Find an equation of the plane through(1,1,1) that contains the linere presented by the parametric equationsx= 2t;y= 1t;z= 2 3t:

Answer:

Width x length

Step-by-step explanation:

Find the width or how wide it is

Then find the length or how long it is

multiply those

Answer:216

Step-by-step explanation:

The average velocity from t = 2s to t = 4s would be - 48 ft/s.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that an object is thrown upward with initial velocity of 48 feet per second from a high of 120 feet. The height of the object t seconds after it is thrown is given by h(t) = - 16t² + 48t + 120.

Average rate of change of velocity with time is called average velocity. Mathematically -

v{avg.} = Δx/Δt                                                         .... Eq { 1 }

Δx = x(4) - x(2)

Δx = - 16(4)² + 48(4) + 120 - {- 16(2)² + 48(2) + 120}

Δx = - 96

Δt = 4 - 2 = 2

So -

v{avg.} = Δx/Δt = -96/2 = - 48 ft/s

Therefore, the average velocity from t = 2s to t = 4s would be - 48 ft/s.

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In summary, the Fourier coefficients for the periodic function y(t) = -3 on the interval -5 ≤ t ≤ 5 are:

c₀ = -3 (DC component)

cₙ = 0 for n ≠ 0 (other coefficients)

To find the Fourier coefficients of the periodic function y(t) = -3 on the interval -5 ≤ t ≤ 5, we can use the formula for Fourier series coefficients:

cn = (1/T) ∫[t₀-T/2, t₀+T/2] y(t) \(e^{(-i2\pi nt/T)}\) dt

where T is the period of the function and n is an integer.

In this case, the function y(t) is constant, y(t) = -3, and the period is T = 10 (since the interval -5 ≤ t ≤ 5 spans 10 units).

To find the Fourier coefficient c₀ (corresponding to the DC component or the average value of the function), we use the formula:

c₀ = (1/T) ∫[-T/2, T/2] y(t) dt

Substituting the given values:

c₀ = (1/10) ∫[-5, 5] (-3) dt

  = (-3/10) \([t]_{-5}^{5}\)

  = (-3/10) [5 - (-5)]

  = (-3/10) [10]

  = -3

Therefore, the DC component (c₀) of the Fourier series of y(t) is -3.

For the other coefficients (cₙ where n ≠ 0), we can calculate them using the formula:

cₙ = (1/T) ∫[-T/2, T/2] y(t)\(e^{(-i2\pi nt/T) }\)dt

Since y(t) is constant, the integral becomes:

cₙ = (1/T) ∫[-T/2, T/2] (-3) \(e^{(-i2\pi nt/T)}\) dt

  = (-3/T) ∫[-T/2, T/2] \(e^{(-i2\pi nt/T)}\) dt

The integral of e^(-i2πnt/T) over the interval [-T/2, T/2] evaluates to 0 when n ≠ 0. This is because the exponential function oscillates and integrates to zero over a symmetric interval.

all the coefficients cₙ for n ≠ 0 are zero.

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Answer: 50.9091 percent

Answer:

-16

Step-by-step explanation:

-16+11=-5 that's it lol

Answer:

m= -16

Step-by-step explanation:

subtract 11 from both sides

-5 - 11 =m + 11 - 11

combine like terms (-5 - 11 and 11 - 11)

m= -16

To solve the equation 7x, we need to clarify the specific goal or condition. If we are looking for the value of x that makes the equation equal to a specific number, such as 0, the solution would be x = 0. However, if we are solving for x in terms of another variable or in an equation with more components, further information is needed to provide a meaningful answer.

The equation 7x represents a linear equation in one variable, where 7 is the coefficient of x. If we are solving for x in an equation of this form, we need an additional equation or condition to determine a unique solution. Without any further information or constraints, the equation 7x does not have a specific solution.

To provide a more comprehensive explanation, let's consider an example. Suppose we have the equation 7x = 21. To solve for x, we divide both sides of the equation by 7:

7x/7 = 21/7

x = 3

In this case, the value of x that satisfies the equation 7x = 21 is x = 3. We can substitute this value back into the equation to verify its correctness:

7(3) = 21

21 = 21

The equation holds true, confirming that x = 3 is the solution. However, without a specific condition or another equation to work with, the equation 7x on its own does not have a unique solution.

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The domain of the graphed function is [-2, 1) U (5, 9]

STEP - BY - STEP EXPLANATION

What to find?

The domain of the graph function.

What are domains?

Domains are sets of x- values for which the function is defined.

Observe from the graph given, the function are defined for set of all x - values between -2 and 1 with -2 included.

Also the function is also defined for a set of all x-values between 5 and 9 with 9 included.

This can be represented using interval notation as [-2, 1) U (5, 9].

Therefore, the correct option is A.[-2, 1) U (5, 9].

Answer:

133.33

Step-by-step explanation:

In 133.33 years, the principal amount of $500 at the rate of 1.5% per year will triple.

Simple interest is an interest which is only based on principal amount, it does not imply on yearly interest.

Given that,

The principal amount put in the bank p= $500

The rate of simple interest r= 1.5 %

Amount will be triple, implies that, Interest would be two times of principal.

Interest = 2 x 500 = 1000

To find the time t, when amount gets triple, use simple interest formula

Interest = (p x r x t)/100

1000 = (500 x 1.5 x t)/100

200/1.5 = t

133.33 = t

The required time in which the money will triple is 133.33 years.

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The measure of the angle 2 is 133° and the measure of the angle 3 is 47°.

They are a lot of  classifications for angles like: complementary angles, supplementary angles, right angles, and others. See below:

From the figure, it is possible to see that:

- the angles 1 and 3 are supplementary angles

- the angles 2 and 3 are supplementary angles

Therefore, if angle1  is 133°, you have:

angle_1 + angle_3 = 180

133 + angle_3 = 180

angle_3=180-133

angle_3=47°

If angle3  is 47°, you have:

angle_3 + angle_2 = 180

47+ angle_2 = 180

angle_2=180-47

angle_2=133°

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Answer:

Step-by-step explanation:

The statements that are True about the Correlations is , "Correlations are a measure used to determine the degree to which two variables are related" , the correct option is (c) .

In the question,

few statements about Correlation is given ,

we need to find the statement that is True .

we know that , Correlation is the term that is used to measure the degree of relationship between two variable ,

the correlation can be negative , positive or 0 ,

and the negative correlation implies that if one variable increases then other variable decreases and vice a versa .

So , from the above information about Correlation ,

we conclude that , the True statement is "Correlations are a measure used to determine the degree to which two variables are related. "

Therefore , the statement in option (c) is True  .

The given question is incomplete , the complete question is

Select the statement below that is true about correlations.

(a) Correlations can only be negative

(b) Correlations are a measure of how much one variable changes as the other variable changes

(c) Correlations are a measure used to determine the degree to which two variables are related.

(d) Correlations are a measure of causation between two variables

(e) A negative correlation implies no relationship between variables

(f) Correlations can only be positive .

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Answer:

Square

4,4,4

Step-by-step explanation:

Answer:

8,000,000

Step-by-step explanation:

Answer:

x = 12

Step-by-step explanation:

A pair of supplementary angles added together MUST equal 180. Therefore, as you are given two angles with the measures of (4x - 24) and 4(2x - 3), they must add together to equal 180. So, we get this equation:

(4x - 24) + 4(2x - 3) = 180

4x - 24 + 8x - 12 = 180 (we distributed 4(2x-3))

12x - 36 = 180

12x = 144

x = 12, -12

Therefore, x is 12 because -12 would mean that (4x-24) and 4(2x-3) are both negative, which is impossible for an angle measure.

Answer:

66

Step-by-step explanation:

\(\binom{12}{2}=\frac{12!}{10!21}=\frac{12 \cdot 11}{2}=66\)

Answer:

see explanation

Step-by-step explanation:

Using \(\sqrt{-1}\) = i, then i² = (\(\sqrt{-1}\) )² = - 1

and i³ = i² × i = - 1 × i = - i

also

\(i^{4}\) = i² × i² = - 1 × - 1 = 1

We can surmise that i raised to any multiple of 4 will equal 1

Given

\(i^{35}\) ( note 35 = 32 + 3 and 32 is a multiple of 4 ), thus

= \(i^{32+3}\)

= 1 × i³ = - i

The probability of having 7 boys in a family with 7 children is 1 out of 128, as there is only one favorable outcome out of 128 total possible outcomes.

To find the probability, we need to calculate n(E) and n(S).

In this case, event E represents the scenario where all 7 children are boys. The sample space S consists of all possible permutations of boys and girls for the 7 children, which is 2^7 = 128.

This is because each child has 2 possibilities (boy or girl), and we multiply these possibilities for all 7 children.

Since event E includes only one specific outcome (all boys), n(E) is equal to 1. Therefore, both n(E) and n(S) are 1 and 128, respectively. The probability of having 7 boys is given by n(E)/n(S) = 1/128.

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Answer:A) -16

Step-by-step explanation:

Answer:

cool

Step-by-step explanation:

Answer:

No problem happy to help.

Since the number of child tickets sold must be a whole number, we round c to the nearest whole number, which is 28.

Let's assume the number of child tickets sold as c and the number of adult tickets sold as a.

From the given information, we can set up the following equations:

1. The total sales from child tickets is $6.10 multiplied by the number of child tickets sold: 6.10c

2. The total sales from adult tickets is $9.70 multiplied by the number of adult tickets sold: 9.70a

3. Three times as many adult tickets were sold as child tickets: a = 3c

4. The total sales for that day is $985.60: 6.10c + 9.70a = 985.60

Substituting the value of a from equation 3 into equation 4, we get:

6.10c + 9.70(3c) = 985.60

6.10c + 29.10c = 985.60

35.20c = 985.60

c = 985.60 / 35.20

c ≈ 27.955

Since the number of child tickets sold must be a whole number, we round c to the nearest whole number, which is 28.

Therefore, 82 child tickets were sold that day.

In more detail, we start by assigning variables to the number of child tickets and adult tickets sold: c for child tickets and a for adult tickets.

From the given information, we know that the price of a child ticket is $6.10 and the price of an adult ticket is $9.70. We can use these prices to calculate the total sales from child tickets (6.10c) and adult tickets (9.70a).

We are also told that three times as many adult tickets were sold as child tickets, which can be represented as a = 3c.

The total sales for that day is given as $985.60, so we can set up the equation 6.10c + 9.70a = 985.60 to represent the total sales from both child and adult tickets.

Substituting the value of a from the equation a = 3c into the equation 6.10c + 9.70a = 985.60, we can solve for c.

After simplifying and solving the equation, we find that c ≈ 27.955. Since the number of child tickets sold must be a whole number, we round c to the nearest whole number, which is 28.

Therefore, 28 child tickets were sold that day.

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Answer:

Step-by-step explanation:

Given g(x)=5x-4 and g(x)=f^{-1}(x)-3

Substituting g(x) =  5x-4 into the second equation we have;

5x-4 =  f^{-1}(x)-3

f^{-1}(x) = 5x-4+3

f^{-1}(x) = 5x-1

To get f(x), let us first make y to be equal  f^{-1}(x)

y = 5x-1

expressing x in terms of y to get f(x), we have;

5x = y+1

x = y/5+1/5

replacing y with x, we will have;

y = x/5 + 1/5

F(x) = x/5 + 1/5

Comparing x/5 + 1/5 with ax+b, a = 1/5 and b = 1/5

5a + 5b = 5(1/5)+ 5(1/5)

5a+5b = 1+1

5a+5b = 2

Answer:

The fraction is 3/10 = .3

Answer:

  B(-6, 0)

Step-by-step explanation:

You want to find B such that ...

  (B -A) = (3/4)(C -A) . . . . the required distance relation

  4(B -A) = 3(C -A) . . . . . . multiply by 4

  4B = 3C +A . . . . . . . . . . add 4A, simplify

Now, we can solve for B and substitute the given coordinates:

  B = (3C +A)/4 = (3(-6, -2) +(-6, 6))/4 = (-24, 0)/4 = (-6, 0)

The coordinates of point B are (-6, 0).

Answer:

the answer your looking for is (-3,-3)

Step-by-step explanation:

Answer:

x= -1

Step-by-step explanation:

1x+4=3x+6

x+4=3x+6

x+4-4=3x+6-4

x=3x+6-4

x=3x+2

x-3x=3x+2-3x

-2x=2

-2x=2

-2/-2=2/-2

x= -1

Answer:

t ≤ − 4

Step-by-step explanation:

Answer: t ≤ -4

Step-by-step explanation:

rearrange the problem 24-(-6*t)≤0  Pull out like factors :24 + 6t  =   6 • (t + 4)

Divide both sides by 6    Subtract  4  from both sides t ≤ -4

The standard deviation of 5, 9, 9, 1, 5, 7, 6 rounded to the nearest tenth is 2.6.

Step 1: Calculate the mean

Mean = (5 + 9 + 9 + 1 + 5 + 7 + 6) / 7 = 42 / 7 = 6

Step 2: Subtract the mean and square the differences

\((5 - 6)^2\) = 1

\((9 - 6)^2\) = 9

\((9 - 6)^2\) = 9

\((1 - 6)^2\) = 25

\((5 - 6)^2\) = 1

\((7 - 6)^2\) = 1

\((6 - 6)^2\) = 0

Step 3: Calculate the mean of the squared differences

Mean = (1 + 9 + 9 + 25 + 1 + 1 + 0) / 7 = 46 / 7 = 6.5714

Step 4: Take the square root of the mean

Standard Deviation = sqrt(6.5714) ≈ 2.5651

Rounded to the nearest tenth, the standard deviation is approximately 2.6.

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Answer: 98

Step-by-step explanation: Subtract the biggest number from the smallest. 100-2=98

Answer:

Step-by-step explanation: