find the general form of the equation of the plane passing through the point and normal to the specified vector or line. point perpendicular to (2, 0, 1) x = 8t, y = 8 – t, z = 9 3t

Answer:

I think it's B because the bigger numbers stay the same an u subtract the smaller numbers

Question 1: The highest power of 2 that is less than 1000 is 2^9 = 512.

Question 4: The decimal equivalent of the hexadecimal number 4AF is 1199.

Question 1: What is the highest power of 2 that is less than 1000?

We know that,

2^ {10} = 1024 which is the smallest number greater than 1000.

Therefore, the highest power of 2 that is less than 1000 is 2^ 9

2^ (9) = 512

Question 2: Express this hexadecimal number in decimal: 4AF

To convert hexadecimal number to decimal number, we multiply each digit of the hexadecimal number by its place value and add the products. We can start from the right and work our way to the left.

4AF in hexadecimal is equal to:

(4 × 16²) + (10 × 16¹) + (15 × 16⁰)

= 1024 + 160 + 15

= 1199

Therefore, the decimal equivalent of the hexadecimal number 4AF is 1199.

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Answer:

I’m going to guess and say that it’s 3? Not sure sorry!

Answer:

1,227

Step-by-step explanation:

3,000 divided by 3 is 1,000

600 divided by 3 is 200

80 divided by 3 is 26 r2

1 + r2 =3

and 3 divided by 3 is 1

1,000 + 200 + 26 + 1 = 1,227

Answer:

-6.67

Step-by-step explanation:

slope is change in y/change in x so using (4, 60) and (1, 80), the slope is:

\(\frac{80-60}{1-4} =\frac{-20}{3} =-6.67\)

Answer: 50 + 80 = 130 So the answer would be |-85-(-50)|.

The conclusion of the symbolised argument is that N implies (O and P). This can be proven using conditional proof and the eighteen rules of inference, or using the rule of conjunctive simplification.

The symbolic argument's conclusion is that N implies (O and P). This can be demonstrated using conditional proof and the eighteen inference rules.

Proof:

1. N ⊃ O (Premise)

2. N ⊃ P (Premise)

3. N (Assumption)

4. O (1,3 Modus Ponens)

5. P (2,3 Modus Ponens)

6. O•P (4,5 Conjunction)

7. N ⊃ (O•P) (3-6 Conditional Proof)

8. N ⊃ (O•P) (2,7 Disjunctive Syllogism)

This leads us to the conclusion that N implies (O and P).

Without the use of conditional proof, the identical result can be reached. The conjunctive simplification rule can be used to do this.

Proof:

1. N ⊃ O (Premise)

2. N ⊃ P (Premise)

3. N (Assumption)

4. O (1,3 Modus Ponens)

5. P (2,3 Modus Ponens)

6. O•P (4,5 Conjunction)

7. N ⊃ (O•P) (Conjunctive Simplification)

Therefore, we have derived the conclusion that N implies (O and P).

Complete Question:

Use conditional proof and the eighteen rules of inference to derive the conclusions of the following symbolized arguments. Having done so, attempt to derive the conclusions without using conditional proof.

1. N ⊃ O

2. N ⊃ P / N ⊃ (O • P)

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A stretch of an exponential growth function is one that contains a constant factor that affects the rate of growth. Of the three functions given, only O fx) = 2^312 meets this criteria.

To determine which of these functions is a stretch of an exponential growth function, we need to look for the presence of a constant factor or coefficient that affects the rate of growth. In the first function, Of(x) = 22(x)3, we see that there is no constant factor present. The base of the exponential function is simply 2, which means that the rate of growth is constant and does not change.
Similarly, in the second function, Of(x) = 3, there is no exponential term present, and therefore no growth or decay is occurring. This function simply returns a constant value of 3 for any input value of x.
In the third function, Of(x) = 2^312, we see that there is a constant factor present in the base of the exponential function. This means that the rate of growth is being affected by this factor, resulting in a steeper curve than the first two functions. Therefore, O fx) = 2^312 is a stretch of an exponential growth function.

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The correct expression for an exponential growth function with a stretch is Of(x) = 2^12x.

The correct expression for an exponential growth function is Of(x) = 212x.

This is because the exponent, 12x, represents the rate at which the function is growing.

A larger value for the exponent results in a steeper growth rate, which indicates a stretch of the exponential growth function.

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The compound inequality that has a solution set of all real numbers is:  x > -2 or x < 1

A mathematical expression known as a compound inequality consists of two or more inequalities linked together by the logical operators "and" or "or." It represents a set of values that simultaneously meet each of the stated inequalities. Take the compound inequality 2x + 3 7 and x - 4 > -2, for instance. We treat this compound inequality as two separate inequalities, 2x + 3 7 and x - 4 > -2, in order to solve it. We first determine the intersection of the solution sets after solving each inequality separately. The values of x in this situation that meet both inequality are: 0 x 3.

1. A compound inequality is an inequality that combines two or more simple inequalities using the words "and" or "or."

2. The solution set of all real numbers means that any number on the number line is a solution to the inequality.

3. In the given inequality, x > -2 or x < 1, we have two simple inequalities connected by "or."

4. If x > -2, we have all numbers greater than -2 (to the right of -2 on the number line) as solutions.

5. If x < 1, we have all numbers less than 1 (to the left of 1 on the number line) as solutions.

6. Since we're using "or," a number only needs to satisfy one of these conditions to be a solution. So, all real numbers satisfy either x > -2 or x < 1, making this the compound inequality with a solution set of all real numbers.

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Answer:

lower quartile - 38

upper quartile - 59

maximum - 62

median - 46.5

minimum - 32

I hope this help. Have a great day!

The solution to the systems of equations graphically is (2, 4)

From the question, we have the following parameters that can be used in our computation:

y = 2x

y = -x + 6

Next, we plot the graph of the system of the equations

See attachment for the graph

From the graph, we have solution to the system to be the point of intersection of the lines

This points are located at (2, 4)

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Answer:

3/5

Step-by-step explanation:

put into fraction form:  21/35

21/35 (divide by 7/7)

3/5

Answer:

We just have to make the ratio into a fraction and simplify:

\(21:35=\frac{21}{35}=\frac{3}{5}\)

\(12:15=\frac{12}{15} =\frac{4}{5}\)

\(8:20=\frac{8}{20}=\frac{2}{5}\)

\(2:10=\frac{2}{10} =\frac{1}{5}\)

Answer: 40

Step-by-step explanation:

38+ 52=90

230-90=40

It has proved that the equation \(e^{(x)} * (dy/dx) = y * e^{(x)} * (dy/dx)\) is linear and the equation \((dy/dx) + x^2 * e^{(x)} * y = e^{(x)}\) is not linear.

The equation \(e^{(x)} * (dy/dx) = y * e^{(x)} * (dy/dx)\) is linear because it can be written in the standard form of a linear first-order ordinary differential equation, which is:
dy/dx + P(x) * y = Q(x)

In this case, we can divide both sides of the equation by \(e^{(x)}\) to obtain:
dy/dx = y * (dy/dx)

Now, we can compare this to the standard form and observe that P(x) = 0 and Q(x) = y * (dy/dx).

Since the equation is in the standard form, it is linear.

On the other hand, the equation \((dy/dx) + x^2 * e^{(x)} * y = e^{(x)}\) is not linear.

While it may seem similar to the standard linear form, the presence of the \(x^2 * e^{(x)} * y\) term is what makes it non-linear.

In a linear equation, the term involving y should be of the form P(x) * y, where P(x) is a function of x only.

However, in this case, the term \(x^2 * e^{(x)} * y\) involves both x and y, making the equation non-linear.

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The given statement: n(n+1)(2n+1) is divisible by 6 for all positive integers n.

Step-by-step explanation: We need to prove that n(n+1)(2n+1) is divisible by 6 for all positive integers n using mathematical induction.

Step 1: First, lets prove the statement for the smallest possible value of n. The smallest value of n is 1. So, let's check whether the given statement is true for n = 1 or not.

\(LHS = 1(1+1)(2*1+1) = 6\)

It is divisible by 6. Hence, the statement is true for n=1.

Step 2: Let's assume that the statement is true for n=k. So, we can say that n(n+1)(2n+1) is divisible by 6 for n=k. i.e., n(n+1)(2n+1) = 6a (for some integer a).

Step 3: We need to prove the statement is true for n=k+1.

So, we need to prove that (k+1){(k+1)+1}[2(k+1)+1] is divisible by 6

Using the assumption we made in step 2.

\(LHS = (k+1){(k+2)}[2k+3] = (k+1)(k+2)(2k+3)LHS = (2k+3)k(k+1)(k+2)LHS = 2[k(k+1)(k+2)] + 3[k(k+1)]\)

Now, k(k+1)(k+2) is divisible by 6 using the assumption made in step 2.

So, LHS = 2[k(k+1)(k+2)] + 3[k(k+1)] is also divisible by 6.

Hence, the statement is true for n=k+1.

Step 4: Using steps 1 to 3, we can say that the given statement is true for n=1 and if it is true for n=k, then it is also true for n=k+1.

Hence, by mathematical induction, we can say that the statement is true for all positive integers n.

Hence, it is proved that n(n+1)(2n+1) is divisible by 6 for all positive integers n.

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Answer:

The answer 168.75 without rounding and rounding its also 168.75

Answer:

x = 11√3

y = 11

Step-by-step explanation:

Let 60 be the reference angle

sin 60 = p/h

√3/2 = x/22

or, 22√3 = 2x

or, x = (22√3)/2

so, x = 11√3

now

\(h^2 = p^2 + b^2\\or, 22^2 = (11\sqrt{3} )^2+y^2\\or, 484 = 363 + y^2\\or, 484-363 = y^2\\or, 121 = y^2\\or, \sqrt{121} = y\\so, y = 11\)

$8\times9\times8\times9 = 5184$

There are a total of $8\times9\times8\times9 = 5184$ positive four-digit integers that are not multiples of 1111 and form an arithmetic sequence. To explain further, the first digit can be any integer from 1 to 8 (not 0 as the number must be four-digits long). Once the first digit is chosen, the second digit can be any integer from 1 to 9. Once both the first and second digits are chosen, the third digit can be any integer from 1 to 8, and finally the fourth digit can be any integer from 1 to 9. Therefore, the total number of four-digit integers that are not multiples of 1111 and form an arithmetic sequence is $8\times9\times8\times9 = 5184$.

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Answer:

f(x) / g(x) = 8^x / 9 --> B

Step-by-step explanation:

You just need to plug in the values

Answer:

B. 8^2/-9

Step-by-step explanation:

I think the first guy is right

The solutions of the system of equations are 8 and -4.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 9 is an equation.

We have,

-4x - y = -28 _____(1)

x + y = 4 _____(2)

x = 4 - y _____(3)

Substituting (3) in (1) we get,

-4(4 - y) - y = -28

-16 + 4y - y = -28

-16 + 3y = -28

3y = -28 + 16

3y = -12

y = -4

Substituting y = -4 in (3) we get,

x = 4 - (-4)

x = 4 + 4

x = 8

Thus,

The value of x is 8.

The value of y is -4.

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When drawing 3 cards from a standard deck without replacement, there is approximately a 16.60% chance of drawing at least one 3 card.

The probability of drawing at least one 3 card from a standard deck of 52 cards without replacement can be calculated using the concept of complementary probability.

We can find the probability of not drawing any 3 cards and subtract it from 1 to get the probability of drawing at least one 3 card.

To find the probability of not drawing any 3 cards, we first determine the number of ways to choose 3 cards from the 52-card deck without replacement, which is denoted as C(52, 3) or "52 choose 3." This can be calculated as:

C(52, 3) = 52! / (3! * (52-3)!) = 22,100.

Now, let's determine the number of ways to choose 3 cards from the 49 non-3 cards in the deck, which is denoted as C(49, 3) or "49 choose 3." This can be calculated as:

C(49, 3) = 49! / (3! * (49-3)!) = 18,424.

Therefore, the probability of not drawing any 3 cards is given by:

P(not drawing any 3 cards) = C(49, 3) / C(52, 3) = 18,424 / 22,100 = 0.8340 (rounded to four decimal places).

Since we want the probability of drawing at least one 3 card, we can subtract the probability of not drawing any 3 cards from 1:

P(at least one 3 card) = 1 - P(not drawing any 3 cards) = 1 - 0.8340 = 0.1660 (rounded to four decimal places).

Therefore, the probability that at least one of the cards drawn is a 3 is approximately 0.1660 or 16.60%.

To summarize, when drawing 3 cards from a standard deck without replacement, there is approximately a 16.60% chance of drawing at least one 3 card.

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Answer:

5

Step-by-step explanation:

To find the points for each question, you must divide the number of points (200) by the number of questions (40) to get the number of points for each question

\(\frac{200}{40}\)

Divide 200 by 40 to get

\(\frac{5}{1}\) or \(5\)

Hope this helps. If you have any follow-up questions, feel free to ask.

Have a great day!

Answer:

5 points

Step-by-step explanation:

200points / 40 questions = 5points/1question

then:

1 questión worths 5 points

Answer:

5230

Step-by-step explanation:

The amount of money in Carson's account after 14 years would be $5231.6

"Compound interest is the interest which is calculated from the original principal plus accumulated interest."

\(A=P(1+\frac{r}{n} )^{nt}\)

where,

A : Final amount

P : Initial amount (principal)

R : interest rate in percentage

r : interest rate (R/100)

n: number of  times the interest is compounded

t :  the overall tenure

For given question,

P = $3900, R = 2.1%, n = 12 (as compounded monthly), t = 14

for R = 2.1%,

\(r=\frac{2.1}{100} \\r=0.021\)

Now, we need to find the value of A.

Using the formula of compound interest,

⇒ \(A=3900 \times (1+\frac{0.021}{12} )^{12\times 14}\)

⇒ \(A=3900\times (1+0.00175)^{168}\)

⇒ \(A=3900\times(1.00175)^{168}\)

⇒ \(A=3900\times 1.3414\)

⇒ \(A=5231.61\)

⇒ \(A\approx \$ 5231.6\)

Hence, there would be $5231.6 in the account after 14 years.

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Answer:

  1.728×10¹⁵

Step-by-step explanation:

You may recall from 3rd grade that multiplying by 10 adds a zero to the right of a number (moves the decimal point 1 place to the right).

An exponent is used to signify repeated multiplication. These facts together are used to translate to/from scientific notation.

  10 = 1 × 10

  100 = 1 × 10 × 10 = 1 × 10²

__

Continuing in like fashion, 5.4×10⁸ represents 5.4 × (1 followed by 8 zeros).

Similarly, 3.2×10⁶ = 3.2 × (1 followed by 6 zeros)

The product will be ...

  (5.4×10⁸)×(3.2×10⁶) = (5.4×3.2) × (1 followed by 8+6 = 14 zeros)

  = 17.28 × 10¹⁴

  = (1.728 × 10) × 10¹⁴ . . . moving the decimal point so there's 1 digit to its left

Adding that extra zero into the count we already have, this becomes ...

  = 1.728×10¹⁵

_____

Additional comment

Your scientific or graphing calculator will have a mode for showing numbers in scientific notation. You can enter these numbers directly into your calculator and have it show you the result in scientific notation.

Or, you can use a spreadsheet with appropriate output cell formatting.

Answer:

1.728×10¹⁵ is the answer

A: 75% of items are classified as C items, 18.75% as B items, and 6.25% as A items.

A-B-C examination is an instrument utilized for stock administration, which orders things into three classifications: A, B, and C, in light of their worth and significance. Classification A things have a high worth however a low volume, and their administration requires close consideration and control. Class B things have moderate worth and volume and require moderate control. Classification C things have a low worth yet a high volume, and their administration can be loose. The reason for the examination is to recognize which things need the most consideration and control, and which things can be dealt with less consideration and cost-actually. The examination assists in streamlining with reviewing levels, decreasing expenses, and expanding benefits.

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Answer:

A. a = 10, b = -9

Step-by-step explanation:

We are given:

(a+bi)-(3-5i) = 7-4i

We know that a and b are both real numbers, and we want to find what a and b are.

For imaginary numbers, a is the real part, and bi is the imaginary part. This means that we consider the real numbers like terms, and the imaginary numbers like terms.

So to start, we can open the equation to become:

a + bi - 3 + 5i = 7 - 4i

Based on what we mentioned above:
a - 3 = 7

  + 3   +3

_____________

a = 10

And:

bi + 5i = -4i

    -5i    -5i

____________j

bi = -9i

Divide both sides by i.

bi = -9i

÷i    ÷i

_________

b = -9

So, a = 10, b= -9. The answer is A.

Answer:

Solid A

Step-by-step explanation:

Surface area of a cube: 6 x a², where a is the side.

= 6 x 6²

= 6 x 36

= 216 cm²

Surface area of the cuboid/rectangular prism: 2(lw + wh + lh), where l is the length, w is the width, h is height.

= 2((5 x 4) + (4 x 8) + (5 x 8))

= 2(20 + 32 + 40)

= 2(92)

= 184 cm²

Therefore, Solid A has the larger surface area compared to Solid B.

Using the information provided in the table, The total holding cost is  $547.50, the total setup cost is $600 and the total cost is  $1,147.50.

To develop a POQ (Periodic Order Quantity) solution use a lot-for-lot solution, which means that we will order exactly what we need for each period.

The missing values can be found on the attached table.

From the table, the total holding cost which is the sum of the holding costs for all periods is $547.50 while the total setup cost which is the sum of the setup costs for all periods is $600.

Therefore, the total cost is the sum of the holding cost and the setup cost and it is calculated as $1,147.50.

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Answer: Approximately 52.87 cm.

Step-by-step explanation:

Circumference is diameter times pie to divide the circumference  by pie.

166/3.14    use 3.14 as an approximation for pie.

166/3.14 = 52.87  rounded to the nearest hundredth

The answer should be 52.8662420382cm you can round however needed

diamete = circumferance divided by pi