3 packs of pens costs $13.85, how many packs of pencil can we buy for $39.60? Form Proportion first

Using it's concept, the average rate of change of the function over the interval [0, 3] is given as follows:

r = -8.

The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function. Hence, over an interval [a,b], the average rate of change is given by the equation presented as follows:

\(r = \frac{f(b) - f(a)}{b - a}\)

In the context of this problem, we want the average rate of change in the interval [0,3], hence the parameters are given from the table as follows:

Hence the average rate of change is given by:

r = (-20 - 4)/(3 - 0) = -24/3 = -8.

The table containing the numeric values of the function is given by the image at the end of the answer.

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The trapezoidal rule is a numerical integration method that uses trapezoids to estimate the area under a curve. The trapezoidal rule can be used for both definite and indefinite integrals. The trapezoidal rule approximation, Tn, to the integral sin r dz is given by:

Tn = (b-a)/2n[f(a) + 2f(a+h) + 2f(a+2h) + ... + 2f(b-h) + f(b)]where h = (b-a)/n. To determine how large n should be so that Tn is accurate to within 0.00001, we can use the error bound given in Section 5.9 of the course text. According to the error bound, the error, E, in the trapezoidal rule approximation is given by:E ≤ ((b-a)³/12n²)max|f''(x)|where f''(x) is the second derivative of f(x). For the integral sin r dz, the second derivative is f''(r) = -sin r. Since the absolute value of sin r is less than or equal to 1, we have:max|f''(r)| = 1.

Substituting this value into the error bound equation gives:E ≤ ((b-a)³/12n²)So we want to choose n so that E ≤ 0.00001. Substituting E and the given values into the inequality gives:((b-a)³/12n²) ≤ 0.00001Simplifying this expression gives:n² ≥ ((b-a)³/(0.00001)(12))n² ≥ (b-a)³/0.00012n ≥ √(b-a)³/0.00012Now we just need to substitute the values of a and b into this expression. Since we don't know the upper limit of integration, we can use the fact that sin r is bounded by -1 and 1 to get an upper bound for the integral.

For example, we could use the interval [0, pi/2], which contains one full period of sin r. Then we have:a = 0b = pi/2Plugging in these values gives:n ≥ √(pi/2)³/0.00012n ≥ 5073.31Since n must be an integer, we round up to the nearest integer to get:n = 5074Therefore, we should choose n to be 5074 so that the trapezoidal rule approximation, Tn, to the integral sin r dz is accurate to within 0.00001.

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Answer:

a) y ∝ x

y = kx

k = y/x

b) y = 7/8

Step-by-step explanation:

Suppose that y varies directly with x and y = 2 when x =16

a)write a direct variation equation that relates x and y

y varies directly with x

Hence:

y ∝ x

y = kx

Where k is constant of proportionality

y = 2 when x =16

Hence:

2 = 16k

k = 2/16

k = 1/8

b) find y when x =7

y = kx

k = 1/8

x = 7

y = 1/8 × 7

y = 7/8

Answer:

Step-by-step explanation:

chiều dài:x,x>0

chiều   rộ:y

\(\left \{ {({x+y)*2=326} \atop {xy=6370}} \right.\)

\(\left \{ {{x+y=163} \atop {xy=6370}} \right.\)

\(\left \{ {{y=163-x} \atop {xy=6370}} \right.\)

\(\left \{ {{y=163-x} \atop {x*(163-x)=6370}} \right.\)

\(\left \{ {{y=163-x} \atop {163x-x^{2} =6370}} \right. \\\)

\(\left \{ {{y=163-x} \atop {x_{1} =98; x_{2} =65}} \right.\)

\(\left \{ {{y=65} \atop {x=98}} \right.\)

Answer:

B. 4 steps

Step-by-step explanation:

\(84 \div 21 = 4\)

84 snacks

21 friends

how many snacks each of her friend gets.

\( \frac{84}{21} \)

\( = 4\)

hence, each of her friend will get 4 snacks.

answer= option B

The sample distribution is a collection of the parameters of all possible samples of a particular size taken from a particular population. The correct answer is option E.

A sampling distribution refers to a probability distribution of a statistic which comes from selecting random samples of a given population. Also known as a finite-sample distribution, it represents the distribution of frequencies on how spread apart various outcomes will be for a specific population.

As sample sizes increase, the sampling distributions approach a normal distribution. With infinite numbers of successive random samples, the mean of the sampling distribution is equal to the population mean (µ). The mean of the sampling distribution of a sample proportion is np, the sample size times the probability of success for each trial (or observation).

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The correct statements are If u and v are orthogonal, then u × v = 0. The vector proj_v u is parallel to v. If u and v are parallel, then u × v = 0.

The statement "If u and v are parallel, then either u · v = |u||v|" is incorrect. The correct statement is "If u and v are parallel, then u · v = |u||v|".

The statement "The expression u.(vw) is meaningful and the result is a scalar" is incorrect. The expression u.(vw) is not meaningful because the dot product is only defined for vectors of the same dimension.

The statement "Suppose u: O. If u × v = u × w, it follows that v = w" is incorrect. The correct statement is "Suppose u ≠ 0. If u × v = u × w, it follows that v - w is parallel to u".

Finally, the statement "The expression u · u can be negative" is incorrect. The dot product u · u is always non-negative, and is only equal to zero if and only if u = 0

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Answer:

I believe the answer is 6.6600 pls let me know if im wrong

Step-by-step explanation:

Answer:

Six and Sixty-six ten thousandths in deciamal form- 6.0066

:)

The confidence interval which shows 90% confidence level for the mean and assumed standard deviation is (2.94 meals, 3.0565 meals).

Given standard deviation=1.4. Sample size =1271, mean=3.

We have to find the confidence interval for 90% confidence level.

We have to find out α level that is the subtraction of 1 by the confidence interval divided by 2.

α=(1-0.90)/2

=0.05

Now we have to find z in the z table as such z has a p value of 1-α so it is z with p value of 1-0.05=0.95

Z=1.44 from z table.

Now find M as such that

M=z* st/\(\sqrt{n}\)

where st is standard deviation ,n is sample size.

M=1.44*1.4/\(\sqrt{1271}\)

=1.44*1.4/35.65

=2.016/35.65

=0.0565

Lower end= mean -M

=3-0.0565

=2.94

Upper end=Mean+ M

=3+0.0565

=3.0565

Hence the confidence interval showing 90% confidence level is (2.94,3.0565).

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Answer:

x = 3 is an extraneous solution

Step-by-step explanation:

Answer:

Option 3

Step-by-step explanation:

Edg2021

Answer:

2

Step-by-step explanation:

28x - 1 = 27x + 1 (being alternate angles)

28x - 27x = 1 + 1

x = 2

Hope it will help :)

Answer:

  (d)  vertical angles theorem

Step-by-step explanation:

Vertical angles have a common vertex and are formed from opposite rays.

__

Angles RQT and PQS share vertex Q, Rays QR and QP are opposite, creating line RP. Rays QT and QS are opposite, creating line ST. Hence angles RQT and PQS are vertical angles. The vertical angles theorem says those angles are congruent.

Answer:

○ f(x) = x² + 3x - 37

Step-by-step explanation:

Based on the given data in the table, we can observe that the function values (f(x)) correspond to different x-values. To determine the polynomial function represented by the data, we need to find the pattern or relationship between the x-values and the corresponding f(x) values.

Looking at the data, we can see that the x-values are increasing by 1 each time, and the corresponding f(x) values seem to be following a pattern. Let's analyze the data:

x | f(x)

--+-----

-8 | -35

-3 | -17

5 | 6

1 | 2

6 | 3

2 | 2

1 | 1

6 | 7

7 | 37

From the given data, it appears that the polynomial function represented by the data is:

f(x) = x² + 3x - 7

None of the provided options exactly matches this polynomial function, but the closest option is:

○ f(x) = x² + 3x - 37

So, the closest function represented by the data is f(x) = x² + 3x - 37.

Integers include zero, a positive natural number, and a negative integer represented by a minus sign, and the missing integers in the given situation are 5 < √48 < 7.

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers.

The inverse additives of the equivalent positive numbers are the negative numbers.

The boldface Z is a common mathematical symbol for the set of integers.

An integer, pronounced "IN-tuh-jer," is a whole number that can be positive, negative, or zero and is not a fraction.

Integer examples include -5, 1, 5, 8, 97, and 3,043. 1.43, 1 3/4, 3.14, and other numbers that are not integers are some examples.

So, we have:
__ < √48 < __

We know that:

√48 = 6.92

Then,

5 < √48 < 7

Therefore, integers include zero, a positive natural number, and a negative integer represented by a minus sign, and the missing integers in the given situation are 5 < √48 < 7.

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Complete question:

Use the integers that are closest to the number in the middle.

__ < √48 < __.

Therefore, the probability that both you and your study group member toss the same number of heads in n coin tosses is given by (2n n) * 2^(-2n).

To show that P(A1 U ... U An) = 1 - Π(1 - P(Ak)) > 1 - exp(ΣP(Ak)), we can use the hint provided, which states that e^x > 1 - x for all x ∈ R.

Let's denote Bk = A1 U ... U Ak, where 1 ≤ k ≤ n. Then we have:

P(Bk) = P(A1 U ... U Ak) = 1 - P(A1' ∩ ... ∩ Ak')

Using the complement rule, we can rewrite this as:

P(Bk) = 1 - P(A1')P(A2')...P(Ak')

Taking the complement again, we get:

P(Bk)' = P(A1)P(A2)...P(Ak)

Now, using the hint e^x > 1 - x, we have:

1 - P(Bk) = 1 - P(A1)P(A2)...P(Ak) < e^(-P(A1)P(A2)...P(Ak))

Taking the product over all k from 1 to n:

Π(1 - P(Bk)) < Π(e^(-P(A1)P(A2)...P(Ak)))

Expanding the product, we have:

1 - P(A1 U ... U An) < e^(-P(A1)P(A2)...P(An))

Taking the complement again, we obtain:

P(A1 U ... U An) > 1 - e^(-P(A1)P(A2)...P(An))

Since e^x > 1 - x for all x ∈ R, we have:

1 - e^(-P(A1)P(A2)...P(An)) < Σ(-P(A1)P(A2)...P(An))

Therefore, we can conclude that:

P(A1 U ... U An) > 1 - Σ(-P(A1)P(A2)...P(An))

Simplifying further:

P(A1 U ... U An) > 1 - exp(ΣP(Ak))

Thus, we have shown that P(A1 U ... U An) = 1 - Π(1 - P(Ak)) > 1 - exp(ΣP(Ak)).

Regarding the second part of the question, to show that the probability of both you and your study group member tossing the same number of heads in n coin tosses is (2n n) * 2^(-2n), we can use the concept of binomial coefficients.

The probability of getting k heads in n coin tosses is given by the binomial distribution formula:

P(k heads in n tosses) = (n choose k) * (1/2)^n

Since both you and your study group member are tossing the same number of heads, we want to find the probability for any particular k, where k ranges from 0 to n.

Therefore, we can sum up the probabilities for all possible values of k:

P(both toss same number of heads) = ∑ (n choose k) * (1/2)^n for k = 0 to n

Using the property of binomial coefficients (n choose k) = (n choose (n-k)), we can rewrite this as:

P(both toss same number of heads) = ∑ (n choose k) * (1/2)^n for k = 0 to n/2

Since the sum of binomial coefficients (n choose k) for k = 0 to n/2 is equal to (2n choose n), we can simplify the expression:

P(both toss same number of heads) = (2n choose n) * (1/2)^n

Finally, simplifying further:

P(both toss same number of heads) = (2n)! / (n! * n!) * (1/2)^n

And since (1/2)^n = 2^(-2n), we have:

P(both toss same number of heads) = (2n n) * 2^(-2n)

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It should be noted that z^4 will be -32 in rectangular form.

Based on the information, z = r(cos θ + i sin θ), and provided positive integer n, then it is implied that:

z^n = r^n (cos nθ + i sin nθ)

In this instance, we need to solve for z^4 in rectangular form when z = -2 - 2i. Firstly, we must calculate |z| and arg(z):

|z| = √((-2)^2 + (-2)^2) = 2√2

arg(z) = arctan(-2/-2) = π/4

Leveraging De Moivre's theorem, we can effectively deduce the value of z^4 as:

z^4 = (2√2)^4 (cos (4π/4) + i sin (4π/4))

= 32 (cos π + i sin π)

= -32

Concludedly, z^4  resolved in rectangular form is -32.

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Answer:

2*400= 2*400*1

2*400

800

or

2 x 400 = 2 x 100 x 4

100 x 4

= 400

I hope this helps:

Sorry if it didn't :(

Answer:

2 x 400 = 2 x 100 x 4

100 x 4

= 400

Step-by-step explanation:

Answer:

the answer is negative correlation

Step-by-step explanation:

Answer:

x ≤ 5

Step-by-step explanation:

Answer:

Maximum number of children among whom 32 red marbles, 144 blue marbles and 176 green marbles can be divided equally is 16.

Step-by-step explanation:

Finding HCF of 32, 144, 176

32 = 2 * 2 * 2 * 2 * 2

144 = 2 * 2 * 3 * 2 * 2 * 3

176 = 2 * 2 * 2 * 11 * 2

HCF = 2 * 2 * 2 * 2 = 16

Answer:

y=2(x+2)(x+3)

Step-by-step explanation:

First, we need to factor the right side:

y=2(x^2+5x+6)

Now, we can have an incomplete equation like this:

y=2(x+_)(x+_)

In the blanks, we need to fill out numbers that add to be 5 and multiply to be 6. What are factors of 6? 6 and 1, 2 and 3. Do 6 and 1 add to be 5? No. Do 2 and 3 add to be 5? Yes!

So, our factored form is

y=2(x+2)(x+3)

Answer:

n ≥ 12.5 weeks

Step-by-step explanation:

Weekly savings = at least $16

n = number of weeks

At least in inequality means ≥

16n ≥ 200

n ≥ 200/16

n ≥ 12.5 weeks

12.5 weeks until she has saved $200

Answer:

Step-by-step explanation:

3 gallons because 3/4 of a gallon covers 1/4 of a wall so you multiply the amount of gallons used for a wall times 4 which is 12/4 (keep the denominator the same ) and then divide 12 by 4 which is 3 gallons

That is absolute value.

or

Therefore,

1 < a <-7/2

Therefore , the solution of the given problem of equation comes out to be it took the aircraft roughly 0.156 hours, or 9.36 minutes, to fly 3,008 miles at a constant speed of 470 miles per hour.

Variable words are commonly used in complex algorithms to show consistency between two contradictory claims. Academic expressions called equations are used to show the equality of various academic numbers. In this case, normalization produces b + 7, in contrast to another algorithm, which can evaluate data from y + 7, divides 12 through two components, and produces y + 7.

Here,

The formula Hayden created is:

=> 470/h = 3008

We must separate h on one side of the equation in order to solve for it. By increasing both parts of the equation by h, we can achieve this:

=> 470 = 3008h

Then, to get h on its own, split the two sides of the equation by 3008:

=> h = 470/3008

By dividing the numerator and denominator by their 2 largest common factor, we can simplify this fraction:

=> h = 235/1504

Therefore, it took the aircraft roughly 0.156 hours, or 9.36 minutes, to fly 3,008 miles at a constant speed of 470 miles per hour.

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a. A is countably infinite.

Countably Infinite Sets: A set is countably infinite if its elements can be put in a one-to-one correspondence with the natural numbers (1, 2, 3, ...).

Examples of countably infinite sets include the set of all integers, the set of all positive even numbers, and the set of all fractions.

Uncountable Sets: An uncountable set is one that has a larger cardinality than the natural numbers.

It cannot be put in a one-to-one correspondence with the natural numbers.

The most well-known uncountable set is the set of real numbers (denoted by ℝ), which includes both rational and irrational numbers.

So option a. A is  countably infinite is correct.

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The correct option is d. Can't tell how big A is.

Based on the information provided, it is not possible to determine the size of set A. The given question presents us with a subset of the real numbers without specifying any additional characteristics or constraints.

Without further details or conditions, it is impossible to definitively classify set A as countably infinite, uncountable, or finite.

To determine the size of a set, we typically need more information such as the cardinality of the set or specific properties that can help us make a classification.

However, in this case, the given question does not provide us with any such information, making it impossible to determine the size of set A.

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Answer:

1. 69

2. 198

3. 50

use subtraction and addition