frac{X - 26.50}{0.65}[/tex]

[tex]X - 26.50 = -2.327*0.65[/tex]

[tex]X = 24.99[/tex]

99th percentile:

X when Z has a pvalue of 0.99. So X when Z = 2.327.

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

[tex]2.327 = \frac{X - 26.50}{0.65}[/tex]

[tex]X - 26.50 = 2.327*0.65[/tex]

[tex]X = 28.01[/tex]

Between 24.99 mpg and 28.01 mpg.

Answer:

There are 172 butterflies  in the conservatory.

Step-by-step explanation:

Given

ratio of butterflies to total number of flying insects is 36 to 100

total number of butterflies / total number of flying insects = 36 / 100 = 9/25

Create a table for how many butterflies there are for 1, 50, and 100 flying insects.

Let the number of butter flies be x

when total no. of insects = 1

total number of butterflies / total number of flying insects  =9/25=x/1

=> 9/25= x/1

=> x = 9/25

____________________________________

when total no. of insects = 50

total number of butterflies / total number of flying insects  =9/25=x/50

=> 9/25= x/50

=> x = 9/25 * 50 = 18

_______________________________________

when total no. of insects = 100

total number of butterflies / total number of flying insects  =9/25=x/100

=> 9/25= x/100

=> x = 9/25 * 100= 36

Thus, table is

butterfly    total no of insects

   9/25            1

     50             18

     100            36

______________________________________________

Given there There are 450 total flying insects in the conservatory

again using the same ratio and taking no. of butterflies as x

total number of butterflies / total number of flying insects  =9/25=x/450

9/25=x/450

=>x = 9/25 * 450 = 9*18 = 172

Thus, there are 172 butterflies  in the conservatory.

Answer:

There are 162 butterflies  in the conservatory.

Step-by-step explanation:

Given

ratio of butterflies to total number of flying insects is 36 to 100

total number of butterflies / total number of flying insects = 36 / 100 = 9/25

Create a table for how many butterflies there are for 1, 50, and 100 flying insects.

Let the number of butter flies be x

when total no. of insects = 1

total number of butterflies / total number of flying insects  =9/25=x/1

=> 9/25= x/1

=> x = 9/25

____________________________________

when total no. of insects = 50

total number of butterflies / total number of flying insects  =9/25=x/50

=> 9/25= x/50

=> x = 9/25 * 50 = 18

_______________________________________

when total no. of insects = 100

total number of butterflies / total number of flying insects  =9/25=x/100

=> 9/25= x/100

=> x = 9/25 * 100= 36

Thus, table is

butterfly    total no of insects

  9/25            1

    50             18

    100            36

______________________________________________

Given there There are 450 total flying insects in the conservatory

again using the same ratio and taking no. of butterflies as x

total number of butterflies / total number of flying insects  =9/25=x/450

9/25=x/450

=>x = 9/25 * 450 = 9*18 = 162

Thus, there are 162 butterflies  in the conservatory.

Answer:

We need to remember that the Z value comes froma normal standard distribution given by:

[tex] Z\sim N(\mu=0,\sigma=1)[/tex]

So then the mean is 0 and all the values in the left are negative. So then if we want to analyze that if A is negative then  value of Z indicates that :

B. the number of standard deviations of an observation is to the left of the mean

Step-by-step explanation:

We need to remember that the Z value comes froma normal standard distribution given by:

[tex] Z\sim N(\mu=0,\sigma=1)[/tex]

And the z score formula is given by:

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

So then the mean is 0 and all the values in the left are negative. So then if we want to analyze that if A is negative then  value of Z indicates that :

B. the number of standard deviations of an observation is to the left of the mean

B. the number of standard deviations of an observation is to the left of the mean

A [tex]Z[/tex] score is a numerical measurement that describes a value's relationship to the mean of a group of values. The value of the [tex]Z[/tex] score tells you how many standard deviations you are away from the mean. A negative [tex]Z[/tex] score reveals the raw score is below the mean average. Also, a negative value of Z indicates that B. the number of standard deviations of an observation is to the left of the mean

For more information:

https://brainly.com/question/17756962?referrer=searchResults

Answer:

3

Step-by-step explanation:

=> 5 x (8-4) ÷ 4 - 2

Solving Brackets

=> 5 × 4 ÷ 4 - 2

Dividing

=> 5 × 1 - 2

Multiplying

=> 5 - 2

Subtracting

=> 3

Answer:

3

Step-by-step explanation:

5 x 4/4-2

5x1-2 (any expression divided by itself equals one)

5-2 (any expression multiplied by one remains the same)

=3

hope this helps love!

Answer:

2m-9

Step-by-step explanation:

m-4+m-5

=m+m-4-5

=2m-9

Answer:

2m-9

Step-by-step explanation:

m-4+m-5

take the like terms

= 2m-4-5

= 2m-9

Sorry if that didn't help

Answer:

120 inches cubed

Step-by-step explanation:

The formula for finding the volume of a rectangular prism is length * width * height.

In this case, 8 inches long is the length, 5 inches is the width, and 3 inches is the height.

So multiplying all of those together gets you 120 inches cubed.

Answer:

Pencil = $0.25

Marker = $1.00

Eraser = $1.75

Step-by-step explanation:

Let P denote pencils, M denote markers and E denote erasers. The quantities of each item and total amounts spent by each person can be modeled into the following linear system:

[tex]7P+8M+7E=22\\4P+8M+6E=19.5\\6P+4M+7E=17.75[/tex]

Solving the linear system:

[tex]7P-4P+8M-8M+7E-6E=22-19.5\\3P+E=2.5\\E=2.5-3P \\\\7P+8M+7E-2*(6P+4M+7E)=22-2*17.75\\-5P-7E=-13.5\\-5P*-7*(2.5-3P)=-13.5\\16P=-13.5+17.5\\P=0.25\\E=2.5-0.25*3\\E=1.75\\7P+8M+7E =22\\7*0.25+8M+7*1.75 =22\\8M=8\\M=1[/tex]

The price of each item is:

Pencil = $0.25

Marker = $1.00

Eraser = $1.75

Answer:

Part A. I chose points (7,1.3) and (48,9.8)

Part B. a. Positive correlation; b.  y = 0.21x - 0.2

Step-by-step explanation:

Part A.

I chose the first and last points on the line — (7 in, 1.3 lb) and (48 in, 9.8 lb).

That put three points on the line, three above it, and four below.

Part B

a. Type of correlation

There is a positive correlation between the length of a puppy and its weight.

You would expect a longer dog to be bigger and weigh more than a shorter dog.

b.  The equation for the line of best fit

The slope-intercept equation for a straight line is

y = mx + b

where m is the slope of the line and b is the y-intercept.

The line passes through the points (7,1.3) and (48, 9.8).

(i) Calculate the slope of the line

\begin{array}{rcl}

[tex]m & = & \dfrac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\ & = & \dfrac{9.8 - 1.3}{48-9}\\\\& = & \dfrac{8.5}{41}\\\\& = & \textbf{0.21 lb/in}\\\\\end{array}[/tex]

The slope of the line is 0.21 lb/in.

(ii) Locate the y-intercept

Put the slope and the coordinates of one point into the slope-intercept formula.

[tex]\begin{array}{rcl}y & = & mx + b\\1.3 & = & 0.21\times7 + b\\1.3 & = & 1.47 + b\\b & = & -0.2\\\end{array}[/tex]

The y-intercept is at (0,-0.2)

(iii) Write the equation for the line

y = 0.21x - 0.2

Answer:

27°

Step-by-step explanation:

Let line AB be extended to touch line DC at point F, thereby forming triangle BCF.

∠ABC + ∠BCE = 180° (sum of interior angles in a transversal).

∠ABC + 48 = 180

∠ABC = 180 - 48 = 132°

Also in triangle ADF, ∠ADF + ∠DFA + ∠FAD = 180 (sum of angle in a straight line)

85 + ∠DFA + 25 = 180

∠DFA + 110 = 180

∠DFA = 180 - 110 = 70

∠DFA = 70

∠DFA + ∠BFC = 180° (sum of angle on a straight line)

∠BFC + 70 = 180

∠BFC = 180-70 = 110

∠BFC = 110°

∠ABC + ∠CBF = 180° (sum of angle on a straight line)

132 + ∠CBF = 180

∠CBF = 1800 - 132 = 42

∠CBF = 42°

In triangle BCF:

∠BFC + ∠CBF + x = 180° (sum of angle in a triangle)

42 + 110 + x = 180

x + 152 = 180

x = 180 - 152

x = 27°

Answer:

22 Degrees

Step-by-step explanation:

First, i extended the line AB, to make a triangle and then i found out that the angle is 70 degrees, and from that i got that the other angle is 110 degrees, so now i know that the triangle (that has X in it) is this formula:

110+48+X=180

so now 180-158=22, so that is the answer

I suppose the curve is [tex]r(\theta)=e^\theta[/tex].

Tangent lines to the curve have slope [tex]\frac{dy}{dx}[/tex]; use the chain rule to get this in polar coordinates.

[tex]\dfrac{dy}{dx}=\dfrac{dy}{d\theta}\dfrac{d\theta}{dx}=\dfrac{\frac{dy}{d\theta}}{\frac{dx}{d\theta}}[/tex]

We have

[tex]y(\theta)=r(\theta)\sin\theta\implies\dfrac{dy}{d\theta}=\dfrac{dr}{d\theta}\sin\theta+r(\theta)\cos\theta[/tex]

[tex]x(\theta)=r(\theta)\cos\theta\implies\dfrac{dx}{d\theta}=\dfrac{dr}{d\theta}\cos\theta-r(\theta)\sin\theta[/tex]

[tex]r(\theta)=e^\theta\implies\dfrac{dr}{d\theta}=e^\theta[/tex]

[tex]\implies\dfrac{dy}{dx}=\dfrac{e^\theta\sin\theta+e^\theta\cos\theta}{e^\theta\cos\theta-e^\theta\sin\theta}=\dfrac{\sin\theta+\cos\theta}{\cos\theta-\sin\theta}[/tex]

The tangent line is horizontal when the slope is 0, which happens wherever the numerator vanishes:

[tex]\sin\theta+\cos\theta=0\implies\sin\theta=-\cos\theta\implies\tan\theta=-1[/tex]

[tex]\implies\theta=\boxed{-\dfrac\pi4+n\pi}[/tex]

(where [tex]n[/tex] is any integer)

The tangent line is vertical when the slope is infinite or undefined, which happens when the denominator is 0:

[tex]\cos\theta-\sin\theta=0\implies\sin\theta=\cos\theta\implies\tan\theta=1[/tex]

[tex]\implies\theta=\boxed{\dfrac\pi4+n\pi}[/tex]

Answer:

Step-by-step explanation:

t=V100-50/4

t=V50/4=1.76≈1.8 s

when h=0

t=V100/4=10/4=2.5 s

Answer:  a) (5√2)/4 ≈ 1.77 seconds

               b) 5/2 = 2.5 seconds

Step-by-step explanation:

[tex]t=\dfrac{\sqrt{100-h}}{4}\\\\\\h=50\rightarrow t=\dfrac{\sqrt{100-50}}{4}\\\\\\.\qquad \qquad =\dfrac{\sqrt{50}}{4}\\\\\\.\qquad \qquad =\large\boxed{\dfrac{5\sqrt2}{4}}\\\\\\\\h=0\rightarrow t=\dfrac{\sqrt{100-0}}{4}\\\\\\.\qquad \qquad =\dfrac{\sqrt{100}}{4}\\\\\\.\qquad \qquad =\dfrac{{10}}{4}\\\\\\.\qquad \qquad =\large\boxed{\dfrac{5}{2}}[/tex]

Answer:

The probability is 40%

Step-by-step explanation:

a) There are ten pieces of paper with ten numbers

Probability of selecting four pieces of paper = 4/10 or 40%

Probability that the four numbers selected will have a sum greater than 82 = 82/205 = 40%

Therefore, the probability of selecting four numbers that have a sum greater than 82 out of ten numbers totalling 205 is 40%.

b) Probability is the ratio of the number of outcomes favourable for the event to the total number of possible outcomes.   In other words, it is a measure of the likelihood of an event (or measure of chance).

Answer: -32

Step-by-step explanation:

I'm just going to plug in and break down the equation to make it more understandable and easier to comprehend

-(3^2) - (4*3) -11

-(9)- (12) -11

-9 - 12 - 11

-21 -11

-32

Answer:

A.

Step-by-step explanation:

Since you are trying to find x, you have to divide both sides by 4 to isolate x and get your answer.

Answer:

$84.80

Step-by-step explanation:

find the difference between accurate price and written price: 74 - 47 = 27

find written total (before Mrs. Taylor found mistake) by undoing the mean calculation: 82.55 x 12 = $990.60

the total expenses is $27 more than what they thought: 990.60 + 27 = 1017.60

divide accurate total by 12 to find mean: 1017.60 / 12 = $84.80

hope this helps :)

Answer:

137

Step-by-step explanation:

sum of angle in a circle = 360°

105 + 118 + x = 360

223 + x = 360

x = 360 - 223

x = 137

Answer:

I tried the question and I got. a/4-b/2-5/2

Step-by-step explanation:

I hope this helps

Answer:

100,000 meters

Step-by-step explanation:

There are 1000 meters in a kilometer so there are 100,000 meters in 100 kilometers.

Answer:

it is 100000 kilometers

Step-by-step explanation:

use the metric system and you get 10000 kilometers.

Answer:

True mean/population mean

Step-by-step explanation:

The standard error in this case gives an estimate on how far the values observed during the course of the experiment ate likely to be from the true mean/population mean.

Answer:

False

True

False

True

Step-by-step explanation:

Easiest and fastest way is to plug each equation into a calc and see if they match the values given. When you do so, you should get your answers.

Answer:

12.5%

Step-by-step explanation:

There is only one number 5 from a total of 8 parts.

1 out of 8.

1/8 = 0.125

P(5) = 12.5%

Answer:

12.5%

Step-by-step explanation:

Spinner divided in parts = 8

Number 5 = 1

P(5) = 12.5%

Answer:

0.13

Step-by-step explanation:

First let's find the probability of finding the first species or the second species:

P(A or B) = P(A) + P(B) - P(A and B)

P(A or B) = 0.61 + 0.08 - 0.28

P(A or B) = 0.41

Then, to find the probability of finding one or another but not both, we just need the symmetric difference of the events, that is: P(A or B) - P(A and B):

P(A or B) - P(A and B) = 0.41 - 0.28 = 0.13

Complete Question

Suppose the weight of Chipotle burritos follows a normal distribution with mean of 450 grams, and variance of 100 grams2 . Define a random variable to be the weight of a randomly chosen burrito.

(a) What is the probability that a Chipotle burrito weighs less than 445 grams? (3 points)

(b) 20% of Chipotle burritos weigh more than what weight

Answer:

a

   [tex]P(X < 445 )= 0.3085[/tex]

b

  [tex]k = 458.42[/tex]

Step-by-step explanation:

From question we are told that

     The population mean is [tex]\mu = 450 \ g[/tex]

      The variance is [tex]var = 100 \ g^2[/tex]

      The  consider weight is  [tex]x = 445 \ g[/tex]

The  standard deviation is mathematically represented as

     [tex]\sigma = \sqrt{var}[/tex]

substituting values

     [tex]\sigma = \sqrt{ 100}[/tex]

     [tex]\sigma = 10[/tex]

Given that weight of Chipotle burritos follows a normal distribution the  the probability that a Chipotle burrito weighs less than x grams is mathematically represented as

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

Where  [tex]\frac{X - \mu }{\sigma }[/tex] is  equal to z (the standardized values of the random number X )

So

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

substituting values

     [tex]P(X < 445 ) = P (Z < \frac{445 - 450 }{10} )[/tex]

      [tex]P(X < 445 ) = P (Z <-0.5 )[/tex]

Now from the normal distribution table  the value for [tex]P (Z <-0.5 )[/tex]  is  

      [tex]P(X < 445 ) = P (Z <-0.5 ) = 0.3085[/tex]

=>   [tex]P(X < 445 )= 0.3085[/tex]

Let the  probability  of the Chipotle burritos weighting more that k be 20% so  

       [tex]P(X > k ) = P ( \frac{X - \mu }{\sigma } > \frac{k - \mu }{\sigma } ) = 0.2[/tex]

=>    [tex]P (Z> \frac{k - \mu }{\sigma } ) = 0.2[/tex]

=>    [tex]P (Z> \frac{k - 450}{10 } ) = 0.2[/tex]

From the normal distribution table the value of z  for  [tex]P (Z> \frac{k - \mu }{\sigma } ) = 0.2[/tex] is  

    [tex]z = 0.8416[/tex]

=>   [tex]\frac{k - 450}{10 } = 0.8416[/tex]

=>   [tex]k = 458.42[/tex]

Answer:

Graphed below.

Step-by-step explanation:

The slope of the line is -1/3.

The y-intercept is at (0, 2).

The x-intercept is at (6, 0).

Answer:

B

Step-by-step explanation:

The range is all values of y. Y goes from -1 to 1. Please mark brainliest.

Answer:

see below

Step-by-step explanation:

The domain of the function is the possible x values

The domain is all real values since x can be any number

The range of the function is the possible y value

The values of y go from -1 to 1 so

-1 ≤y≤1

Answer:

x=35

Step-by-step explanation:

Answer:

B. 533in²

Step-by-step explanation:

Step 1: Find the area of the rectangle

A = lw

A = (29)13

A = 377

Step 2: Find the leg of the triangle

13 + 11 = 24

Step 3: Find the area of the triangle

A = 1/2bh

A = 1/2(24)(13)

A = 12(13)

A = 156

Step 3: Add the areas of the 2 figures together

377 + 156 = 533

Answer:

900.

Step-by-step explanation:

66 tens are 660.

and 24 tens are 240.

so, It is 900!