What is the difference between 4.5 and - 3.75

The area enclosed by the line y = x - 1 and the parabola \(y^2 = 2x + 6\) can be determined by evaluating the definite integral of \((x - 1) - (2x + 6)^{0.5\) from x = -1 to x = 3.

The area enclosed by the line y=x-1 and the parabola \(y^2=2x+6\) is a region bounded by these two curves. To find this area, we need to determine the points where the line and the parabola intersect.

The first step is to set the equations equal to each other: \(x-1 = (2x+6)^{0.5\). By squaring both sides, we get \(x^2 - 2x - 7 = 0\). Solving this quadratic equation, we find x = -1 and x = 3 as the x-coordinates of the intersection points.

Next, we substitute these x-values back into either equation to find the corresponding y-values. For the line, when x = -1, y = -2, and when x = 3, y = 2. For the parabola, we have y = ±\((2x+6)^{0.5\). Substituting x = -1 and x = 3, we get y = ±2 and y = ±4, respectively.

Now, we have four points of intersection: (-1, -2), (-1, 2), (3, -4), and (3, 4). To calculate the area enclosed, we integrate the difference between the line and the parabola from x = -1 to x = 3. The integral of (x - 1) - (2x + 6)^0.5 with respect to x gives us the desired area.

In conclusion, the area enclosed by the line y = x - 1 and the parabola y^2 = 2x + 6 can be found by integrating (x - 1) -\((2x+6)^{0.5\) from x = -1 to x = 3. This will give us the numerical value of the area.

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Answer:

623, 529

Step-by-step explanation:

Let's rewrite the problem: 6.8% of what number is 42,400?

Represent the problem as an equation.

0.068 * n = 42,400 (6.8% = 0.068)

0.068/0.068 = 0

42,400/0.068 = 623,529.4117647059

Round this value to the nearest whole number to receive: 623, 529

Answer:

617647

Step-by-step explanation:

6.8% = 42 400

Divide 42 400 by 6.8 to get 1%

1%     = 6176.47058823529....

Multiply this by 100 to get 100%

100% = 617647.0588

We can check it by doing 617647.0588 * 6.8% = 42 400

Nearest whole number= 617647

Answer:

the answer is 10

Step-by-step explanation:

i got it right on edge 2020

Answer:

EF= 10

Step-by-step explanation:

Answer:

oh sorry it's cuboid ithought I said square

Step-by-step explanation:

Using trigonometric function the value of x is 51.3°.

What is trigonometric function?

The functions of an angle in a triangle are known as trigonometric functions, commonly referred to as circular functions. In other words, these trig functions provide the relationship between a triangle's angles and sides. There are five fundamental trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.

Here Let us take the given right triangle as ABC.

∠A = x , ∠B = 90° and AB = 25 , AC= 40

Now using Cosine ratio then

Cos  A = \(\frac{adjacent}{hypotenuse}\)

=> cos x = \(\frac{25}{40}\)

=> cos x = \(\frac{5}{8}\)

=> x = \(cos^{-1}\frac{5}{8}\)

=> x = 51.3°

Hence the value of x is 51.3°.

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Answer:

∠B

∠Y

Step-by-step explanation:

we know that

In the right triangle ABC

----> opposite side to angle B divided by the adjacent side to angle B

substitute the values

Remember that

If two triangles are similar, then the corresponding sides are proportional and the corresponding angles are congruent

so

∠A=∠W

∠B=∠Y

∠C=∠Z

Answer:x=4 y=2

Step-by-step explanation:

Add the equations in order to solve for the first variable. Plug this value into the other equations in order to solve for the remaining variables.

Point Form:

(4,2)

Equation Form:

x=4, y=2

The local minimum values are 1, and the local maximum values are 0.

To find the local maximum and minimum values of the function M(t) = 6t³ + 9t² - 20t + 6 using the First Derivative Test, we follow these steps:

Find the derivative of the function:

M'(t) = 18t² + 18t - 20.

Set the derivative equal to zero and solve for t to find the critical points:

18t² + 18t - 20 = 0.

Using the quadratic formula, we get:

t = (-18 ± √(18² - 4(18)(-20))) / (2(18))

t = (-18 ± √(324 + 1440)) / 36

t = (-18 ± √1764) / 36

t = (-18 ± 42) / 36.

Simplifying, we have two possible critical points:

t1 = (-18 + 42) / 36 = 24 / 36 = 2/3

t2 = (-18 - 42) / 36 = -60 / 36 = -5/3.

Analyze the intervals formed by the critical points and the endpoints of the domain:

We consider the intervals (-∞, -5/3), (-5/3, 2/3), and (2/3, +∞).

Test the sign of the derivative in each interval:

For (-∞, -5/3), we choose a test value t = -2. Plugging this value into M'(t), we get M'(-2) = 18(-2)² + 18(-2) - 20 = 72 - 36 - 20 = 16, which is positive.

For (-5/3, 2/3), we choose a test value t = 0. Plugging this value into M'(t), we get M'(0) = 18(0)² + 18(0) - 20 = -20, which is negative.

For (2/3, +∞), we choose a test value t = 1. Plugging this value into M'(t), we get M'(1) = 18(1)² + 18(1) - 20 = 16, which is positive.

Apply the First Derivative Test:

Since the derivative changes from positive to negative at t = 0, this indicates a local maximum. And since the derivative changes from negative to positive at t = 1, this indicates a local minimum.

Therefore, the local minimum value is at t = 1, and the local maximum value is at t = 0.

The local minimum values are 1, and the local maximum values are 0.

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Answer:

16.5

Step-by-step explanation:

Answer:

33/2

Step-by-step explanation:

Answer:

2\(x^3\) - 7\(x^2\) + 8x -3

Step-by-step explanation:

To multiply a binomial (2 terms) by a trinomial (3 terms):

Multiply the first term of the binomial by the each term of the trinomial.

Multiply the second term of the binomial by each term of the trinomial.

Combine the expressions and simplify.

(2x-3)*(\(x^2\)-2x+1)

(2x * \(x^2\)) + (2x * -2x) + (2x * 1)

(2\(x^3\)) + (-4\(x^2\)) + (2x)

(2x-3) * (\(x^2\)-2x+1)

(-3 * \(x^2\)) + (-3 * -2x) + (-3 * 1)

(-3\(x^2\)) + (6x) + (-3)

[2\(x^3\) + -4\(x^2\) + 2x] + [-3\(x^2\) + 6x + -3]

2\(x^3\) - 7\(x^2\) + 8x -3

give me brainliest please

Answer:

This means that your score is lower than her score.

Answer:

Step-by-step explanation:

5.40/12= 0.45

6.72/16=0.42

Answer:

The 16 pack

Step-by-step explanation:

Pack 1: $5.40 for 12

Pack 2: $6.72 for 16

Therefore the 16 pack is the better buy because you purchase an extra 4 sodas for $0.03 less.

Therefore,Total patients with pneumonia or bronchitis = 25 + 30 - 10= 45Thus, there are a total of 45 patients diagnosed with pneumonia or bronchitis or both.

Among 50 patients admitted to a clinic, 25 are diagnosed with pneumonia, 30 with bronchitis, and 10 with both pneumonia and bronchitis. The number of patients with pneumonia or bronchitis (or both) can be determined as follows:Let A denote the number of patients diagnosed with pneumonia and B denote the number of patients diagnosed with bronchitis.

According to the inclusion-exclusion principle, the total number of patients with pneumonia or bronchitis is given by:Total patients with pneumonia or bronchitis = \(A + B - (A ∩ B)\)where A ∩ B represents the intersection of the sets A and B.In this case, A = 25, B = 30, and A ∩ B = 10.

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Suppose the average yearly salary of an individual whose final degree is a​ master's is ​$ 41 thousand less than twice that of an individual. the average yearly salary of an individual with each of these final degrees is: $50,000 (Bachelor's degree) and $59,000 (Master's degree )

Let x represent the average yearly salary of an individual with the bachelor's degree

Let (2x-41000) represent the   average yearly salary of an individual with the master's degree

Let the sum of these salaries = 109000

So, x + (2x-41000) = 109000

Simplify and solve:

3x = 109000 + 41,000

3x = 150,000

Divide both side by 3x

x= 150,000/3

x = 50,000 (Bachelor's degree)

So,

(2x-41000)

= 2(50,000) - 41,000

=100,000 - 41,000

= $59,000 (Master's degree )

Therefore the average yearly salary is $50,000 (Bachelor's degree) and $59,000 (Master's degree )

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On adding the integers we get:

The collection of whole numbers and negative numbers is known as an integer in mathematics. Integers, like whole numbers, do not include the fractional portion. Integers can therefore be defined as numbers that can be positive, negative, or zero but not as fractions.

For, (-78) + (98)

Step 1: Locate the first number, which is -78.

Step 2: Locate the second number, which is 98.

Step 3: Add the two numbers together by starting with the first number and counting up or down according to the sign of the second number. In this case, 98 is positive, so we count up 98 from -78.

Step 4: The answer is 20

Similarly, solving for the rest of the sub-parts we get:

2. 45+23=68

3. 67+56=123

4. 98 + (-73)=25

5. -971+237= -734

Therefore, On adding the integers we get:

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According to the given percentages, 18% of the students at the orientation are male arts majors.

The statement correctly calculates that 60% of the students at the orientation are men and 30% are arts majors.

To determine the percentage of students who are male arts majors, we multiply these two percentages together: 60% x 30% = 18%. Therefore, 18% of the students at the orientation are male arts majors.

This calculation follows the principles of probability, where the intersection of two events (being a male and being an arts major) is determined by multiplying the probabilities of each event occurring individually.

In this case, it results in 18% of the students meeting both criteria.


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Question - Sixty percent of the students at an orientation are men and 30% of the students at the orientation are arts majors. Therefore, 60% X 30% = 18% of the students at the orientation are male arts majors.

R

cor_matrix <- cor(college[, c("apps", "accept", "enroll", "top10perc", "outstate")])

In this code, we directly calculate the correlation matrix by passing the subset of variables (`apps`, `accept`, `enroll`, `top10perc`, and `outstate`) from the `college` data frame to the `cor()` function. The resulting correlation matrix is stored in the `cor_matrix` variable.

Based on the given hints, you can subset the variables into their own data frame, check if the data frame includes all the variables correctly, and then run the `cor()` command to calculate the correlation matrix for those variables.

Here's an example code snippet that demonstrates this process:

R

# Subset the variables into a new data frame

subcollege <- data.frame(

 apps = college$apps,

 accept = college$accept,

 enroll = college$enroll,

 top10perc = college$top10perc,

 outstate = college$outstate

)

# Check the structure of the new data frame

str(subcollege)

# Calculate the correlation matrix

cor_matrix <- cor(subcollege)

# Print the correlation matrix

print(cor_matrix)

In this example, `college` refers to the original data frame that contains all the variables.

We create a new data frame called `subcollege` and extract the desired variables (`apps`, `accept`, `enroll`, `top10perc`, and `outstate`) from the `college` data frame using the `$` operator. The `str()` function is used to inspect the structure of the new data frame.

Finally, we calculate the correlation matrix using the `cor()` function and store the result in the `cor_matrix` variable. We print the correlation matrix using `print(cor_matrix)`.

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The probability that it rains at least one day this weekend is \($\frac{a}{b}$\),  so the value of a+b is given as 107.

Calculating the likelihood of experiments happening is one of the branches of mathematics known as probability. We can determine everything from the likelihood of receiving heads or tails when tossing a coin to the likelihood of making a research blunder, for instance, using a probability.

Let x be the probability that it rains on Sunday given that it doesn't rain on Saturday then we have,

3/5x + 2/5(2x) = 3/10

7/5x = 3/10

x = 3/14.

Therefore, the probability that it doesn't rain on either day is,

\($\left(1-\dfrac{3}{14}\right)\left(\dfrac{3}{5}\right)=\dfrac{33}{70}$\)

Therefore, the probability that rains on at least one of the days is

\($1-\dfrac{33}{70}=\dfrac{37}{70}$\),

so adding up the 2 numbers, we have,

37 + 70 = 107.

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Complete question;

There is a 40% chance of rain on Saturday and a 30% chance of rain on Sunday. However, it is twice as likely to rain on Sunday if it rains on Saturday than if it does not rain on Saturday. The probability that it rains at least one day this weekend is \($\frac{a}{b}$\), where a and b are relatively prime positive integers. Find a+b.

Answer: 5.7 (rounded)

Step-by-step explanation: The formula to find the diagonal of a square is \(\sqrt{2\) * a, where a is a side length on the square. Since we are solving for half of a diagonal, we use this formula and divide our result by two. We start by multiplying root 2 by 8 and we get 11.31371, next we divide by two and we get 5.656855 which is 5.7 when rounded.

Answer: 57 R3

‎‎‎‎‎‎‎‎‎‎‎‎‎ ‎‎ ‎

Answer:

57 R 3

Step-by-step explanation:

6 goes into 34 5 times with 4 extra, pull down the 5, and 6 goes into 45 7 times with 3 extra. So the answer is 57 R 3.

Yes, your friend is not correct about the stem and leaf plot.

The stem and leaf plot made by your friend is:

Stem | Leaves

2 | 5, 6

4 | 2, 4, 7

5 | 0, 1, 5, 5

Key : 4 | 2 = 42

When the data points from these are taken, we have :

25 , 26 , 42 , 44 , 47 , 50, 51, 55, 55

This is the same as the data provided of :

51, 25, 47, 42, 55, 26, 50, 44, 55

So, your friend's stem and leaf plot is indeed correct.

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The grower should plant 59 trees per acre to maximize her harvest, and the maximum harvest she can achieve is approximately 3540 bushels.

To determine the number of trees the plum grower should plant per acre to maximize her harvest, we can set up an equation and use calculus to find the optimal solution. Let's denote the number of additional trees planted as x.

The yield of each tree can be represented by the equation:

Yield = 126 - 2x

The total yield per acre is then given by:

Total Yield = (26 + x) * (126 - 2x)

To maximize the harvest, we need to find the value of x that maximizes the total yield. We can achieve this by finding the maximum point of the quadratic equation representing the total yield.

Differentiating the equation with respect to x and setting it equal to zero, we can find the critical point:

d(Total Yield)/dx = -4x + 252 - 2(26 + x) = 0

Simplifying the equation, we get:

-4x + 252 - 52 - 2x = 0

-6x + 200 = 0

x = 200/6

x ≈ 33.33

Since we cannot have a fraction of a tree, the grower should plant 33 additional trees per acre to maximize her harvest. This gives a total of 26 + 33 = 59 trees per acre.

To find the maximum harvest, we substitute the value of x into the equation for the total yield:

Total Yield = (26 + 33) * (126 - 2 * 33)

Total Yield ≈ 59 * 60

Total Yield ≈ 3540 bushels

Therefore, the grower should plant 59 trees per acre to maximize her harvest, and the maximum harvest she can achieve is approximately 3540 bushels.

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Answer:

there are 8 for any four leg creatures : there are 4 for a human

Step-by-step explanation:

Answer:

i think 6 hours so sry if i am wrong good luck

Step-by-step explanation:

The approximate length of a basketball court, which is 94 feet, in meters can be calculated by converting the given measurement using the conversion factor we can find the approximate length is 28.658 meters.

We know that 1 meter ≈ 3.28 feet.

Dividing 94 feet by 3.28, we get approximately 28.658 meters. Therefore, the approximate length of a basketball court that measures 94 feet is approximately 28.658 meters.

To convert feet to meters, we multiply the number of feet by the conversion factor of 1 meter ≈ 3.28 feet. In this case, we multiply 94 feet by the reciprocal of 3.28 (which is approximately 0.3048), resulting in approximately 28.658 meters.

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Answer:

y=-3/2+3

Step-by-step explanation:

so you have to solve for y

Answer:

y - 1 = (-2/3)(x + 9)

Step-by-step explanation:

Here you are given a point on a line and the slope of the line.  You'll need to apply the "point-slope" formula

y - k = m(x - h) (Memorize this)

Then m = slope = -2/3, h = -9 and k = 1.

Making the appropriate substitutions, we get:

y - 1 = (-2/3)(x + 9)

Answer:

1. 16 teachers  2. 8 tutor  3. 6 teachers

Step-by-step explanation:

Given:

The vertices of a right triangle are:

\((-3,4),(3,4),(3,-4)\)

To find:

The length of the hypotenuse of the given right triangle.

Solution:

Let the vertices of the right triangle are \(A(-3,4),B(3,4),C(3,-4)\).

The distance formula is:

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Using distance formula, we get

\(AB=\sqrt{(3-(-3))^2+(4-4)^2}\)

\(AB=\sqrt{(3+3)^2+(0)^2}\)

\(AB=\sqrt{(6)^2+0}\)

\(AB=\sqrt{36}\)

\(AB=6\)

Similarly,

\(BC=\sqrt{(3-3)^2+(-4-4)^2}\)

\(BC=\sqrt{(0)^2+(-8)^2}\)

\(BC=\sqrt{64}\)

\(BC=8\)

And,

\(AC=\sqrt{(3-(-3))^2+(-4-4)^2}\)

\(AC=\sqrt{(6)^2+(-8)^2}\)

\(AC=\sqrt{36+64}\)

\(AC=\sqrt{100}\)

\(AC=10\)

Now, taking sum of squares of two smaller sides, we get

\(AB^2+BC^2=6^2+8^2\)

\(AB^2+BC^2=36+64\)

\(AB^2+BC^2=100\)

\(AB^2+BC^2=AC^2\)

By the definition of the Pythagoras theorem, AC is the hypotenuse of the given triangle.

Therefore, the length of the hypotenuse is 10 units.