Find the derivative of the function. 3 X° +5 y= (3x + 1)(4x +3) y' = y0 (Simplify your answer.)

Answer:

A

Step-by-step explanation:

Opposite sides are equal

Answer:

1.0

Step-by-step explanation:

We should assume that 4x = x+3 according to the task description.

4x = x+3

3x = 3

x = 1

Answer:

\(f(x) = \frac{(2x - 1)(3x - 2)}{9x - 4} \\ open \: brackets \\ = \frac{(6 {x}^{2} - 4x - 3x + 2) }{9x - 4} \\ = \frac{6 {x}^{2} - 7x + 2 }{9x - 4} \\ let \: x \: be \: 1 \\ f(1) = \frac{(6 - 7 + 2)}{(9 - 4)} \\ = \frac{1}{5} \)

Answer:

Total cost= $39

Step-by-step explanation:

Giving the following information:

At the theater, they sell a bag of popcorn for $5.50 and a drink for $3.75.

First, we will establish the total cost formula:

Total cost= 5.5p + 3.75d

p= number of bags of popcorn

d= number of drinks

Now, for 3 bags and 6 drinks:

Total cost= 5.5*3 + 3.75*6

Total cost= $39

The fractions to show the value of each 9 in the decima 0.999 are 9/10, 9/100, 9/1000.

To write the fraction that shows the value of each 9 in the decimal 0.999, we can use the following method

The digit 9 in the tenths place represents 9/10 or 0.9.

The digit 9 in the hundredths place represents 9/100 or 0.09.

The digit 9 in the thousandths place represents 9/1000 or 0.009.

Thus, the fractions are

0.9 = 9/10

0.09 = 9/100

0.009 = 9/1000

The value of the 9 on the left is related to the value of the 9 in the middle by a factor of 10.

The value of the 9 on the right is related to the value of the 9 in the middle by a factor of 10, so the 9 on the right is one-tenth the value of the 9 in the middle.

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Tripling the linear size of an object multiplies its area by a factor of nine.

When the linear size of an object is tripled, the area of the object is multiplied by 9.

This can be understood by considering the relationship between the linear size and the area of an object. If we assume that the object has a regular shape and the linear size refers to the length of its sides, then the area is directly proportional to the square of the linear size.

Let's denote the initial linear size of the object as L and the initial area as A. When the linear size is tripled, it becomes 3L. According to the square proportionality, the new area (A') can be expressed as:

A' = (3L)^2

A' = 9L^2

Comparing A' with the initial area A, we can see that A' is 9 times larger than A. Therefore, tripling the linear size of an object multiplies its area by 9.

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Answer:

she needs 13 containers because their are 13 pounds and each hold 1 pound

Using the confidence interval, the margin of error is 0.02.

In the given equation we have to find the margin of error.

The resulting confidence interval for the proportion of students applying for college is (0.65,0.69).

Let p = population proportion of students applying for college

P = Sample proportion of students applying for college

ME = margin of error

So the confidence interval

CI = (P-ME, P+ME)

From the given question;

(P-ME, P+ME) = (0.65,0.69)

So lower bound= P-ME = 0.65............................(1)

Upper Bound = P+ME = 0.69............................(2)

Simplifying the Equation 1 and 2

Add equation 1 and 2 we get

2P = 1.34

Divide by 2 on both side we get

P = 0.67

Putting the value of P in the equation 2

P+ME = 0.69

0.67+ME=0.69

Subtract 0.67 on both side we get

ME = 0.02

Hence, the margin of error is 0.02.

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Answer:

12 units

Step-by-step explanation:

The side that is on the opposite side of the triangle as angle C is the side labeled as 12 units in length

The total displacement of the car after 5hrs is 0km.

                s =sf– si

where, s = displacement.

In the given graph, there is the change in distance covered with the time that is:

Thus, the displacement will be 0 km as the final point and initial point are the same.

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The Taylor series expansion of a function is a representation of the function as an infinite sum of terms. It allows us to approximate the function by considering a finite number of terms.

To find the first four nonzero terms of the Taylor series for the function (1+16x)^(1/3), we can use the general formula for the Taylor series expansion of a function centered around a given point. The Taylor series expansion of a function f(x) centered around a point a is given by:

f(x) = f(a) + f'(a)(x - a)/1! + f''(a)(x - a)^2/2! + f'''(a)(x - a)^3/3! + ...

In this case, the function is (1+16x)^(1/3). To find the first four nonzero terms, we need to calculate the function and its derivatives evaluated at the point a = 0. Let's start by finding the first derivative:
f'(x) = (1/3)(1+16x)^(-2/3) * 16

Evaluating the first derivative at a = 0 gives:
f'(0) = (1/3)(1+16*0)^(-2/3) * 16 = (1/3)(1)^(2/3) * 16 = (1/3) * 16 = 16/3
Now, let's find the second derivative: f''(x) = (1/3)(-2/3)(1+16x)^(-5/3) * 16
Evaluating the second derivative at a = 0 gives:

f''(0) = (1/3)(-2/3)(1+16*0)^(-5/3) * 16 = (1/3)(-2/3)(1)^(5/3) * 16 = -(2/3) * 16 = -32/3

Continuing this process, we can find the third and fourth derivatives:

f'''(x) = (1/3)(-2/3)(-5/3)(1+16x)^(-8/3) * 16
f''''(x) = (1/3)(-2/3)(-5/3)(-8/3)(1+16x)^(-11/3) * 16

Evaluating the third derivative at a = 0 gives:

f'''(0) = (1/3)(-2/3)(-5/3)(1+16*0)^(-8/3) * 16 = (1/3)(-2/3)(-5/3)(1)^(8/3) * 16 = (2/3)(5/3) * 16 = 160/9

Evaluating the fourth derivative at a = 0 gives:

f''''(0) = (1/3)(-2/3)(-5/3)(-8/3)(1+16*0)^(-11/3) * 16 = (1/3)(-2/3)(-5/3)(-8/3)(1)^(11/3) * 16 = -(2/3)(5/3)(8/3) * 16 = -640/27

Therefore, the first four nonzero terms of the Taylor series for (1+16x)^(1/3) centered around a = 0 are: (1+16x)^(1/3) ≈ 1 + (16/3)x - (32/3)x^2 + (160/9)x.

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Answer:

Y=10

Step-by-step explanation:

Answer:

D. 1.3

Step-by-step explanation:

5(1.3) = 6.5

Since the value of r is .2 less than b, b would be 1.5

2(1.5) = 3

6.5+3=9.5

The number of square inches of cloth cut from the square will be 1,017.36 square inches. Then the correct option is A.

It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

Let r be the radius of the circle. Then the area of the circle will be

A = πr² square units

The radius is given as,

r = 36 / 2

r = 18 inches

The area of the circle is given as,

A = π x (18)²

A = 3.14 x 324

A = 1,017.36 square inches

The number of square inches of cloth cut from the square will be 1,017.36 square inches. Then the correct option is A.

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The complete question is given below.

A circle is cut from a square piece of cloth, as shown:

A square, one side labeled as 36 inches, has a circle inside it. The circle touches all the sides of the square. The portion of the square outside the circle is shaded.

How many square inches of cloth is cut from the square?

(π = 3.14)

1,017.36 in2

1,489.24 in2

1,182.96 in2

1,276.00 in2

On solving the provided question we can say that  the equation of the line will be  y+11 = 0.

The slope of a line is how steeply it slopes from left to right. The slope of a line is determined by dividing its rise (vertical change) by its slope, which is its horizontal change. Regardless of whatever two locations on the line you pick, the slope of the line is always constant (it never changes).

To find the coordinates of two points on the line, choose two. Find the difference between these two locations' y-coordinates (gradients). Find the difference between these two places' x coordinates (runs). Divide the change in the y coordinate by the difference in the x coordinate (slope/history or slope).

Here,

slope, m= 0 as these are parallel line.

so the equation of the line will be

y-y1 = m(x-x1)

y+11 = 0

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The sample mean of the weights at the birth of the randomly chosen infants is 7.6 pounds.

Given: The sample of seven infants was selected randomly and the weights are: {9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6} (in pounds)

What is a sample?

A sample can be defined as a part of something big or a whole. It can be some of the elements from a given set of elements.

For example: Let us consider the set of natural numbers. The set of natural numbers has an infinite number of elements in it. We choose some numbers from the set, say {2, 7, 9, 10, 99, 200, 234}. These chosen numbers are known as samples from the set of natural numbers.

What is the sample mean?

The sample mean is the average value of the samples or it is the mean of all the elements which exist in the given sample.

The sample mean is denoted by x⁻ which is pronounced as x bar.

The formula to calculate sample mean (x⁻) is:

Sample Mean (x⁻) = Summation of all the elements in the sample / Total number of elements in the sample.

x⁻ = ∑xₙ / n

where,

∑xₙ = Summation of all the elements in the sample

n = Total number of elements in the sample

x⁻ = Sample mean

Now let's solve the given question:

The given sample is {9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6}

The summation of the elements in the sample is:

∑xₙ = 9.0 + 7.3 + 6.0 + 8.8 + 6.8 + 8.4 + 6.6

∑xₙ = 52.9

The total number of elements in the sample is:

n = 7

Therefore, the sample mean (x⁻) is:

x⁻ = ∑xₙ / n

x⁻ = 52.9 / 7

x⁻ = 7.5571 ≈ 7.6

Hence the sample mean of the weights at the birth of the randomly chosen infants is 7.6 pounds.

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Disclaimer: The question is incomplete. The complete question is mentioned below:
Question: A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. What is the sample mean?

Answer:

e

Step-by-step explanation:

Answer:

x = 70 and the labeled angles are 110 and 70

Step-by-step explanation:

This is a trapezoid, the bases are parallel.

Since the bases are parallel, given two angles are supplementary and their sum is equal to 180:

x + 40 + x = 180 add like terms

2x + 40 = 180 subtract 40 from both sides

2x = 140 divide both sides by 2

x = 70 and the labeled angles are 110 and 70

Answer:

Youre welcome

Step-by-step explanation:

Answer:

95 degrees

Step-by-step explanation:

First find the angles within the triangle. 180 - 43 - 52 = 85, so the missing angle within the triangle is 85. The exterior angle would be supplementary to that, so 180 - 85 = 95.

The true statements are (A) 30×400 ml equal the total number of milliliters for 30 bowls of soup

(B) 30 bowls of soup hold 12,000 ml, which is same as 12 Litres

(C) Noah can multiply the number of bowls of soup by 1,000 to find the number of litres

(D) If each family member has 2 bowls of soup , Noah need to make 24 litres of soup

There are 30 people and each person is served soup in a 400 ml bowl, so the total amount of soup needed is 30 × 400 ml = 12,000 ml.

Option A is true

30 bowls of soup hold 30 × 400 ml = 12,000 ml, which is the same as 12 litres (since 1 litre = 1,000 ml).

Option B is true

Since 1 litre = 1,000 ml

Noah can multiply the number of bowls of soup by 1,000 to find the number of litres.

For example, 30 bowls of soup hold 12,000 ml = 12 litres.

Option C is true

If each family member has 2 bowls of soup, then the total amount of soup needed is

30 × 2 × 400 ml

= 24,000 ml, which is 24 litres (since 1 litre = 1,000 ml).

Option D is true.

Noah needs to make 24 litres of soup, and each pot contains 6 litres of soup.

Therefore, he would need to make 24 ÷ 6 = 4 pots of soup to serve each family member 2 bowls of soup.

Option E is false.

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Noah is making soup for a family reunion of 30 people. Each pot he makes contains 6 liters of soup. He uses bowl that 400mL to serve the soup to his family

Select all the true statements

(A) 30×400 ml equal the total number of milliliters for 30 bowls of soup

(B) 30 bowls of soup hold 12,000 ml, which is same as 12 Litres

(C) Noah can multiply the number of bowls of soup by 1,000 to find the number of litres

(D) If each family member has 2 bowls of soup , Noah need to make 24 litres of soup

(E) Noah would need to make 2 pots of soup for each family member to have 2 bowls of soup

The values of c and d in the expression 3√6 √10 √5 are c = 6 and d = 2, and d = 30.

To work out the values of c and d in the expression 3√6 √10 √5, we can simplify the square roots and find their product.

First, let's simplify the square roots:

√6 can be written as 2√3.

√10 remains as it is.

√5 remains as it is.

Now, we can substitute these values back into the original expression:

3√6 √10 √5 = 3 * 2√3 * √10 * √5

Next, we can simplify the expression further:

3 * 2√3 * √10 * √5 = 6√3 * √(10 * 5) = 6√3 * √50 = 6√3 * 5√2 = 30√6√2

To write this in the form C = 5cvd10, where c and d are integers, we need to determine the values of c and d.

From the simplified expression 30√6√2, we can see that c = 6 and d = 2.

Therefore, the values of c and d in the expression 3√6 √10 √5 can be written as c = 6 and d = 2.

Furthermore, from the given information d = 30 (2), we can conclude that the value of d is indeed 30, confirming our result.

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The points determined by the real numbers 3.2, 9.5, 50, and 263 are all located on the unit circle at their respective distances from the origin.

The unit circle is a circle of radius 1 centered at the origin of a coordinate system, usually the Cartesian coordinate system. In this system, a point (x,y) is determined by its real number x, where x is the horizontal distance from the origin and y is the vertical distance from the origin. For example, the point determined by the real number 3.2 is located at (3.2, 0), since 3.2 is the horizontal distance from the origin. Similarly, the point determined by the real number 9.5 is located at (9.5, 0).

The point determined by the real number 50 is located at (50, 0). Finally, the point determined by the real number 263 is located at (263, 0). The unit circle is often used in trigonometry to describe the position of points on the circle with an angle in standard position (in radians). For example, if the point determined by the real number 3.2 has an angle in standard position of 3.2 radians, then the point located at (3.2, 0) on the unit circle is the same point. Similarly, if the point determined by the real number 9.5 has an angle in standard position of 9.5 radians, then the point located at (9.5, 0) on the unit circle is the same point. The same is true for the points determined by the real numbers 50 and 263, respectively.

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This is an example of stratified random sampling as the population is divided into two groups males and females and 200 samples are selected from each group.

Given that,

A researcher asks all 1000 employees to engage in a questionnaire survey to look at various areas of employee job satisfaction with the goal of selecting a sample of 200 males and 200 women.

A crucial element of the sampling method known as stratified random sampling is the division of a population into smaller subgroups known as strata

Therefore, the population is separated into two categories, males and females, and 200 samples are chosen from each group in this stratified random sampling example.

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Answer:

Answer is B.

Step-by-step explanation:

-2x (4x+5)

-8x^2 - 10x

Hippoty Hoppity, distributive property.

Multiply -2x by 4x, both have X's, so you combine them to get x^2 (X squared).

Hope this helped. Good luck on your finals.

The domain of a function is the set of all inputs for which the function remains valid. Since the graph shows the number of coffee stores after 1992. The domain will only makes sense for positive numbers, since a negative year doesn't make any sense. Therefore, the domain is:

Answer: 6

Step-by-step explanation: 169/33=5.12121212121 so on. However, you still need a bus for the desimal people so you have to add another bus