A particle moves at a constant speed along a line through P= (-1, 6, 7) to point Q = (-4, - 4, - 5). Find the parametric equations for its potions at time t if the partide passes through P at time t = 3 and through point Q at time t = 5
x(t) = y(t) =
z(t) =

Answer:

\(4^{21}\)

Step-by-step explanation:

\(\frac{4^{12}}{4^{-9}}\\\)

Given 4 = a

From the properties of exponents for the example...

\(\frac{a^4}{a^{-2}} = \frac{a*a*a*a}{\frac{1}{a^2} } = (a*a*a*a)*a^2 = a^4 * a^2 = a^{4+2} = a^6\)

Therefore, the answer is....

\(4^{12}*4^{9} = 4^{12+9} = 4^{21}\)

Answer:

Let the two numbers be x and y

Given ,

\(x + y = 95 \: \: ...(1)\)

Also ,

\(y = x + 15 \: \: ...(2)\)

Substiting equation 2 in equation 1 ,

\(x + x + 15 = 95 \\ \dashrightarrow \: 2x + 15 = 95 \\ \dashrightarrow \: 2x = 95 - 15 \\ \dashrightarrow \: 2x = 80 \\ \: \: \: \: dividing \: both \: sides \: by \: 2 \: \\ \dashrightarrow \: \cancel\frac{2x}{2} = \cancel\frac{80}{2} \\ \\ \dashrightarrow \: \: \boxed{ x = 40}\)

Now , y = x + 15

therefore ,

\( y = 40 + 15 \\ \dashrightarrow \boxed{ y = 55 } \)

Hence ,

the two numbers are 40 and 55 .

hope helpful! :)

Answer:

n=21

Step-by-step explanation:

We must find n.

Remember PEMDAS. First we must do the Parentheses. Lets do distributive property by multiplying a number that is immediately outside the parentheses with each number inside the parentheses. Lets do this one side at a time.

First lets do 5(n - 7). We get 5n - 35

Now 2(n + 14) is 2n + 28

Okay...... now we have \(5n-35=2n+28\)

Now lets do OPPOSITES!!!! We must do the opposite of each thing to both sides.

The opposite of -35 is positive 35. Lets add 35 to both sides. We get:

\(5n=2n+63\)

Now lets do the opposite of 2n which is -2n

\(3n=63\)

this is looking quite nice isnt it..........

The opposite of 3 times n is 3 DIVIDED BY n. So lets divide both sides by 3

\(n=21\)

amazing.......

Answer:

608.33

Step-by-step explanation:

Figure 4 is the image of square LMNP after the translation (x,y) -> (x + 5, y - 3).

The four translation rules are defined as follows:

The translation rule in the context of this problem is given as follows:

(x,y) -> (x + 5, y - 3).

Hence the translation is defined as follows:

Hence Figure 4 is the image of square LMNP after the translation (x,y) -> (x + 5, y - 3).

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Answer:

opotion has not correct answer

answer is 15.

Answer:

\(3^\frac{7}{10}\)    or      \(\sqrt[10]{3^7}\)

Step-by-step explanation:

\(\left(\sqrt{3}\right)\left(\sqrt[5]{3}\right)=\sqrt[10]{3^7}\quad\)

(√3)(\(\sqrt[5]{3}\)) = √3 · \(\sqrt[5]{3}\)

{√3 = \(3^{\frac{1}{2}}\)}                 {radical rule: \(\sqrt{x}=x^1^/^2\)}

\(\sqrt3\)\(\sqrt[5]{3}\) =  \(3^{\frac{1}{2}}\) · \(\sqrt[5]{3}\)

{\(\sqrt[5]{3}\) = \(3^{\frac{1}{5}}\)}                  {radical rule: \(\sqrt[n]{x} = x^1^/^n\)}

 \(3^{\frac{1}{2}}\) · \(\sqrt[5]{3}\) =   \(3^{\frac{1}{2}}\) · \(3^{\frac{1}{5}}\)     {exponent rule:  \(a^x*a^y=a^x^+^y\)}

                (1/2 + 1/5 = 5/10 + 2/10 = 7/10)

              \(=3^\frac{7}{10}\)        {opposite of radical rule: \(\sqrt[n]{x} = x^1^/^n\) ;  \(x^\frac{a}{b}=\sqrt[b]{x^a}\)}

             = \(\sqrt[10]{3^7}\)

so, the simplified version of this equation can either be written as:

\(3^\frac{7}{10}\)    or      \(\sqrt[10]{3^7}\)

hope this helps!!

(I can't clearly see the last option, but if it's either of these, then it's correct)

Answer:

30/x

Where x is the number

Answer:

there is no table so we are therefore unable to answer this question

Step-by-step explanation:

sorry

Answer:

A straight line dividng the data into two equal parts.

Step-by-step explanation:

A scatter plot is drawn by representing  the numbers with the dots on the specific points to interpret their values.The best line of fit for scatter plot data is a straight line. It divides the data  into two parts. Some points may lie above the  data and some below the data. Some points may lie on the line. All the points can also lie on the line and none of the points can also lie on the line.

Answer:

120 degrees because angles on a straight line add up to 180 degrees

An equation for the function graphed above is \(y = \frac{12(x - 1)}{(x + 3)(x - 4)}\).

In Mathematics and Geometry, the vertical asymptote of a function simply refers to the value of x (x-value) which makes its denominator equal to zero (0).

By critically observing the graph of the rational function shown above, we can logically deduce that its vertical asymptotes include the following;

x = -3 ⇒ x + 3 = 0.

x = 4 ⇒ x - 4 = 0.

In this context, an equation that represent its denominator is given by the following quadratic function:

Q(x) = (x + 3)(x - 4)

Assuming the leading coefficient of the function P(x) is represented by a;

P(x) = a(x - 1)

By evaluating and solving for the leading coefficient "a" in this function, we have;

f(x) = P(x)/Q(x)

f(x) = a(x - 1)/[(x + 3)(x - 4)]

f(0) = a(0 - 1)/[(0 + 3)(0 - 4)]

f(0) = -a/[(3)(-4)]

f(0) = a/12

Since the y-intercept of this graph is located at (0, 1), the value of the leading coefficient (a) is given by;

1 = a/12

1 = a/12

a = 12 × 1

a = 12

By substituting the value of the leading coefficient (a) into the function, we have the following;

f(x) = P(x)/Q(x)

f(x) = y = 12(x - 1)/[(x + 3)(x - 4)]

\(f(x) = y = \frac{12(x - 1)}{(x + 3)(x - 4)}\)

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Answer:

$(x - 1425)/3

Step-by-step explanation:

Let total monthly budget be x

Amount spent on mortgage = $1425

Remaining balance after spending on mortgage = x - $1425

Amount spent on recreational activities = one-third of the balance

Expressing amount spent on recreational activities as an equation will give;

Amount spent on recreational activities = 1/3 of x - $1425

= 1/3 × ( x - $1425)

= ( x - $1425)/3

Hence the required equation is;

R = $(x - 1425)/3

R means recreational activities

We want to write an equation for the amount of money that she uses on recreational activities.

The equation is: r(x) = (1/3)*(x - $1,425).

We know that her total monthly budget is x dollars.

She spends $1,425 on her mortgage.

So the remaining budget is (x - $1,425).

We know that she uses one-third of it on recreational activities, then the equation we want is just:

r(x) = (1/3)*(x - $1,425).

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Step-by-step explanation:

Assuming that the company only consists of men and women, then the ratio of women to the total number of employees in the company is 5 : (7 + 5) = 5 : 12.

Since there are 140 women working for the company, there are 140 * 12/5 = 336 employees.

There are 840 ways for NASA to make this selection. Total number of ways melissa and wade can sit together is 96.

We can use the combination formula to solve this problem. The number of ways to choose 2 men from 6 is C(6,2) = 15, and the number of ways to choose 3 women from 8 is C(8,3) = 56. To find the total number of ways to make the selection, we multiply these values together: 15 x 56 = 840.

To solve this problem, we can treat Melissa and Wade as a single unit and then arrange the other 3 people and the Melissa-Wade unit in 4 seats. There are 4 ways to arrange Melissa and Wade (MW, WM, AMW, WMA). After that, we have 4 seats left, and we need to arrange 3 people (Anna, Chris, and Nora) and the Melissa-Wade unit in those seats. There are 4 people to arrange in 4 seats, so there are 4! = 24 ways to do this. Therefore, the total number of ways to seat Melissa and Wade together is 4 x 24 = 96.

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The trucking company will need 12 truckloads to move the pile of pebbles.

How to find the volume of the cone?

The volume of a cone can be calculated using the formula:

V = (1/3)πr²h

where V is the volume, r is the radius of the base, h is the height, and π is a constant approximately equal to 3.14.

We are given that the pile of pebbles has a height of 10 yards and a base diameter of 6 yards, which means that the radius is 3 yards.

We can use these values to calculate the volume of the pile:

V = (1/3) × 3.14 × 3² × 10

V = 94.2 yd³

Therefore, the pile has a volume of 94.2 cubic yards.

If each truck holds 7.85 yd³ of pebbles, the number of truckloads required can be calculated by dividing the total volume of the pile by the volume of each truck:

Number of truckloads = Volume of pile / Volume of each truck

Number of truckloads = 94.2 / 7.85

Number of truckloads = 12

Therefore, the trucking company will need 12 truckloads to move the pile of pebbles.

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Answer:

x = 21

Step-by-step explanation:

4x = 84

Divide each side by 4

4x/4 = 84/4

x = 21

Answer:

x = 21

Step-by-step explanation:

84/4 = 21

x=21

Answer:

-0.544m

Step-by-step explanation:

The height of the barnacle is approximately is, 0.657 meters.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

We are given that;

Graph y = sin(x)

Boat travel= 7m

Now,

Let y be the height of the barnacle and x be the distance the boat has traveled

i.e, x = 7 meters

to find the height y :

Substitute the value of x =7 meters in [1] we have;

y = sin(7)

≈0.657.

Therefore, by algebra the answer will be 0.657 meters.

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The base change property is useful in simplifying equations where the logarithmic terms have different base. In order to solve an equation containing logarithmic functions, all the logarithmic terms should have the same base.

Examples given below:

Answer:

Mr. Holms used 1/10 of the whole carton for each serving.

Step-by-step explanation:

Mr. Holms used 4/5 of the carton, which means he has 1/5 of the carton remaining from a whole carton and if he divides 1/5 among 2 servings he gets 1/5 divided by 2 is 1/10.

Check Your Answer: 4/5 divided among 2 servings would be 4/5+ 1/10 + 1/10 = 8/10 + 1/10 + 1/10 = 10/10 = 1 whole carton.

Gigi makes a scale drawing of a patio the drawing, The two scales are

This is further explained below.

Generally, In mathematics, a dimension is a measurement that may be taken in one direction to determine the size or distance of an item, area, or space.

To put it another way, it is the process of determining the dimensions of anything by calculating its length, breadth, and height.

Actual ratio measurements with a scale of 1

For the Lenght

Length=7 cm

Length =7*5

Lenght=35 ft

Width=5 cm

Width=5*5

Width=25 ft

Therefore

The dimensions are 35 ft by 25 ft

Find the actual dimensions of a ratio with the scale 2

A scale of 2 is equal to

1 cm/8 ft

For Length=7 cm

L=7*8

L=56 ft

For Width=5 cm

W=5*8

W=40 ft

In conclusion, The dimensions are 56ft by 40f

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Answer:

8.808 kilometers

Step-by-step explanation:

Think about it like this: The kilometers run and the kilometers needed to be run would add to ten. Therefore the equation is this:
1.192 + x = 10

To isolate the variable ("x"), we need to subtract 1.192 from 10.

x = 10 - 1.192

x = 8.808

The total spending figures indicate that Joe's demand for pizza is elastic as his total spending decreases when the price decreases, suggesting he is responsive to price changes.

a. The demand curve for Joe's pizza can be plotted by using the equation Q = 30 - 2P, where Q represents the quantity of pizza consumed and P represents the price per slice.

On the graph, the vertical axis represents the price (P), and the horizontal axis represents the quantity (Q). The vertical intercept occurs when Q is 0, which corresponds to P = 15. The horizontal intercept occurs when P is 0, which corresponds to Q = 30.

b. The total spending on pizza at P = 5 is $100, and the total spending at P = 4 is $88. This information indicates that Joe's total spending decreases as the price of pizza decreases.

Based on this, we can infer that Joe's elasticity of demand for pizza between P = 5 and P = 4 is elastic. When the price decreases from $5 to $4, the total spending decreases, indicating that the demand is responsive to price changes.

c. When P = 9, we can substitute this value into the demand function to calculate the corresponding quantity: Q = 30 - 2(9) = 30 - 18 = 12. To calculate Joe's consumer surplus, we need to find the area of the triangle formed by the demand curve and the price line.

The consumer surplus is given by (1/2) ˣ  (9 - P) ˣ  Q = (1/2) ˣ (9 - 9) ˣ  12 = 0.d. If the price of pizza rises to $15 per slice, we can again substitute this value into the demand function to find the corresponding quantity: Q = 30 - 2(15) = 30 - 30 = 0.

Joe's consumer surplus at this new price would be zero since he is not consuming any pizza at that price, resulting in no surplus.

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The mean is 18.6.

Given the following information; z = 2.25, x = 22.2, and σ = 1.6, to find the mean, we have to apply the formula for z-score. z = (x - μ)/σWhere; z-score is represented by z, the value of X is represented by x, the mean is represented by μ and the standard deviation is represented by σSubstituting the values into the equation above;2.25 = (22.2 - μ)/1.6Multiplying both sides of the equation by 1.6, we have;1.6(2.25) = (22.2 - μ)3.6 = 22.2 - μ Subtracting 22.2 from both sides of the equation;3.6 - 22.2 = - μ-18.6 = - μ Multiplying both sides of the equation by -1, we have;μ = 18.6

Simply said, a z-score, also known as a standard score, informs you of how far a data point is from the mean. Technically speaking, however, it's a measurement of how many standard deviations a raw score is from or above the population mean.

You can plot a z-score on a normal distribution curve. Z-scores range from -3 standard deviations, which would fall to the extreme left of the normal distribution curve, to +3 standard deviations, which would fall to the far right. You must be aware of the mean and population standard deviation in order to use a z-score.

The z-score can show you how that person's weight compares to the mean weight of the general population.

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Answer:divide 69.00 by 3 and do the same for the others

Step-by-step explanation:

Answer:

\(a_{n}\) = 5n

Step-by-step explanation:

There is a common difference d between consecutive terms

d = 10 - 5 = 15 - 10 = 20 - 15 = 25 - 20 = 30 - 25 = 5

This indicates the sequence is arithmetic with explicit formula

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 5 and d = 5 , then

\(a_{n}\) = 5 + 5(n - 1) = 5 + 5n - 5 = 5n

Let us assume that the starting temperature is x ℉.

According to the problem statement:

Over a period of 6 hours, the temperature rose 4℉, rose 3℉ more, dropped 2℉, rose 1℉, dropped 2℉, and then dropped 3℉ more.

So, the temperature will increase by 4 + 3 + 1 = 8℉ in total and decrease by 2 + 2 + 3 = 7℉ in total.

And the net increase in temperature will be 8 - 7 = 1℉.

Let the final temperature after all these changes be y ℉.

Therefore, y = x + 1℉

We are also given that the temperature at the end of the 6-hour periods was -5℉.

Therefore,

we can write: y = -5 ℉ = x + 1℉- 6℉ = x=> Starting temperature is -6℉.

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Answer:

24 feet

Step-by-step explanation:

12 ÷ 18=16/y

2y=3*16

y=24

The expression \(-2\vec C+6\vec D\) in the ordered pair notation is (16,-16).

The vector components of a vector are represented as the ordered pair of its x and y components.

For example, if a vector has x - component 'a' and y- component 'b' , then the ordered pair notation for the vector is (a, b), where the vector is \(a \vec i+b \vec j\).

Now the vector C has its x- component = -2

y- component of C = -1

Therefore, ordered pair notation of C = (-2, -1)

x- component of D = 2

y-component of D = -3

Therefore, ordered pair notation of D = (2,-3)

So the expression  \(-2\vec C+6\vec D\) = -2 (-2,-1) +6 (2,-3) = (4,2) + (12, -18)

= (16, -16)  in the ordered pair notation.

That is, the vector \(\bold {-2\vec C+6\vec D}\) is a vector with x-component 16 and y-component -16.

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The objective of this research is to collect data on a specific component of the off-campus student population.The amount of time they spend travelling to courses each week.

a) The population for this study is all off-campus students at this college, and the sample is a random sample of 45 off-campus students who are polled. The sample is chosen at random to be representative of the entire population.

b) The data being gathered is the amount of time the surveyed students spend each week travelling to school. Because it reflects a numerical measurement, this is quantitative data. This information will be used to calculate the average commuting time for off-campus students and to identify any possible concerns or areas for improvement in commuting.

c) This is a descriptive research, since it seeks to characterise and summarise the features of the off-campus student population in terms of commuting time. The study's purpose is to better understand off-campus students' commuting patterns and gather ideas into how to enhance their commuting experience.

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