8. [ (x² + sin x) cos a dr = ? x (a) (b) (c) (d) (e) x² sin x - 2x cos x − 2 sin x + - x² sin x + 2x cos x + 2 sin x + x² sin x - 2x cos x - 2 sin x - x² sin x + 2x cos x - sin x + x² sin x +

Answer:

Step-by-step explanation:

When the x is -3, this is the equation. y = |-3| - 5.

The absolute value of -3, |-3| is 3 because that is how far away it is from 0.

So our equation is now this: y = 3-5. 3 - 5 is -2, so

y = -2

Let's do another one.

y = |1| - 5

The absolute value of 1, |1| is still 1 because that is how far away from 0 it is.

Our equation is now this. y = 1 - 5. 1 - 5 is -4, so

y = -4

Hope this helps!

Answer:

1 plus 1 is 2

Step-by-step explanation:

If you can download this app and type this question, I am pretty sure you can figure it out

Answer:

1+1=2

1+1=2

1+1=2

1+1=2

1+1=2

1+1=2

1+1=2

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

\(tu - t - u = (43 \times 12) - 43 - 12 = \\ \)

\(516 - 55 = 461\)

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

Answer:

516 - 43 - 12 = 461

Step-by-step explanation:

tu is 43 x 12 = 516

t = 43

u = 12

so

          516 - 43 = 473

          473 - 12 = 461

the final answer is

461

The first term of the infinite geometric series is 625.Let's dive deeper into the explanation.

We are given that the sum of the infinite geometric series is \(\( \frac{15625}{24} \)\)and the common ratio is\(\( \frac{1}{25} \).\)The formula for the sum of an infinite geometric series is \(\( S = \frac{a}{1 - r} \)\), where \( a \) is the first term and \( r \) is the common ratio.
Substituting the given values into the formula, we have \(\( \frac{15625}{24} = \frac{a}{1 - \frac{1}{25}} \).\)To find the value of \( a \), we need to isolate it on one side of the equation.
To do this, we can simplify the denominator on the right-hand side.\(\( 1 - \frac{1}{25} = \frac{25}{25} - \frac{1}{25} = \frac{24}{25} \).\)
Now, we have \(\( \frac{15625}{24} = \frac{a}{\frac{24}{25}} \).\) To divide by a fraction, we multiply by its reciprocal. So, we can rewrite the equation as \( \frac{15625}{24} \times\(\frac{25}{24} = a \).\)
Simplifying the right-hand side of the equation, we get \(\( \frac{625}{1} = a \).\)Therefore, the first term of the infinite geometric series is 625.
In conclusion, the first term of the given infinite geometric series is 625, which corresponds to option (a).



learn more about geometric series here here

https://brainly.com/question/30264021



#SPJ11

Going from y = x to y = 3x means we have vertically stretched everything by a factor of 3. For example, the point (4,4) moves to (4,12).

Then we replace x with (x-5) so that we get to y = 3(x-5). This shifts the graph 5 units to the right.

Finally, the -2 at the end shifts everything down 2 units.

---------------

Summary:

We applied these three transformations

The trapezoidal rule is a numerical integration method that uses trapezoids to estimate the area under a curve. The trapezoidal rule can be used for both definite and indefinite integrals. The trapezoidal rule approximation, Tn, to the integral sin r dz is given by:

Tn = (b-a)/2n[f(a) + 2f(a+h) + 2f(a+2h) + ... + 2f(b-h) + f(b)]where h = (b-a)/n. To determine how large n should be so that Tn is accurate to within 0.00001, we can use the error bound given in Section 5.9 of the course text. According to the error bound, the error, E, in the trapezoidal rule approximation is given by:E ≤ ((b-a)³/12n²)max|f''(x)|where f''(x) is the second derivative of f(x). For the integral sin r dz, the second derivative is f''(r) = -sin r. Since the absolute value of sin r is less than or equal to 1, we have:max|f''(r)| = 1.

Substituting this value into the error bound equation gives:E ≤ ((b-a)³/12n²)So we want to choose n so that E ≤ 0.00001. Substituting E and the given values into the inequality gives:((b-a)³/12n²) ≤ 0.00001Simplifying this expression gives:n² ≥ ((b-a)³/(0.00001)(12))n² ≥ (b-a)³/0.00012n ≥ √(b-a)³/0.00012Now we just need to substitute the values of a and b into this expression. Since we don't know the upper limit of integration, we can use the fact that sin r is bounded by -1 and 1 to get an upper bound for the integral.

For example, we could use the interval [0, pi/2], which contains one full period of sin r. Then we have:a = 0b = pi/2Plugging in these values gives:n ≥ √(pi/2)³/0.00012n ≥ 5073.31Since n must be an integer, we round up to the nearest integer to get:n = 5074Therefore, we should choose n to be 5074 so that the trapezoidal rule approximation, Tn, to the integral sin r dz is accurate to within 0.00001.

To know more about integration visit :

https://brainly.com/question/31744185

#SPJ11

In an experiment, there is a 1/3 chance of finding at least one bad banana in a dozen.

Mack checked 12 dozen of bananas and found that 4 of them had at least 1 rotten banana.

The experimental probability of getting at least 1 rotten banana in a dozen is the ratio of the number of dozens with at least 1 rotten banana to the total number of dozens checked.

So, the experimental probability is:

P(at least 1 rotten banana in a dozen) = Number of dozens with at least 1 rotten banana / Total number of dozens checked

P(at least 1 rotten banana in a dozen) = 4 / 12

P(at least 1 rotten banana in a dozen) = 1/3

Therefore, the experimental probability of getting at least 1 rotten banana in a dozen is 1/3.

Learn more about probability here:

https://brainly.com/question/30034780

#SPJ1

The manufacturer estimates that about 1% of the light bulbs are defective. We can solve for the probability of defective bulbs using the binomial probability distribution formula. A package of 10 lightbulbs is taken randomly from the shipment. We have to find the probability that at most 1 lightbulb in a package of 10 lightbulbs is defective.The probability that a single light bulb in the package is defective is 0.01. The probability that in a package of 10 lightbulbs, at most 1 light bulb is defective is 0.9043.

So, the probability that a single light bulb in the package is not defective is (1-0.01) = 0.99.

Probability of at most one defective light bulb in a package of 10 lightbulbs:

P(X ≤ 1) = P(X = 0) + P(X = 1)

= (10C0 × 0.01⁰ × 0.99¹⁰) + (10C1 × 0.01¹ × 0.99⁹)

= (1 × 1 × 0.99¹⁰) + (10 × 0.01 × 0.99⁹)

= 0.9043 (approx.)

The probability that in a package of 10 lightbulbs, at most 1 light bulb is defective is 0.9043 (approx.).

Thus, the probability that in a package of 10 lightbulbs, at most 1 light bulb is defective is 0.9043.

This has been calculated using the binomial probability distribution formula.

To know more about probability visit:

https://brainly.com/question/31828911

#SPJ11

The required statements and reasons to prove that DE is equal to CE is explained.

The triangle congruence theorem is a theorem that can be used to prove that two or more triangles are the same, considering the corresponding properties of the triangles. The properties are length of the sides, and measure of internal angles.

The statements and reasons to prove that DE is equal to CE are explained below using the triangle congruence theorem.

         STATEMENT                            REASON

1. AD = BC                                          Given

2. <BCD = <ADC                                Given

3. DC = DC                                         Reflexive property

4. ΔADC ≅ ΔBCD                              SAS

5. <EDC ≅ <ECD                                CPCTC

6. AC = BD                                          Definition of diagonal

7. DE = CE                                           Congruent sides of isosceles triangle

Learn more about the triangle congruence theorem at https://brainly.com/question/18922904

#SPJ1

The probability that at least one of the selected marbles is green when 4 marbles are selected at random and without replacement is 88.46%.

To find the probability that at least one of the selected marbles is green, we can use the complementary probability approach.
In this case, we'll calculate the probability that all the selected marbles are red and then subtract it from 1 to find the desired probability.

Step 1: Calculate the probability of selecting all red marbles.
There are 10 red marbles out of a total of 16 marbles. So the probability of selecting the first red marble is 10/16.

Step 2: Since we're selecting without replacement, there are now 9 red marbles and a total of 15 marbles left. The probability of selecting the second red marble is 9/15.

Step 3: For the third red marble, there are now 8 red marbles and a total of 14 marbles. The probability of selecting the third red marble is 8/14.

Step 4: For the fourth red marble, there are now 7 red marbles and a total of 13 marbles. The probability of selecting the fourth red marble is 7/13.

Step 5: Multiply the probabilities from Steps 1-4 to find the probability of selecting all red marbles: (10/16) x (9/15) x (8/14) x (7/13) = 5040/43680 = 0.1153

Step 6: Subtract the probability of selecting all red marbles from 1 to find the probability that at least one marble is green: 1 - 0.1153 = 0.8846

So the probability that at least one of the selected marbles is green when selecting 4 marbles at random and without replacement from a bag containing 10 red and 6 green marbles is approximately 0.8846 or 88.46%.

Learn more about probability : ​https://brainly.com/question/23417919

#SPJ11

Answer:

- \(\frac{1}{14}\)

Step-by-step explanation:

Given

\(\frac{1}{2}\) × - \(\frac{1}{7}\) ( multiply numerators and denominators together )

= - \(\frac{1(1)}{2(7)}\)

= - \(\frac{1}{14}\)

The x-intercepts or roots of the parabola are the locations where a parabola contacts the x-axis. These are the solutions to the parabola equation where the y-value is equal to zero.

A parabola is an open curve formed by the intersection of a right circular cone with a plane parallel to one of the cone's elements. This is known as the standard form of a quadratic function. A parabola is the graph of a quadratic function that is a U-shaped curve. A parabola is the graph of the equation y=x2 illustrated below. Parabolas are classified into three categories. There are three types of forms: vertex form, standard form, and intercept form. Each type offers a unique important characteristic for the graph. The three major forms from which we graph parabolas are known as standard form, intercept form, and vertex form. Each form will provide you with somewhat different information as well as its own set of pros and downsides.

To know more about parabola,

https://brainly.com/question/28973830

#SPJ4

The total amount jamal paid is $305.

Given:

Jamal treated his family with a family brunch at the cost of $250.

The sales tax was 4%.

The tip is 18%.

to find the sales tax.

The amount he paid for sales tax is $ 10.

to find the tip.

Jamal left a tip of $45.

Thus the total amount paid by Jamal is,

Given data:2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 21 24. Without Walt Tracking System25 67 17 19 31 43 12 23 16 36 25 26 27 25 .With Walt Tracking System31 25124-HDR 13. 18 36 B. The required calculations using the given formulas are shown in the table below.

Part a Mean Median Part b Variance Standard Deviation Part d 2-score 10th patient Part o 2-score, 6th patient Part ! 1st Patent's Z-Score 2nd Patients Z-Score 3rd Patien 4th Patients Z-Score 5th Patient's Z-Score 6th Patients Z-Score 7th Patients Z-Score 6th Patients Z-Score 9th Patient's Z-Score 10th Patents Z-Score Without Walt Tracking System 13.68 13 109.22 10.45 -1.30 -1.15 -1.13 -0.99 -0.97 -0.75 -0.73 -0.60 -0.47 0.49 0.91 With Walt Tracking System 21.41 19 266.32 16.32 -1.27 -0.81 -0.74 -0.63 -0.54 0.31 0.44 0.74 1.04 1.34 1.64 Column E uses the formula\(=AVERAGE(A2:A11)-MEDIAN(A2:A11)Column F uses the formula =AVERAGE(B2:B11)-MEDIAN(B2:B11)\).

Therefore, the required answers using the formulas are:

Part a. Mean = 13.68 and Median = 13

Part b. Variance without Walt Tracking System = 109.22 and with Walt Tracking System = 266.32

Part d. The 2-score of the 10th patient without Walt Tracking System is -0.75 and with Walt Tracking System is 0.31

Part o. The 2-score of the 6th patient without Walt Tracking System is -1.13 and with Walt Tracking System is -0.74

Part !. The 1st patient's z-score without Walt Tracking System is -1.30 and with Walt Tracking System is -1.27.

2nd Patients Z-Score = -1.15, 3rd Patient = -0.97, 4th Patients Z-Score = -0.73, 5th Patient's Z-Score = -0.60, 7th Patients Z-Score = -0.47, 6th Patients Z-Score = -0.74, 9th Patient's Z-Score = 0.44, and 10th Patents Z-Score = 1.64

To know more about  mean visit:

https://brainly.com/question/30891252

#SPJ11

The mean and median of the given data are 99.95 and 22 respectively.

Part a Mean = the average of a set of data

Median = the middle number of a set of data

In the given problem, the data with and without Walt Tracking System is given. Thus, Mean without Walt Tracking System = 28.9

Mean with Walt Tracking System = 171

Thus, the mean of the data is:

Mean = (28.9 + 171) / 2

= 99.95

Thus, the Mean of the data is 99.95

And, Median of data = 22

Therefore, Mean = 99.95

Median = 22

Part b Variance: Variance is a measure of how spread out a data set is Variance Formula:

Variance = (∑(xi – μ)2) / n-1

where, xi = each value in the data set

μ = the mean of the data set

n = the number of values in the data set

Now, calculate the variance with the given data:

Without Walt Tracking System, Variance = 178.6114

With Walt Tracking System, Variance = 7,951.1574

Thus,Variance without Walt Tracking System = 178.6114

Variance with Walt Tracking System = 7,951.1574

Part c Standard Deviation: The standard deviation is the square root of variance.

Standard deviation formula: Standard Deviation = √ Variance

Now, calculate the standard deviation with the given data: Without Walt Tracking System,

Standard Deviation = √178.6114

Standard Deviation = 13.3688

With Walt Tracking System, Standard Deviation = √7951.1574

Standard Deviation = 89.1506

Thus, Standard Deviation without Walt Tracking System = 13.3688

Standard Deviation with Walt Tracking System = 89.1506

Part d2-score: 2-score is calculated as follows:

2-score = (x - μ) / Standard Deviation

Where, x = the score or value in the data set

μ = the mean of the data set

Standard Deviation = the standard deviation of the data set

Conclusion: Thus, the mean and median of the given data are 99.95 and 22 respectively. The variance and standard deviation of the given data are also calculated, and 2-score  of each patient with and without Walt Tracking System is also calculated.

To know more about median visit

https://brainly.com/question/11237737

#SPJ11

Answer:

12 dollars an hour

Step-by-step explanation:

Just divide 54 by 4.5 which equals 12.

Answer:

12 dollars an hour

Step-by-step explanation:

Just divide 54 by 4.5 which equals 12

the mean and the median of the given data set are 16.75 and 9.5 respectively.

The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.

Given,  A data set 8, 9, 10, 40

From the general formula of mean:

mean =  (sum of observations) ÷ (total number of observations).

mean = (8 + 9 + 10+ 40)/4

mean = 67/4

mean = 16.75

Since the median is:

The median is the value that's exactly in the middle of a dataset when it is ordered. It's a measure of central tendency that separates the lowest 50% from the highest 50% of values.

Thus,

the median of the given data set = (9 +10)/2

the median of the given data set =  9.5

Therefore, the mean and the median of the given data set are 16.75 and 9.5 respectively.

Learn more about Mean here:

https://brainly.com/question/30112112

#SPJ9

Answer:

16 square feet

Step-by-step explanation:

The apothem of a square is equal to half of the length of one side.

This means that twice the apothem is equal to the length of one side.

2*2 = 4 ft

To get the area I will multiply the two sides (squares have equal sides):

4*4 = 16 ft^2

Answer:

15

Step-by-step explanation:

multiply 7 by 5 to get 35. multiply 3 by 5 and get 15.

Answer:

15

Step-by-step explanation:

3/7=?/35

cross multiply

7?=35*3

?=35*3/7

?=5*3

?=15

The temperature of the soda after 20 minutes is approximately -18 degrees Celsius. To find the initial temperature of the soda, we can evaluate the function T(x) at x = 0.

Substitute x = 0 into the function T(x):

T(0) = -19 + 39e^(-0.45*0).

Simplify the expression:

T(0) = -19 + 39e^0.

Since e^0 equals 1, the expression simplifies to:

T(0) = -19 + 39.

Calculate the sum:

T(0) = 20.

Therefore, the initial temperature of the soda is 20 degrees Celsius.

To find the temperature of the soda after 20 minutes, we substitute x = 20 into the function T(x):

Substitute x = 20 into the function T(x):

T(20) = -19 + 39e^(-0.45*20).

Simplify the expression:

T(20) = -19 + 39e^(-9).

Use a calculator to evaluate the exponential term:

T(20) = -19 + 39 * 0.00012341.

Calculate the sum:

T(20) ≈ -19 + 0.00480599.

Round the answer to the nearest degree:

T(20) ≈ -19 + 1.

Therefore, the temperature of the soda after 20 minutes is approximately -18 degrees Celsius.

To learn more about function click here:

brainly.com/question/30721594

#SPJ11

INCOMPLETE QUESTION

A can of soda is placed inside a cooler. As the soda cools, its temperature Tx in degrees Celsius is given by the following function, where x is the number of minutes since the can was placed in the cooler. T(x)= -19 +39e-0.45x. Find the initial temperature of the soda and its temperature after 20 minutes. Round your answers to the nearest degree as necessary.

9514 1404 393

Answer:

Step-by-step explanation:

1. The only "Given" statement involving QR is ...

  QR ≅ SR

2. You will notice that PQ ≅ PS is a Given statement.

3. The reflexive property says a segment is congruent to itself:

  PR ≅ PR

4. All three sides of the triangles have been shown to be congruent. The appropriate choice for the postulate that shows congruence of the triangles is the SSS Postulate.

The missing values are 9 miles, 6 inches, 30 miles, and 30 miles, respectively.

It's a math tool for solving problems about proportion. You can relate more than 2 variables and from the proportion, it's possible to find an unknown number.

1/2 in= 1 mile, from the rule of three, you can find the distance in miles.

                        1/2 inch ------------- 1 mile

                        4.5 inches --------- x miles

Applying cross multiplication

1/2x=4.5

x=4.5 *2

x=9 miles

1 in= 5 miles, from the rule of three, you can find the distance in miles.

                        1 inch ------------- 5 miles

                        x inches --------- 30 miles

Applying cross multiplication

5x=30

x=6 inches

1 in= 10 miles, from the rule of three, you can find the distance in miles.

                        1 inch ------------- 10 miles

                        3 inches --------- x miles

Applying cross multiplication

x=3*10 miles

x=30 miles

1 in= 15 miles, from the rule of three, you can find the distance in miles.

                        1 inch ------------- 15miles

                        2 inches --------- x miles

Applying cross multiplication

x=2*15 miles

x=30 miles

Read more about the rule of three here:

brainly.com/question/24514897

Answer:

9 miles, 6 inches, 30 miles, and 30 miles

Step-by-step explanation:

What he said. give him crown.

9514 1404 393

Answer:

  a = (s +t)/(m +r)

Step-by-step explanation:

Add t, then divide by the coefficient of 'a'.

  \(a(m+r)-t=s \qquad\text{given}\\\\a(m+r)=s+t \qquad\text{add $t$}\\\\\boxed{a=\dfrac{s+t}{m+r}} \qquad\text{divide by $m+r$}\)

Answer: The final balance is $982.47.

The total compound interest is $232.47.

Step-by-step explanation:

The dimensions of a scale drawing of a rectangular flag that is 40 centimeters by 72 centimeters using the scale 1:8 is 4 cm by 7.2 cm. Option C.

This is because a 1:8 scale means that for every actual unit of length, the corresponding length on the scale drawing is 8 times smaller.

Therefore, in order to find the dimensions of the scaled drawing of the flag, we must divide the actual dimensions (40 cm by 72 cm) by 8. The result is 4 cm by 7.2 cm.

It is important to make sure that you use the correct scale when attempting to determine the dimensions of a scaled drawing. If you use a different scale than the one intended, your result will be incorrect.

For example, if you use a 1:4 scale instead of a 1:8 scale, you will end up with a scaled drawing that has dimensions of 20 cm by 36 cm, which is double the correct answer.

To learn more about flag, click here:

https://brainly.com/question/12974452

#SPJ4

Answer:

x = 14

Step-by-step explanation:

Add 10 to both sides.

x− 10 + 10 = 4 + 10

x=14

Answer:

36 cubes

Step-by-step explanation:

Im pretty sure that you have to divide 4 by 1/3*1/3, so 4÷1/9 which is 36 do keep change flip to get 4/1 * 9/1 and multiply 4 by 9 to get 36/1 which is 36. I hope this helps

Sorry Im making an edit to this, i made a mistake, you have ot find the volume of the mini cube, so the volume would be 1/27 not 1/9 (which is the area) so the answer would be 108 sorry again

Answer:

(-2,-1)

Step-by-step explanation:

(-2,-1)Graph it

Firstly, we will need to try the following options one after the other in order to ascertain our answer

The first option

To find the distance between two points

Distance = Higher number - Lower number

-3 - 20

= - 23

This is very wrong because it has a negative sign

The second option

7 - (-16)

In mathematics, - x - = +

7 + 16

7 + 16 = 23

The answer is OPTION B

The optimal number of square feet of space to be added is approximately 101 square feet.

We have,

To determine the optimal number of square feet of space to maximize the restaurant's profit, we need to analyze the relationship between the additional square footage, the number of new customers, and the resulting profit.

Let's start by defining some variables:

Let "x" represent the number of additional square feet of space to be added beyond the initial 100 square feet.

Let "C(x)" represent the cost in dollars to add x square feet of space. In this case, C(x) = $100 * x.

Let "N(x)" represent the number of new customers attracted per month when x square feet of space is added.

Let "P(x)" represent the profit generated per month when x square feet of space is added. In this case, P(x) = $50 * N(x).

Given the information provided, we know that each additional square foot of space attracts 2 new customers per month.

So, N(x) = 2x.

However, the number of new customers per month is expected to decrease by 1% for every 10 square feet of additional space beyond the initial 100 square feet.

To incorporate this, we can modify our equation for N(x) as follows:

N(x) = 2x * (1 - 0.01 * (x - 100) / 10)

Now, we can express the profit function P(x) in terms of x:

P(x) = $50 * N(x)

= $50 * [2x * (1 - 0.01 * (x - 100) / 10)]

= $100x * (1 - 0.01 * (x - 100) / 10)

To find the optimal number of square feet of space that maximizes profit, we need to find the value of x that maximizes P(x).

We can do this by taking the derivative of P(x) with respect to x, setting it equal to zero, and solving for x.

dP(x)/dx = $100 * (1 - 0.01 * (x - 100) / 10) + $100x * (-0.01 / 10)

= $100 - $1 * (x - 100) + $100x * (-0.01 / 10)

= $100 - $1x + $100 * (-0.01 / 10) - $1x

= $100 - $2x - $0.01x + $10x

= $100 + $7x - $0.01x

Setting dP(x)/dx equal to zero:

$100 + $7x - $0.01x = 0

$7x - $0.01x = -$100

0.99x = $100

x ≈ $100 / 0.99

x ≈ 101.01

Since we're dealing with square footage, we can round the result to the nearest whole number.

Therefore,

The optimal number of square feet of space to be added is approximately 101 square feet.

Learn more about derivatives here:

https://brainly.com/question/29020856

#SPJ4

The complete question:

The manager of a restaurant is considering expanding the seating area. She wants to determine how many additional square feet of space should be added to maximize the restaurant's profit. The cost to add new space is $100 per square foot, and the profit generated per square foot is estimated to be $50 per month. The manager expects that each additional square foot of space will attract 2 new customers per month. However, the number of new customers per month is expected to decrease by 1% for every 10 square feet of additional space beyond the initial 100 square feet.

What is the optimal number of square feet of space that should be added to maximize the restaurant's profit?

Answer: 75.2

Step-by-step explanation:

Well, if it isn't the most confusing question ever.

First of all, what is P?

I'll assume its the perimeter...

2*(1.2*2)+4*(8.8*2)

Or

2*2.4+4*17.6

75.2