Which equation could be used to solve the problem?



Mr. Guzman drove his car 1080 miles in 6 weeks.



If he drove the same distance every week, which equation shows how far he drove each week (d)?



A.


d = 6 ÷ 1080



B.


d = 1080 – 6


C.


d = 1080 • 6


D.


d = 1080 ÷ 6

Final answer:

Maria can convert 500 centimeters to meters by dividing by 100. So, she would end up with 5 meters since each meter contains 100 centimeters.

Explanation:

Maria wants to convert 500 centimeters to meters to determine how many meters she has. Conversion between centimeters and meters is a common mathematical process. Since there are 100 centimeters in a meter, Maria needs to divide the number of centimeters by 100 to get the measurement in meters. So, she would calculate 500 cm ÷ 100, which equals 5 meters.

To visualize this, imagine you have a ruler that measures in centimeters. If you laid out rulers end to end until you reached 500 centimeters, you would have the equivalent length of 5 meters because every 100 centimeters make up 1 meter.

Example:

If we had 200 cm, we would divide by 100 and find that 200 cm equals 2 m. Comparing this to a meter stick, which measures 1 meter, we can see that 200 cm is greater than 1 m and would require using the meter stick twice to measure the entire length.

Answer:    5/8 inch longer than 3/8 inch

Step-by-step explanation:  Each whole number, and also one inch, can be represented as a fraction. Thus one inch can be displayed as 4/4 or 5/5, or as our case can be 8/8. This means that every whole number, even one inch, can have as many parts as possible in a fraction, which depends on what type of fraction is displayed. Thus, one inch can have a maximum of 8/8 or 6/6, etc.

To determine how much one inch is longer than 3/8 inch, we will display one inch as 8/8 inches and reduce 3/8 inch from it.

The result is 8/8 - 3/8 = 5/8 inch. So one inch is 5/8 inch longer than 3/8 inch.

The tangent line to the curve at (0, 2) is y = 2x + 2, and the normal line is y = -1/2x + 2.

To find the equations of the tangent line and normal line to the curve at the given point (0, 2) for the function y = [tex]x^{4} +2e^{x}[/tex], we first need to determine the derivative of the function at that point.

1. Differentiate the function y =[tex]x^{4} +2e^{x}[/tex] with respect to x:

dy/dx = [tex]4x^{3} +2e^{x}[/tex]

2. Evaluate the derivative at the given point (0, 2):

dy/dx |(0, 2) = [tex]4(0)^{3}[/tex] + 2[tex]e^{0}[/tex] = 2

3. The slope of the tangent line at the point (0, 2) is 2.

4. Use the point-slope form to find the equation of the tangent line:

y - 2 = 2(x - 0)

y = 2x + 2

5. The slope of the normal line is the negative reciprocal of 2, which is -1/2.

6. Use the point-slope form to find the equation of the normal line:

y - 2 = (-1/2)(x - 0)

Simplify:

y = -1/2x + 2.

Question- Find the equation of the tangent line and normal line to the curve at a given point y=[tex]x^{4} +2e^{x}[/tex], (0, 2).

Final answer:

The derivative of 3g(x) is 3g'(x), obtained by taking the derivative of the function and multiplying it by the constant.

Explanation:

Derivative of 3g(x):

Yes, the derivative of 3g(x) is indeed **3g'(x)**.

When you have a constant multiplied by a function, you can simply take the derivative of the function and multiply it by the constant to find the derivative of the entire expression. In this case, the derivative of 3g(x) would be 3 times the derivative of g(x), which is 3g'(x).

Final answer:

Calculating possibilities ranges from completing a quiz to creating secret codes, with correct answers including 108 ways to complete a quiz and 234,000 combinations for a secret code. The arrangement of the word EXPERIMENT yields 1,209,600 unique arrangements, and other questions involve calculating probabilities and combinations in different scenarios.

Explanation:

Calculating Various Probabilities and Combinations

Let's break down each part of the question to provide clear and step-by-step solutions.

1. Completing a Quiz

For the quiz with 2 true-or-false questions and 3 multiple-choice questions (each with 3 options), the number of ways to complete the quiz can be calculated as 22 * 33, which equals 4 * 27 = 108. So, the correct answer is 108 ways.

2. Creating a Secret Code

For a secret code consisting of 2 digits (10 options each, but cannot repeat, so 10*9), 2 letters (26 options each, but cannot repeat, so 26*25), followed by 1 symbol from 4 options, the total number of combinations is 10*9*26*25*4 = 234,000. Thus, the correct choice is 234,000 combinations.

3. Arrangements of the Word EXPERIMENT

To find the number of distinct arrangements of the letters in EXPERIMENT, considering the repeated letters, the formula is the total factorial divided by the product of factorials of each repeated letter: 10!/ (2! * 3!), which calculates to 1,209,600. Therefore, option a is correct.

4. Sending Students to a Summer Dance Program

To determine how many ways a dance instructor can send 4 of her 11 students to a summer dance program, we use combinations: 11C4 = 330. So, the answer is 330 ways, option a.

5. Probability of Starting a Car

With 5 keys, the probability that a randomly chosen key starts the car is 1/5, which translates to 20%, option c.

6. Probability of Choosing a Losing Card

If the winning probability is 2.9%, the losing probability is 100% - 2.9% = 97.1%, thus the correct answer is option d.

The line which contains point A is line l.

Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.

Now from the given diagram, lines l and m lie in plane P.

And the point lies on the line l are A, B and C.

The point lies on the line m are B and D.

Point E lies in plane P.

Thus, the line which contains point A is line l.

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Final answer:

The measure of one interior angle of a regular convex 31-gon is approximately 168.39 degrees, calculated by dividing the sum of the interior angles, 5220 degrees, by the number of sides.

Explanation:

The measure of one interior angle of a regular convex 31-gon can be calculated using the formula for the sum of the interior angles of a polygon, which is (n - 2) × 180°, where n is the number of sides. For a 31-gon, the sum of the interior angles is,

(31 - 2) × 180°

= 29 × 180°

= 5220°.

To find the measure of one interior angle, you divide the total sum by the number of sides, so it is 5220° ÷ 31 ≈ 168.39°.

Answer:

[tex]-3x^{2} -6x-7[/tex]

Step-by-step explanation:

The given expression is :

[tex]\frac{-3x^{3}+5x+14}{x-2}[/tex]

Factoring [tex]-3x^{3}+5x+14[/tex]

Factor out common term -1

[tex]3x^{3}-5x-14[/tex]

Now dividing leading coefficients of numerator and divisor.

[tex]\frac{3x^{3}}{x}=3x^{2}[/tex]

Multiplying x-2 with [tex]3x^{2}[/tex] = [tex]3x^{3}-6x^{2}[/tex]

Subtracting [tex]3x^{3}-6x^{2}[/tex] from [tex]3x^{3}-5x-14[/tex]

we get [tex]6x^{2} -5x-4[/tex]

Therefore, [tex]\frac{-3x^{3}+5x+14}{x-2}[/tex] = [tex]3x^{2} +\frac{6x^{2}-5x-14}{x-2}[/tex]

Now repeating these same steps until (x-2) is factored out, we get the quotient as :

[tex]-3x^{2} -6x-7[/tex]

Answer:

Step-by-step explanation:

Alright, lets get started.

Given that:

[tex]\frac{(x^2-4)}{(x+2)}=(x-2)[/tex]

(x-2) could be written as [tex]\frac{x-2}{1}[/tex]

[tex]\frac{(x^2-4)}{(x+2)}=\frac{(x-2)}{1}[/tex]

Doing cross multiply

[tex](x+2)(x-2)=(x^2-4)*1[/tex]

[tex](x+2)(x-2)=(x^2-4)[/tex]

It means the blank part is (x-2)   :    Answer

Hope it will help :)

We are given that the titanic is found 3,797 m below sea level. This is simply equivalent to 3.797 km or 3.8 km when rounded off to one decimal.

We should take note that the letter k in km means kilo and a kilo is equivalent to 1000. So this means that for 1 km there is exactly 1000 m. So to convert, simply multiply a value with unit m with this conversion factor. Conversion factor = 1 km / 1000 m

Depth of titanic = 3,797 m (1 km / 1000 m)

Depth of titanic = 3.797 km = 3.8 km

to find x divide 16 by the sin of 30

16 / sin(30) = 32

 if you need 2 decimal places it would be 32.00

Answer:

16  sin30 = 32

Step-by-step explanation:

You would have to wait approximately 3691.86 years for 1/5 of the radium to disappear, considering its half-life of 1590 years.

The decay of a substance with a half-life can be modeled using the formula [tex]\(N(t) = N_0 \left(\frac{1}{2}\right)^{\frac{t}{T_{\text{half}}}}\)[/tex], where:

- [tex]\(N(t)\)[/tex] is the remaining quantity after time \(t\),

- [tex]\(N_0\)[/tex] is the initial quantity,

- [tex]\(T_{\text{half}}\)[/tex] is the half-life.

In this case, [tex]\(N(t) = \frac{1}{5}N_0\)[/tex] and [tex]\(T_{\text{half}} = 1590\)[/tex] years.

Substituting these values into the formula and solving for \(t\):

[tex]\[ \frac{1}{5}N_0 = N_0 \left(\frac{1}{2}\right)^{\frac{t}{1590}} \][/tex]

Solving this equation yields[tex]\(t \approx 3691.86\)[/tex] years.

Therefore, you would have to wait approximately 3691.86 years for 1/5 of the radium to disappear, considering its half-life of 1590 years.

The expression  4(3x-2)-2(4x+5) in it's simplest binomial form is 4x - 18.

We can classify algebraic expressions in terms of how many terms they have. If an algebraic expression has only one term we call it a monomial, having two terms makes it a binomial and having more than two terms makes it a polynomial

We know a binomial consists of two terms separated by any of the arithmetic operations.

Given,  4(3x-2)-2(4x+5).

First, we will distribute the terms.

= 12x - 8 - 8x - 10.

= 4x - 18.

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Elements in the same Group have the same number of valence electrons.

Elements in the same Period  have the same number of electron shells.

Metallic elements become Less reactive as you move left to right in a period.

Metallic elements become More  reactive as you move top to bottom in a group.

To compute for combinations, we will use the method nCr = n! / r! * (n - r)!

Where: n signifies the number of items, and r signifies the number of items being selected at a time.

Solution

1.       11C5 = 11!/ 5! * (11-5)! = 462 ways

2.       6C5 = 6!/ 5! * (6-5)! = 6 ways

3.       6/462 = 1/77 or 0.1230 is the probability that the selected group will consist of all men.

The calculation involves using combinations to find the total number of ways to select 5 people from 11, and then to find the probability of selecting 5 men by dividing the number of ways to select 5 men from 6 by the total number of selections.

The student's question deals with the topic of combinatorics, specifically the selection of groups and calculation of probabilities using the hypergeometric distribution. To find how many ways 5 people can be selected from a group of 11 (6 men and 5 women), we use the combination formula [tex]C(n, k) = n! / (k!(n-k)!).[/tex]

For the first part of the question, selecting 5 people out of 11, the calculation is C(11, 5). To calculate the number of ways 5 men can be selected from 6 men, we use C(6,5).

Lastly, to find the probability that the selected group will consist of all men, we divide the number of ways to select 5 men by the total number of ways to select 5 people from the whole group:

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