If u(x) = -2x² +3 and V(x) =
X
what is the range of (u.v)(x)?

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Work Shown:

Before we can use derivatives, we need to find the value of s when (x,y) = (15,20)

s^2 = x^2+y^2

s^2 = 15^2+20^2

s^2 = 225+400

s^2 = 625

s = sqrt(625)

s = 25

-----------

Now we can apply the derivative to both sides to get the following.  Don't forget to use the chain rule.

s^2 = x^2 + y^2

d/dt[s^2] = d/dt[x^2 + y^2]

d/dt[s^2] = d/dt[x^2] + d/dt[y^2]

2s*ds/dt = 2x*dx/dt + 2y*dy/dt

2(25)*ds/dt = 2(15)*5 + 2(20)*(10)

50*ds/dt = 150 + 400

50*ds/dt = 550

ds/dt = 550/50

ds/dt = 11

-----------

Side note: The information t = 40 is never used. It's just extra info.

The true and false statements from the given options are classified below -

A rational number is a number that can be expressed in the form of p/q, where [p] and [q] of two integers and denominator [q] cannot be zero.

Given are the sentences describing the properties of rational numbers.

The statements which are true from the given ones are as follows -

The statements which are false from the given ones are as follows -

Therefore, the true and false statements from the given options are classified above.

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The value of k is 18.

If x + 2 is a factor of f(x) = x^3 + 5x + k, it means that when x = -2, the expression f(x) becomes zero.

Substituting x = -2 into f(x), we have:

f(-2) = (-2)³ + 5(-2) + k

= -8 - 10 + k

= -18 + k

Since f(-2) should equal zero, we have:

-18 + k = 0

k = 18

Therefore, the value of k is 18.

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Answer:

it is the domain

Step-by-step explanation:

because if you put 5x on the other side it will be a -5

Answer:

Step-by-step explanation:

Typically yes you need to know

Mean

Median

Mode

and Range

Mean = average, add all numbers then divide by how many

Median = midpoint, middle number.  Be sure to list numbers from small to large if there are 2 middle numbers (this happens when there are an even amount), take the average of the 2 middle numbers

Mode = numbers that occurs the most in the list of numbers

Range = This is the largest number minus the smallest number.  

Answer:

34

Step-by-step explanation:

4r² + 3s² - rs ← substitute r = - 1, s = 3 into the expression

= 4(- 1)² + 3(3)² - (- 1)(3)

= 4(1) + 3(9) - (- 3)

= 4 + 27 + 3

= 34

Example: (2x - 4) x=7 so (2x (x=7) - 4) =18

The linear Diophantine equation k = x'x+y'y has integer solutions, say x' = x and y' = y

Linear Diophantine equations are a special class of equations in which we are looking for integer solutions instead of real ones. These equations play a vital role in number theory, cryptography, and computer science.

The given linear Diophantine equation is ax+by=c, where a, b, and c are integers, and x, y are unknowns that we are looking for. Suppose there is a solution to this equation, i.e., we can find integers x and y that satisfy this equation. Then, we can say that 'c' must satisfy a specific condition.

To understand this condition, we need to introduce the concept of the greatest common divisor (GCD) of two integers. The GCD of two integers a and b is the largest positive integer that divides both a and b without leaving a remainder. We denote the GCD of a and b by (a, b).

Now, the condition that 'c' must satisfy is given by the following theorem.

Theorem: A necessary and sufficient condition for the linear Diophantine equation ax+by=c to have an integer solution (x, y) is that (a, b) divides c.

Suppose there is an integer solution (x, y) to the given equation. Then, we can write:

c = ax+by

Let d be the GCD of a and b, i.e., d = (a, b). We can express a and b in terms of d as follows:

a = dm and b = dn, where m and n are integers.

Substituting these values of a and b in the given equation, we get:

c = dmx+dny

Dividing both sides by d, we get:

(c/d) = mx+ny

Since m, n, x, and y are integers, (c/d) must also be an integer. This means that (a, b) divides c, i.e., (a, b) | c.

Conversely, suppose (a, b) | c. Then, we can write c = k(a, b) for some integer k. Now, we need to show that there exist integers x and y that satisfy the equation ax+by=c.

Since (a, b) divides a and b, we can write:

a = (a, b)x' and b = (a, b)y'

where x' and y' are integers. Substituting these values of a and b in the given equation, we get:

k(a, b) = (a, b)x'x+(a, b)y'y

Dividing both sides by (a, b), we get:

k = x'x+y'y

This is a linear Diophantine equation in x' and y' with constant term k. It is a well-known fact that such equations have integer solutions if and only if (k, (a, b)) = d, where d = GCD(k, (a, b)).

But we know that (k, (a, b)) = (k, c), since (a, b) divides c. Hence, we have:

d = (k, c) = (x'x+y'y, k(a, b)) = (x'x+y'y, ka, kb)

But d divides ka and kb, since it is a common divisor of a and b. Hence, d divides x'x+y'y.

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Complete Question:

Suppose a,b, and c are integers and that there is a solution to the linear Diophantine equation ax+by=c, that is, suppose there are integers x and y that satisfy the equation ax+by=c. what condition must c satisfy in terms of a and b?

We write the linear function as f(x)=3.5x+1 for the graph.

Linear function means a linear equation. As per given statement, we need to write an equation for straight line. We are given four-point in the XY coordinate.

We use the formula line passes through two points. The required function

should be in the form f(x) =mx+b or y=mx+b

given points are (0,1) (1,4.5) , (-1,-2.5) (-2,-6)

slope of line passes through first two points is=m= (y₂-y₁)/(x₂-x₁)= 3.5

slop of last two points is = m= 3.5

hence, four points lies in the same straight line

the equation of line, y= 3.5x+b

as the line passes through (-2,-6)

                                  -6=3.5×(-2)+b

                                 b=1, b is a constant

         hence, the linear function is f(x)=y=3.5x+1

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By answering the presented question, we may conclude that Therefore, triangle the length of the base AB is approximately 20.88 centimeters.

A triangle is a closed, double-symmetrical shape composed of three line segments known as sides that intersect at three places known as vertices. Triangles are distinguished by their sides and angles. Triangles can be equilateral (all factions equal), isosceles, or scalene based on their sides. Triangles are classified as acute (all angles are fewer than 90 degrees), good (one angle is equal to 90 degrees), or orbicular (all angles are higher than 90 degrees) (all angles greater than 90 degrees). The region of a triangle can be calculated using the formula A = (1/2)bh, where an is the neighbourhood, b is the triangle's base, and h is the triangle's height.

the length of the base AB,

Area = (1/2) * base * height

\(CB^2 = CD^2 + BD^2\\9^2 = x^2 + (AB - x)^2\\81 = x^2 + (AB^2 - 2ABx + x^2)\\AB^2 - 2ABx + 2x^2 = 81\\\)

We also know that the area of the triangle is:

\(46 = (1/2) * AB * CB\\46 = (1/2) * AB * \sqrt(x^2 + 81)\\Now we can solve for AB in terms of x:AB = (2 * 46) / \sqrt(x^2 + 81)\\AB = 92 / \sqrt(x^2 + 81)\\(92 / \sqrt(x^2 + 81))^2 - 2(92 / \sqrt(x^2 + 81))x + 2x^2 = 81\\\)

\(8464 / (x^2 + 81) - (184x) /sqrt(x^2 + 81) + 2x^2 = 81\\8464 - 184x(x^2 + 81) + 2x^2(x^2 + 81) * sqrt(x^2 + 81) = 81(x^2 + 81)\\2x^4 - 181x^2 + 7743 = 0\\x^2 = (181 + \sqrt(181^2 - 427743)) / (2*2)\\x^2 = (181 + sqrt(129961)) / 4\\x^2 = (181 + 361) / 4\\x^2 = 90^2 / 4\\x = 45\sqrt(2) / 2\\\)

\(AB = 92 / \sqrt(x^2 + 81)\\AB = 92 / \sqrt((45sqrt(2) / 2)^2 + 81)\\AB = 92 / \sqrt(4050)\\AB ≈ 20.88 cm\\\)

Therefore, the length of the base AB is approximately 20.88 centimeters.

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A boutique owner needs to sell $1,200 in clothing each week. This week, she is within $125 of her goal. The variable in the equation is

A variable is a quantity that could change depending on the circumstances of an experiment or mathematical problem.

Typically, a variable is denoted by a single letter. The general symbols for variables most frequently used are the letters x, y, and z.

In the context of the problem, the boutique owner wants to make $1,200 in clothing each week. This amount in made by the number of items sold as this is added to get to the amount the boutique owner is targeting

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The coordinates of the point on the directed line segment from (-7, 9) to (3, -1) that partitions the segment into a ratio of 2 to 3 are (-3, 5).

To find the coordinates of the point that divides the directed line segment from (-7, 9) to (3, -1) into a ratio of 2 to 3, we can use the section formula.

Let's label the coordinates of the desired point as (x, y). According to the section formula, the x-coordinate of the point is given by:

x = (2 * 3 + 3 * (-7)) / (2 + 3) = (6 - 21) / 5 = -15 / 5 = -3

Similarly, the y-coordinate of the point is given by:

y = (2 * (-1) + 3 * 9) / (2 + 3) = (-2 + 27) / 5 = 25 / 5 = 5

Therefore, the coordinates of the point that divides the line segment in a ratio of 2 to 3 are (-3, 5).

To understand this conceptually, consider the line segment as a distance from the starting point (-7, 9) to the ending point (3, -1). The ratio of 2 to 3 means that the desired point is two-thirds of the way from the starting point and one-third of the way from the ending point. By calculating the x and y coordinates using the section formula, we find that the desired point is located at (-3, 5).

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According to the problem the length of the label is 121 over 28 cm.

A label is a piece of text, image, or other object used to identify and describe an item, product, or object. Labels are typically used to provide information about an item, such as its size, manufacturer, contents, or use. Labels can also be used for labeling items for sale, for labeling items for storage, or for labeling items for shipment.

The length of the label can be calculated using the circumference formula, C = π x d, where C is the circumference and d is the diameter.
The diameter of the can is 2 and three fourths cm, so the circumference is 22 over 7 x 2 and three fourths, which is equal to 121 over 7.
To get the length of the label, divide 121 over 7 by the number of labels needed - in this case, 4.
So, the length of the label is 121 over 28 cm.

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Answer: hii :)

1.  2x-8=11x-10 = 2/9

2. 6x-6=3x+1 = 7/3

3. 1/2x+4=1/3x+1 = -18

4. -2/5x+1/3=1/2x+1/4 = 5/54

5. I dont know the answer to <3

Step-by-step explanation:

Hopefully this helps you,

Sorry for being late on the question.

- Matthew

1/2% is read as 1.2 out of one hundred

so divide 100/1.2 which the answer would be 83.33333333 or 83.3

The P-value is between 0.025 and 0.05. and t = -1.85

On the SAT exam a total of 25 minutes is allotted for students to answer 20 math questions without the use of a calculator.

Therefore tests the hypotheses:

\(H_0\) : μ = 25 versus Ha: μ < 25,

where μ = the true mean amount of time needed by students at this school to complete this portion of the exam.

The alternative hypothesis is:

\(H_1:\mu < 25\)

The test statistic is given by:

\(t=\frac{x-\mu}{\frac{s}{\sqrt{n} } }\)

The parameters are:

the values of the parameters are:

x = 23.5 , \(\mu=25\) , s = 4.8, n = 35

Plug all the values in above formula of t- statistic is:

\(t = \frac{23.5-25}{\frac{4.8}{\sqrt{35} } }\)

t = -1.85

Using a t-distribution , with a left-tailed test, as we are testing if the mean is less than a value and 35 - 1 = 34 df, the p-value is of 0.0365.

t = –1.85; the P-value is between 0.025 and 0.05.

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Answer:

14 mins

Step-by-step explanation:

2/6 = x/42

6x=84

x=14

According to the concept of algebraic expression and arithmetic, the correct answers are A) Number of adults = N - 25. B) Number of adults when N = 124: 124 - 25 = 99

A) Let's denote the number of children as N. Since there are 25 fewer adults than children, the number of adults can be expressed as N - 25.

B) If there are 124 children, we substitute N with 124 in the expression from part A. Thus, the number of adults would be 124 - 25 = 99.

To arrive at these answers, we used the given information that there are "N" children and 25 fewer adults than children. By substituting the value of N, we determined the number of adults in terms of N and then calculated the specific number of adults when N is equal to 124.

Note: The given question is incomplete. The complete question is:

Some adults and children are watching a musical. there are 'N' number of children. There are 25 fewer adults than children.

A) find the number of adults in terms of 'N'.

B) if there are 124 children how many adults are there?​

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Answer:

35.733

Step-by-step explanation:

have a common denominator then do the math

Answer:

give me tha answer please

The height of the building, using similar triangles, is given by:

36 feet.

Similar triangles are two triangles that share these two features, which are listed as follows:

The second bullet point, regarding proportional side lengths, is especially relevant in the context of this problem, as a proportional relationship is built to find the height h of the building.

From the similar triangles, the equivalent side lengths are presented as follows:

Hence the proportional relationship that models this situation is presented as follows:

3/18 = 6/h.

Applying cross multiplication, the height of the building is obtained as follows:

3h = 18 x 6

h = 6 x 6 (simplifying by 3)

h = 36 feet.

The diagram is given by the image shown at the end of the answer.

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Answer and Step-by-step explanation:

Solution:

Given:

Let A is the event of a person over 50 diagnosed by health service.

B1 is the event that an adult over 50 actually has diabetes.

B2 is the event that an adult over 50 does not have diabetes.

P (B1) = 8% = 0.08

And P (B2) = 1 – P (B1)

                  = 1 – 0.08

                  = 0.92

Correctly diagnose of all persons with diabetes= 95%

P (A/B1) = 0.95

Incorrectly diagnose of all persons without diabetes=   2%

P (A/B2) = 0.02

(a) ) the community health service will diagnose an adult over 50 as having diabetes.

P (B1) P (A/B1) = (0.08) (0.95) = 0.076

P (B2) p (A/B2) = (0.92) (0.02) =0.0184

P (B1) P (A/B1) + P (B2) p (A/B2) =  0.076 + 0.0184

                                                     = 0.0944

(b)  A person over 50 diagnosed by the health service as having diabetes actually has the disease.

By using formula:

P (B1/A) = P (B1) P (A/B1) / P (B1) P(A/B1) + P (B2) P (A/B2)

Put all the given values:

= (0.08) (0.95) / (0.08) (0.95) + (0.92) (0.02)

=0.076 / 0.076 + 0.0184

=0.076 / 0.0944

= 0.8050

Using conditional probability, it is found that there is a:

a) 0.0944 = 9.44% probability that the community health service will diagnose an adult over 50 as having diabetes.

b) 0.8051 = 80.51% probability that a person over 50 diagnosed by the health service as having diabetes actually has the disease.

Conditional Probability

\(P(B|A) = \frac{P(A \cap B)}{P(A)}\)

In which

Item a:

The percentages of a positive test is:

Hence:

\(P(A) = 0.95(0.08) + 0.02(0.92) = 0.0944\)

0.0944 = 9.44% probability that the community health service will diagnose an adult over 50 as having diabetes.

Item b:

From item a, \(P(A) = 0.0944\).

The probability of both a positive test and having the disease is:

\(P(A \cap B) = 0.95(0.08)\)

Hence, the conditional probability is:

\(P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.95(0.08)}{0.0944} = 0.8051\)

0.8051 = 80.51% probability that a person over 50 diagnosed by the health service as having diabetes actually has the disease.

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Answer: x = sqrt(10)

Step-by-step explanation:

You can use the Pythagorean Theorem to solve:

a^2 + b^2 = c^2

You are given one leg (sqrt6) and the hypotenuse (4) and are asked to solve for the other leg (x). Plugging everything into the equation, you get:

(sqrt6)^2 + b^2 = (4)^2

Now, you can solve for b:

b^2 = 4^2 - (sqrt6)^2

b^2 = 16 - 6

b^2 = 10

b = sqrt(10)

In this case, b is equivalent to x, so your answer is x = sqrt(10).

Answer:

x = √10

Step-by-step explanation:

C^2 = A^2 + B^2

4^2 = (√6)^2 + x^2

16 = 6 + x^2

x^2 = 10

x = √10

The correct answer is B. The sample represents a proportion of the population.

A point estimate is a single value used to estimate a population's unknown parameter. The sample proportion (denoted by p), in the context of determining the population proportion, is a widely used point estimate. The sample proportion is determined by dividing the sample's success rate by the sample size.

The sample must be representative of the population for it to be a reliable point estimate of the population proportion. To accurately reflect the proportions of various groups or categories present in the population, the sample should be chosen at random.

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Let:

y1 = altitude of the plane A

y2 = altitude of the plane B

Let's find the equation for plane A:

And for plane B:

So:

Answer:

2 minutes

Using proportions, it is found that the equivalent cost in U.S. dollars per gallon would be of 5.11.

In September 2016, the cost of gasoline in Berlin was around 1.21 euros per liter. Hence, per gallon, that is, per 3.785 liters, we use a rule of three to find the cost.

1.21 euros - 1 liter

x euros - 3.785 liters

Applying cross multiplication:

\(x = 1.21(3.785) = 4.57985\)

Cost of 4.57986 euros per gallon. Since 1 U.S dollar is equivalent to approximately 0.896 euros, we have that:

1 dollar - 0.896 euros

x dollars - 4.57986 euros

Applying cross multiplication again:

\(0.896x = 4.57986\)

\(x = \frac{4.57986}{0.896}\)

\(x = 5.11\)

The equivalent cost in U.S. dollars per gallon would be of 5.11.

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Let f(x) = lnx and g(x) = log₂x. for all 0 < x < 1, f(x) < g(x): True.

In this scenario and exercise, we would determine the corresponding output value for the functions f(x) and g(x) under the given mathematical operation and independent variables.

When x = 1, the output value for f(x) based on the table of values is given by;

f(x) = lnx

f(1) = ln(1).

f(1) = 0.

When x = 2, the output value for f(x) based on the table of values is given by;

f(x) = lnx

f(2) = ln(2).

f(2) = 0.69314718

When x = 1, the output value for g(x) based on the table of values is given by;

g(x) = log₂x

g(1) = log₂(1)

g(1) = 0.

When x = 2, the output value for g(x) based on the table of values is given by;

g(x) = log₂x

g(2) = log₂(2)

g(2) = 1.

In this context, we can logically deduce that the function f(x) is less than function g(x) for all 0 < x < 1.

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Answer:

A.

Step-by-step explanation:

The vertical line test is a way of finding out if a relation is a function.

Graph the relation.

Then imagine a vertical line moving from left to right over the graph of the relation.

If the vertical line intersects at most one point of the graph in any position you place the vertical line, then the relation is a function.

This function passes the vertical test since it never intersects more than one point on the vertical line at a time.

Answer: A.

Answer:

Jim walked 17/28 for miles than Russel

Step-by-step explanation:

First you turn 6/7 and 1/4 to have the same denominators. In that case you find the least common multiple which is 28.

7: 7, 14, 21, 28

4: 4, 8, 12, 16, 20, 24, 28

Next you multiply the top and the bottom of your fraction my the factor you used to get 28 for your denominator

6/7 x 4/4 = 24/28

1/4 x 7/7 = 7/28

Lastly, you subtract the products you got.

24/28 - 7/28 = 17/28