The following recipe is for 16 crepes: • 1/4 cup margarine, 3 tbs sugar, 1/2 cup orange juice, • 1 tbs grated orange rind, and 1/2 cup toasted almonds. You need to serve 5 crepes per person for 8 guests. How much of each ingredient is needed?

Answer:

1.25x + 2x ≤ 20

X + X = 12

Step-by-step explanation:

a) The first four nonzero terms of the Taylor series for \(f(x) = e^x\)centered at a = ln(10) are:

10, 10(x - ln(10)), \(\dfrac{5(x - ln(10))^2}{2}\), \(\dfrac{(x - ln(10))^3}{3!}\)

b) The power series using summation notation is:

\(\sum_{n=0}^{\infty} \dfrac{(10 (x - ln(10))^n)}{ n!}\)

a)

To find the first four nonzero terms of the Taylor series for the function \(f(x) = e^x\) centered at a = ln(10), we can use the formula for the Taylor series expansion:

\(f(x) = f(a) + \dfrac{f'(a)(x - a)}{1!} + \dfrac{f''(a)(x - a)^2}{2!} + \dfrac{f'''(a)(x - a)^3}{3!} + ...\)

First, let's calculate the derivatives of \(f(x) = e^x\):

\(f(x) = e^x\\f'(x) = e^x\\f''(x) = e^x\\f'''(x) = e^x\)

Now, let's evaluate these derivatives at a = ln(10):

\(f(a) = e^{(ln(10))}\ = 10\\f'(a) =e^{(ln(10))}\ = 10\\f''(a) =e^{(ln(10))}\ = 10\\f'''(a) = e^(ln(10)) = 10\)

Plugging these values into the Taylor series formula:

\(f(x) = 10 + 10\dfrac{(x - ln(10))}{1!} + \dfrac{10(x - ln(10))^2}{2!} + \dfrac{10(x - ln(10))^3}{3!}\)

Simplifying the terms:

\(f(x) = 10 + 10(x - ln(10)) + \dfrac{10(x - ln(10))^2}{2} + \dfrac{10(x - ln(10))^3}{3!}\)

Therefore, the first four nonzero terms of the Taylor series for \(f(x) = e^x\)centered at a = ln(10) are:

10, 10(x - ln(10)), \(\dfrac{5(x - ln(10))^2}{2}\), \(\dfrac{(x - ln(10))^3}{3!}\)

b) To write the power series using summation notation, we can rewrite the Taylor series as:

\(\sum_{n=0}^{\infty} \dfrac{(10 (x - ln(10))^n)}{ n!}\)

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Answer:

f(3)=5

f(0)= -7

Step-by-step explanation:

replace

4(3)-7

f(3)=5

f(0)=4(0)-7

f(0)=0-7

f(0)= -7

Answer:37.68

Brainliest pls

Answer:

The circumference of the circle is 75.36cm

Step-by-step explanation:

There are two ways you can solve this, one is by using the radius and multiplying it by 2 and then pi which is 3.14, and the other is to use the diameter which is the radius times 2, and the thingy gave you the diameter, and you multiply it by 3.14 which is pi

Answer:

Step-by-step explanation:

For the first 30 hours, Andrew will earn 4(30) = $120.  For each additional hour beyond 30 that Andrew works, he will earn 5(h - 30).  Therefore, the function that gives Andrew's total wages when he works more than 30 hours is:

w = 120 + 5(h - 30).  

So, if he works 35 hours, he will earn:

120 + 5(35 - 30) = 120 + 5(5) = 120 + 25 = $145.

If he works 42 hours, he will earn:

120 + 5(42 - 30) = 120 + 5(12) = 120 + 60 = $180.

I hope this helps!

If two methods agree perfectly in a method comparison study, the slope equals 1.0 and the y-intercept equals 0.0. Therefore, option (b) is the correct answer.

In a method comparison study, the goal is to compare the agreement between two different measurement methods or instruments. The relationship between the measurements obtained from the two methods can be described by a linear equation of the form y = mx + b, where y represents the measurements from one method, x represents the measurements from the other method, m represents the slope, and b represents the y-intercept.

When the two methods agree perfectly, it means that there is a one-to-one relationship between the measurements obtained from each method. In other words, for every x value, the corresponding y value is the same. This indicates that the slope of the line connecting the measurements is 1.0, reflecting a direct proportional relationship.

Additionally, when the two methods agree perfectly, there is no systematic difference or offset between the measurements. This means that the line connecting the measurements intersects the y-axis at 0.0, indicating that the y-intercept is 0.0.

Therefore, in a perfect agreement scenario, the slope equals 1.0 and the y-intercept equals 0.0, which corresponds to option (b).

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Answer:

2y=-1/8x+7

Step-by-step explanation:

Answer:

Rewrite equestion

8x - 2y= -7

Each puppy would weigh approximately 2.13 grams if all the puppies weighed the same amount.

To estimate the weight of each puppy, we need to subtract the weight of the basket from the total weight of the basket and puppies to find the total weight of the puppies.

Total weight of puppies = Total weight of basket and puppies - Weight of basket alone

= 2,977 - 1,077 = 1,900 grams

Then we divide the total weight of the puppies by the number of puppies to find the weight of each puppy:

Weight of each puppy = Total weight of puppies / Number of puppies

= 1,900 / 888

= approximately 2.13 grams

Each puppy would weigh approximately 2.13 grams if all the puppies weighed the same amount.

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Answer:

Step-by-step explanation:

12x + 105 = 55x + 0
=> 12x + 105 = 55x
=> 55x - 12x = 105
=> 43x = 105
=> x = 105/43
12y = 155
=> y = 155/12

The theoretical probability of event E, denoted by P(E), is the number of favorable outcomes divided by the total number of possible outcomes.

The theoretical probability of an event E, denoted by P(E), is the ratio of the number of favorable outcomes to the total number of possible outcomes in a given sample space.

In other words, it represents the likelihood of occurrence of event E based on the underlying theoretical assumptions.

Theoretical probability is derived from a theoretical or mathematical model and is based on the assumption that all outcomes in the sample space are equally likely.

It provides a theoretical expectation of the probability of an event occurring under ideal conditions.

To calculate the theoretical probability, we divide the number of favorable outcomes (the outcomes that meet the criteria for event E) by the total number of possible outcomes in the sample space.

This ratio represents the probability of event E occurring.

For example, if we have a fair six-sided die and we want to calculate the theoretical probability of rolling a 3, there is only one favorable outcome (rolling a 3) out of six possible outcomes (numbers 1 to 6).

Therefore, the theoretical probability of rolling a 3 is 1/6 or approximately 0.1667.

It's important to note that theoretical probability assumes ideal conditions and equal likelihood of all outcomes, which may not always reflect the real-world situation.

In practice, empirical probability based on observed frequencies is often used when actual data is available.

In summary, the theoretical probability of event E is the ratio of the number of favorable outcomes to the total number of possible outcomes in the sample space, providing a mathematical estimate of the likelihood of event E occurring.

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Answer:

m∠JKM = 63°

m∠MKL = 27°

Step-by-step explanation:

Since ∠JKL is a right angle. This means that by summing up both m∠JKM and m∠MKL will result in the same as ∠JKL figure. Thus, m∠JKM + m∠MKL = m∠JKL which is 90° by a right angle definition.

\(\displaystyle{\left(12x+3\right)+\left(6x-3\right) = 90}\)

Solve the equation for x:

\(\displaystyle{12x+3+6x-3 = 90}\\\\\displaystyle{18x=90}\\\\\displaystyle{x=5}\)

We know that x = 5. Next, we are going to substitute x = 5 in m∠JKM and m∠MKL. Thus,

m∠JKM = 12(5) + 3 = 60 - 3 = 63°

m∠MKL = 6(5) - 3 = 30 - 3 = 27°

Answer:

-3, -13, -23, -33, -43

Step-by-step explanation:

An atithmetic sequence has a common difference between each term

in -3, -13, -23, -33, -43

the difference between terms is a constant -10

Solving the question asked, we can say: If you win tonight, your odds of winning the next game are \($58.33\%$\). After that, if you lose, you have a \($38.88 \%$\) chance of winning the game.

Probability theory is a branch of mathematics that measures the probability that an event or statement is true. The probability of an event is a number between 0 and 1, with approximately 0 indicating that the event is unlikely and 1 indicating that it is certain. Probability is a numerical representation of the disease that a particular event will occur. Another way to express probability is as a percentage from 0% to 100% or 0 to 1. Proportion of occurrences in the complete set of equally likely possibilities leading to a particular occurrence compared to the total number of outcomes.

\($$\begin{aligned}& (2 / 3+1 / 2) / 2=X \\& 1,666 / 2=X \\& 0.58333=X \\& ((2 / 3+1 / 2 / 2) x 2 / 3=X \\& 0.58333 x 0.666=X .3888=X\end{aligned}$$\)

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Answer:

x = 13

Step-by-step explanation:

3x + 5 = 44

3x = 39

x = 13

The type of sampling used in this scenario is A Systematic sampling.

Systematic sampling involves selecting every kth element from a population list after randomly selecting a starting point. In this case, Christopher collects data from all the band members in his class, indicating that he is sampling systematically from a known list of band members.

This method ensures that every band member in the class has an equal chance of being selected, and it simplifies the process by following a predetermined systematic approach rather than relying on random selection or stratification.

Therefore, the type of sampling used in this scenario is A Systematic sampling.

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Complete question is below

To study the sleeping habits of all band members in his school, Christopher collects data from all the band members in his class. Which type of sampling is used? Select the correct answer below:

A Systematic sampling

B Stratified sampling

C Cluster sampling

D Convenience sampling

Answer:

\(\frac{-x^{2}+5x-1}{2x^{2} -x-1}\)

Step-by-step explanation:

Answer:x+42+3x = 90

Combine like terms:

3x+x = 4x

42+4x = 90

Subtract 42 to both sides

90-42 = 48

Divide 4 by 48

48/4 = 12

X = 12

100% right

Step-by-step explanation:

Answer:

comparing the means of three or more groups

Step-by-step explanation:

5x + (x+6) + 3x

5x + x + 6 + 3x

Combine like terms

5x+ x + 3x + 6

9x +6

One is 9x +6

It can also be

(5x+x ) +3x+6

6x+6 +3x

You are going at a speed of 4.0 km/h. A mile is 1609.0 metres long, and an hour is 60.0 minutes long.

3.0 kilometres per minute is equal to (2.5 * 1609.0)/60.0 miles per hour. Walking at 2.5 miles per hour results in a speed of 4.0 kilometres per minute. Because there are more metres in a mile than in a kilometre, the conversion between miles and kilometres is not a straightforward one-to-one conversion. A mile is 1609.0 metres long, and an hour is 60.0 minutes long. You must first convert 2.5 miles per hour to metres, and then divide the result by 60.0 minutes to obtain the speed in kilometres per minute. (2.5 * 1609.0)/60.0 = 4.0 kilometres per minute is the calculation.

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Answer:

central angle ( θ) = 1.91875radians

central angle ( θ) in degrees = 109.92degree

Step-by-step explanation:

Given:

diameter of 320 millimeters

Then the Radius of the circular

brake drum can be calculated as

Radius =Diameter/2

Radius = 320 millimeters/ 2

Radius= 160 millimeters

central angle ( θ) = arc/r

central angle ( θ) = 307 millimeters /160 millimeters

central angle ( θ) = 1.91875radians

Than to convert it to degrees we have

1rad × 180/π = degree

Where π =3.142

central angle ( θ) = 1.91875radians * 180/π

Therefore,central angle ( θ) in degrees = 109.92degree

Answer:

The answer is "\(5x+10y+5z\)"

Step-by-step explanation:

Given value:

\(\to \frac{1}{2}(10x + 20y +10z)\)

Using the distributive property.

If there are three integers a,b and c then:

\(a \cdot(b+c) =a \cdot b + a \cdot c\)

\(\to \frac{1}{2}(10x) +\frac{1}{2}(20y+10z)\\\\\to (5x) +\frac{1}{2}(20y+10z)\)

Again apply the distributive property

 \(\to (5x) +(10y+5z)\\\\\to (5x+10y+5z)\)

Or

\(\to \frac{1}{2}(10x + 20y +10z)\)

take common 2 from the equation:

\(\to \frac{1}{2}\times 2 (5x + 10y +5z)\\\\\to (5x + 10y +5z)\\\)

Answer:

5x+10y+5z

Step-by-step explanation:

The IQR for the data is 4.75.

The interquartile range is the difference between the third quartile and the first quartile.

Third quartile = 3/4(n + 1)

First quartile = 1/4 x (n + 1)

The data arranged in ascending order is: 10, 12, 14, 15, 15.5, 16, 17.5, 18, 19

First quartile = (12 + 14) / 2 = 13

Third quartile = (17.5 + 18) / 2 = 17.75

IQR = 17.75 - 13 = 4.75

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Answer:  

4

Step-by-step explanation:

The correct answer is option d. The theoretical Probability of spinning a multiple of 3 with one spin is 0.

The theoretical probability of an event, we need to identify the number of favorable outcomes (the desired event) and the total number of possible outcomes.

In this case, the event is spinning a multiple of 3 on the spinner. Let's examine the possible outcomes and identify the favorable outcomes:

Possible outcomes on the spinner: {1, 2, 3, 4, 5, 6}

Favorable outcomes (multiples of 3): {3, 6}

The total number of possible outcomes is 6, and the number of favorable outcomes is 2.

The theoretical probability of spinning a multiple of 3 can be calculated as:

P(multiple of 3) = (Number of favorable outcomes) / (Total number of possible outcomes)

P(multiple of 3) = 2 / 6

Simplifying the fraction, we get:

P(multiple of 3) = 1 / 3

Therefore, the correct answer is option d. The theoretical probability of spinning a multiple of 3 with one spin is 0.

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Answer:

9x +24y = -8

Step-by-step explanation:

2y + 3/4 x = -2/3 ( multiple by 4)

24y + 9 x = -8 (move x to the front)

9x + 24y = -8