The approximation of I = S. cos (x2 + 5) dx using simple Simpson's rule is:

Answer:

x = 59

Step-by-step explanation:

x−2=57

Add 2 to each side

x−2+2=57+2

x = 59

Answer:

X=59

Step-by-step explanation:

x−2=57

to isolate X you would have to add 2 to each side. x-2(+2)=x and 57(+2)=59

Answer:

x=-2/k

Step-by-step explanation:

Answer:

There’s this thing photomath it can give an answer

Step-by-step explanation:

The probability that their hospital stay is greater than 6 days is approximately 0.6985.

(a) To find the probability that their hospital stay is from 5 to 6 days, we need to calculate the z-scores for both values using the formula z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.
For 5 days: z = (5 - 7.37) / 2.60 = -0.9
For 6 days: z = (6 - 7.37) / 2.60 = -0.52

Next, we need to find the corresponding probabilities using a z-table or a calculator. From the z-table, we find that the probability of z being less than -0.9 is 0.1841, and the probability of z being less than -0.52 is 0.3015.

To find the probability of the hospital stay being between 5 and 6 days, we subtract the probability of z being less than -0.9 from the probability of z being less than -0.52:
P(5 ≤ X ≤ 6) = P(X ≤ 6) - P(X ≤ 5)

= 0.3015 - 0.1841

= 0.1174
Therefore, the probability that their hospital stay is from 5 to 6 days is approximately 0.1174.

(b) To find the probability that their hospital stay is greater than 6 days, we need to find the probability of z being greater than -0.52.

From the z-table, we find that the probability of z being less than -0.52 is 0.3015.

Therefore, the probability that their hospital stay is greater than 6 days is approximately

1 - 0.3015 = 0.6985,

rounded to five decimal places.

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Answer:

Yes

Step-by-step explanation:

Yes because if you insert -39 for x and 42 for y then your equation is:

42 = -39 + 81

If you were to solve this equation it would be true.

With the volume of water poured at rate 8 m³/minute, when the height of water is 5 meters, the water will be rising at rate 0.23 m/minute.

Let:

r = radius of water at an instant

h = level of water at an instant

Then,  due to similarity property:

r/h =  4/6 = 2/3

Or,

r = 2/3 . h

The volume of the poured water is:

V = 1/3. πr².h

Substitute r = 2/3 . h into the formula:

V = 1/3. π(2/3. h)².h

V = 4/27. πh³

Take the derivative with respect to t:

dV/dt = 4/27 . 3πh² . dh/dt

dV/dt = 4/9 . πh² . dh/dt

Substitute: dV/dt = 8 m³/minute and h = 5 m:

8 = 4/9 .  π .5² . dh/dt

dh/dt = 0.23 m/minute.

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The probability of drawing a white ball on the second draw, without replacing the first ball, is 8/13.

To solve this problem, we need to use conditional probability.

The probability of drawing a white ball on the first draw is 8/13 (since there are 8 white balls and 13 total balls in the urn).

If a white ball is drawn on the first draw, then there will be 7 white balls and 5 black balls left in the urn. So the probability of drawing a white ball on the second draw, given that a white ball was drawn on the first draw, is 7/12.

If a black ball is drawn on the first draw, then there will be 8 white balls and 4 black balls left in the urn. So the probability of drawing a white ball on the second draw, given that a black ball was drawn on the first draw, is 8/12.

Now we can use the law of total probability to find the overall probability of drawing a white ball on the second draw:

P(white on second draw) = P(white on first draw) * P(white on second draw | white on first draw) + P(black on first draw) * P(white on second draw | black on first draw)
= (8/13) * (7/12) + (5/13) * (8/12)
= 56/156 + 40/156
= 96/156
= 8/13

Therefore, the probability of drawing a white ball on the second draw, without replacing the first ball, is 8/13.

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Based on the constructed difference table, the next term of this sequence 6, −2, −3, 7, 32, 76, . . . is 143.

In Mathematics, a sequence can be defined as a series of real and natural numbers in which each term or list of elements are ordered in a particular order and repetitions are allowed.

In Mathematics, a difference table can be defined as a type of table that is constructed by subtracting adjacent elements (entries) in a sequence, and then repeating the process with next those elements (entries).

Number            Difference from previous             Difference of differences

6

-2                               -8                                          

-3                               -1                                                7            

7                                 10                                              11            4

32                               25                                             15            4

76                              44                                               19            4

143                            67                                                23           4

First column: -2 - 6 = -8; -3 - (-2) = 1; ....... 143 - 76 = 67.

Second column: -1 - (-8) = 7; 10 - (-1) = 11; .... 67 - 44 = 23.

Third column: 11 - 7 = 4; 15 - 11 = 4 .... 23 - 19 = 4.

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Answer:

124

Step-by-step explanation:

The sum of interior angles in a triangle is equal to 180:

m<R + m<S + m<T = 180

11x + 3 + x + 15 + 2x + 8 = 180 add like terms

14x + 26 = 180 subtract 26 from both sides

14x = 154 divide both sides by 14

x = 11 to find m<R replace x with 11

11*11 + 3 = 124

Apply angle sum property

\(\\ \rm\rightarrowtail 11x+3+x+15+2x+8=180\)

\(\\ \rm\rightarrowtail 14x+26=180\)

\(\\ \rm\rightarrowtail 14x=154\)

\(\\ \rm\rightarrowtail x=11\)

Therefore, The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming the null hypothesis is true. If the p-value is less than the significance level, reject the null hypothesis; otherwise, fail to reject it.

To find the p-value from the t statistic on TI-84, you will need to perform a hypothesis test. Here are the steps:1. Enter your data into the calculator and choose the appropriate test.2. Calculate the t statistic by dividing the sample mean by the standard error.3. Determine the degrees of freedom. This is n-1 for a one-sample t-test or n1+n2-2 for a two-sample t-test. 4. Use the t-distribution table to find the critical value for your test.5. Calculate the p-value using the t-distribution function on the calculator.6. Compare the p-value to the significance level (usually 0.05) to determine whether to reject or fail to reject the null hypothesis.7.

Therefore, The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming the null hypothesis is true. If the p-value is less than the significance level, reject the null hypothesis; otherwise, fail to reject it.

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Nicole can rent the facility for 5 hours. Nicole can rent the facility for 5 hours and still receive a deposit refund if there is no damage.

To calculate the number of hours Nicole can rent the facility for and still receive a deposit refund, we need to consider the cost of renting the facility and the refund policy.

The facility requires a $74 deposit, and half of the deposit is refunded if there is no damage. So Nicole will receive a refund of $74/2 = $37 if there is no damage.

The cost per hour to rent the facility is $57.

Let's assume Nicole can rent the facility for x hours. The total cost of renting the facility would be the deposit plus the cost per hour multiplied by the number of hours:

Total cost = $74 + $57x

For Nicole to receive a refund, the total cost should not exceed her budget of $379. So we can set up the following equation:

$74 + $57x ≤ $379

Subtracting $74 from both sides of the equation, we get:

$57x ≤ $305

Dividing both sides of the equation by $57, we find:

x ≤ $305 / $57

x ≤ 5.35

Since the number of hours cannot be a fraction, Nicole can rent the facility for a maximum of 5 hours.

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Let the length of the wall be l.

The width is 4ft less than its length.

Therefore, the width is l - 4.

The wall is rectangular, therefore

Hence,

Hence, the length of the wall is 14 feet

Answer:

dependeria de que position estan las lineas

The closest value to 6.28 is 10 cubic feet. Therefore, the correct answer is: A. 10 cubic feet

To calculate the approximate volume of concrete that Angel will use, we need to determine the volume of the slab.

The slab is in the shape of a cylinder, and its volume can be calculated using the formula:

V = πr²h

where V is the volume, r is the radius, and h is the height of the cylinder.

From the given information, we know that the slab is 6 inches tall. However, we need to convert the dimensions to the same unit before proceeding with the calculations. Let's convert the dimensions to feet:

Height = 6 inches = 6/12 feet = 0.5 feet

Radius = 2 feet

Now we can substitute the values into the formula to find the volume:

V = π(2²)(0.5)

 = π(4)(0.5)

 = 2π cubic feet

Approximating π to 3.14, we can calculate the volume:

V ≈ 2(3.14)

 ≈ 6.28 cubic feet

Therefore, the approximate volume of concrete that Angel will use is 6.28 cubic feet.

Looking at the given answer choices, the closest value to 6.28 is 10 cubic feet. Therefore, the correct answer is:

A. 10 cubic feet

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Answer: 318 km²

Let's find the areas of the triangles

Formula: base x height / 2

9 x 6 = 54

54/2 = 27

Multiply by 2 since there are two triangles (I know, we already got the areas from 9 x 6)

27 x 2 = 54

Now let's try to find the areas of all the rectangular sides

Formula: length x width

9 x 11 = 99

8 x 11 = 88

7 x 11 = 77

99 + 88 + 77 = 264

Add up all the areas

264 + 54 = 318

Answer:

Yes

Step-by-step explanation:

It is a random sample of students because they are just random people that Jackie is asking, its not only people in on grade, or only people on the basketball team.

Step-by-step explanation:

my instagram account bdq.frk follow please

Donald will have $210 at the end of the year

Given that the principal amount Donald is having at the start of the year is $200 and the rate of interest per annum is 5%.

Since the interest is not compounded, at the end of the year the amount of interest he will be earning = 0.05 x 200 = $10 (since interest is not compounded)

From, the above analysis, Donald is earning $10 of interest per annum from $200.

Now, Total money Donald will be having in 1 year = principal amount + interest earned money = $200 + $10 = $210

From the above solution, we can conclude that Donals is having $210 in total for one year.

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To solve the compound inequality we need to solve each inequality, then we have:

Now we need to remember that the word OR means the union of the solution sets for each inequality then the solution is:

Answer:

Tank A fills up faster.

Step-by-step explanation:

Tank A is y = 13x

Tank B is y = 11x

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We can write our linear equation as:

y + 1 = (4/3)*(x + 1)

or

y - 3 = (4/3)*(x - 2)

If a linear equation passes through two points (x₁, y₁) and (x₂, y₂), then the slope is:

a = (y₂ - y₁)/(x₂ - x₁).

Here the line passes through (-1, -1) and (2, 3), so the slope is:

a = (3 + 1)/(2 + 1) = 4/3

Now, if a line has a slope a and passes through a point (x₁, y₁),then we can write that line as:

y - y₁ = a*(x - x₁)

So with our two points, we can write our line as:

y + 1 = (4/3)*(x + 1)

y - 3 = (4/3)*(x - 2)

The correct option is the first one.

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The average annual increase in fuel price: This is a continuous random variable as it can take on any value within a range.

A car's speed at different times: This is a continuous random variable as well since a car's speed can vary continuously. The number of cars passing through a toll booth in an hour: This is a discrete random variable as it can only take on whole number values.

The number of phone calls made in a day: This is also a discrete random variable as it can only take on whole number values.  The salaries of employees in an office: This is a continuous random variable as salaries can take on any value within a range.
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Answer:

x = 1

Step-by-step explanation:

2x + 3y = 20

2x + 3(10-4x) = 20

2x + 30 - 12x = 20

combine like terms

-10x + 30 =  20

        -30      -30

-10x = -10

divide both sides by -10

x = 1

Hope this Helps!!!

The solution of the linear equations y = 10 - 4x and 2x + 3y = 20 will be (1, 6).

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equations are given below.

y = 10 - 4x              ...1

2x + 3y = 20          ...2

Substitute equation 1 in equation 2, then we have

2x + 3(10 - 4x) = 20

2x + 30 - 12x = 20

10x = 10

x = 1

Then the value of the variable 'y' will be given as,

y = 10 - 4(1)

y = 10 - 4

y = 6

The solution of the linear equations y = 10 - 4x and 2x + 3y = 20 will be (1, 6).

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Using a logistic growth model with an initial population of 27 blackberry plants, an 80% growth rate per month, and a carrying capacity of 120 plants, the estimated number of plants after 4 months is 97.

The logistic growth model is a mathematical model used to describe population growth when there are limiting factors such as available resources or space. It assumes that the population growth rate is proportional to both the current population and the difference between the carrying capacity and the current population.

In this case, the initial population is 27 blackberry plants, and the growth rate is 80% per month. The carrying capacity of the yard is 120 plants, meaning it can only sustain that many blackberry plants. Using the logistic growth model, we can estimate the population after 4 months.

To calculate the estimated number of plants after 4 months, we can use the logistic growth formula:

N(t) = K / (1 + ((K - N0) / N0) *\(e^(-rt)\))

where N(t) is the population at time t, K is the carrying capacity, N0 is the initial population, r is the growth rate, and e is the base of the natural logarithm.

Plugging in the given values, we have N0 = 27, K = 120, r = 0.8, and t = 4. Solving the equation, we find that N(4) is approximately 97. Therefore, the estimated number of blackberry plants after 4 months is 97.

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a. 30.15% of the employees cost more than $1,500 per year for dental expenses.

b. 65.49% of the employees cost between $1,500 and $2,000 per year for dental expenses.

c. The percentage of employees who did not have any dental expense is 0.1%.

d. The cost of the 10% of employees who incurred the highest dental expenses is $1,796.4 (approx).

a. Probability that dental expenses cost more than $1,500 per year

So, we have to find the probability of employees costing more than $1,500 per year for dental expenses.

Let X be the amount paid per year for dental expenses. X follows normal distribution with mean μ = $1,280 and standard deviation σ = $420.

We have to find P(X > $1,500).Here, z = (X - μ) / σ = ($1,500 - $1,280) / $420 = 0.52P(X > $1,500) = P(Z > 0.52) = 0.3015 or 30.15%.

Therefore, 30.15% of the employees cost more than $1,500 per year for dental expenses.

b. Probability that dental expenses cost between $1,500 and $2,000 per year

Now we have to find the probability of the employees who cost between $1,500 and $2,000 per year for dental expenses.

Let X be the amount paid per year for dental expenses. X follows a normal distribution with mean μ = $1,280 and standard deviation σ = $420.

We have to find P($1,500 < X < $2,000).Here, z1 = (X1 - μ) / σ = ($1,500 - $1,280) / $420 = 0.52z2 = (X2 - μ) / σ = ($2,000 - $1,280) / $420 = 1.71P(0.52 < Z < 1.71) = P(Z < 1.71) - P(Z < 0.52) = 0.9564 - 0.3015 = 0.6549 or 65.49%.

Therefore, 65.49% of the employees cost between $1,500 and $2,000 per year for dental expenses.

c. Probability of employees having no dental expenses.Now we have to find the probability of employees having no dental expenses.

Let X be the amount paid per year for dental expenses. X follows normal distribution with mean μ = $1,280 and standard deviation σ = $420. We have to find P(X = 0).

Here, z = (X - μ) / σ = (0 - $1,280) / $420 = -3.05Now, P(X = 0) is P(X < 0.5), which is same as P(Z < -3.05 + 0.0013) = P(Z < -3.05) = 0.001 or 0.1%.

Therefore, the percentage of employees who did not have any dental expense is 0.1%.

d. Cost of the 10% of employees who incurred the highest dental expenses

We have to find the dental expenses of the 10% of employees who incurred the highest dental expenses.

Let X be the amount paid per year for dental expenses. X follows a normal distribution with mean μ = $1,280 and standard deviation σ = $420.

We have to find the 90th percentile, z0.9.

Using standard normal table, we can find the z-score corresponding to 0.9, which is 1.28.

The amount, X corresponding to z0.9 is:X = μ + z0.9 σ = $1,280 + 1.28 × $420 = $1,796.4

Therefore, the cost of the 10% of employees who incurred the highest dental expenses is $1,796.4 (approx).

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Answer:

x = 4/√2

y = 4/√2

Step-by-step explanation:

Hypotenuse = 4

θ = 45°

x = Opposite side

y = Adjacent Side

a) Solving for x = Opposite side

We solve using Trigonometry function of Sine

sin θ = Opposite/Hypotenuse

sin 45 = x/4

Cross Multiply

x = sin 45 × 4

Note that : sin 45 = 1/√2

x = 1/√2 × 4

x = 4/√2

b) Solving for y

We solve using Trigonometric function of Cosine

cos θ = Adjacent/Hypotenuse

cos 45 = x/4

Cross Multiply

x = cos 45 × 4

Note that : cos 45 = 1/√2

x = 1/√2 × 4

y = 4/√2

Answer:

\((244 - n)n \\ n = 3 \\ (244 - 3) \times 3 \\ = (241) \times 3 \\ = 723\)

Answer:

(not my answer but) its 268

Step-by-step explanation:

Answer:

1. y=2x+4

2. y=x

3. y=-1/2x+1

4. y=-x+1

Step-by-step explanation:

the formula for these are y=mx+b. Your slope would be m and y intercept would be b. so y=2x+4 would mean that the slope is 2 and y intercept is 4. you can find the points by checking what points are on the blue line.

Answer:

63

Step-by-step explanation:

Using the triangle PAN we know that PA = 18 m and PN = 42m

And we can see that Triangle DOR is bigger than Triangle PAN

Therefore it the same shape but bigger.

Hence we can do 27/18=1.5

Then, 42 x 1.5= 63

Hence x = 63