find the curvature of r(t) = 3t, t2, t3 at the point (3, 1, 1).

0.688 will be the probability of getting a nickel from the jar.

Given,

Probability;-

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

Here,

The number of fortunate situations divided by the total number of coins would be the product between the probability of each occurrence and the likelihood of each event.

Therefore,

P(nickel) = 19/69

P(penny) = 17/68

That is,

P = 19/69 × 17/68

P = 323/4692

P = 0.0688

That is,

The probability of getting nickel from the jar is 0.06888

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Answer: see below

Step-by-step explanation:

The denominator of the equations cannot equal zero.

a. [tex]9+y^{2}[/tex] [tex]= 0[/tex]

[tex]y^{2} = -9[/tex]

[tex]\sqrt{y^{2} } = \sqrt{-9}[/tex]

[tex]y=-3i,3i[/tex]

The domain is all real numbers.

D:xE(−∞,∞)

b.3x(x+12)=0

3x=0, x+12=0

x=0,x=-12

D:xE(−∞.-12) U (-12,0) U (0,∞)

c.(a+1)(a-4)=0

a+1=0, a-4=0

a=1, a=4

D:xE(−∞.1) U (1,4) U (4,∞)

Answer:

x=12

Step-by-step explanation:

5x-4 is vertically opposite and 124 + 5x-4 should add up to 180 because they are cointerior anglesthen you look for the value of x by 124+5x-4=180

124-4+5x-4=180

x=12

Answer: B

Step-by-step explanation:

Let's pick 2 points ( 0,80) ( 5, 70)

The rate of change or slope is rise/run

We see that the y decrease by 10 and x increases by 5, so the slope is

-10/5 = -2 ft/s

So the aswer is B

Answer:

lol

Step-by-step explanation:

hahahaha

Answer:

No

Step-by-step explanation:

The cost of running six seminars is [tex]10000+1500+6(400+250)=\$15400[/tex].

The revenue earned is about [tex]1500(6)=\$9000[/tex].

Since the revenue is significantly less than the cost, there will not be a profit.

Answer:

Step-by-step explanation:

You want the equations of the graphed parallel lines with y-intercepts of 2 and -1, and a rise/run of 3/1.

The slope-intercept form equation with slope m and y-intercept b is ...

  y = mx +b

Each of these lines rises 3 units for each 1 unit to the right, so has a slope of ...

  m = rise/run = 3/1 = 3

The red line crosses the y-axis at y=2, so its equation is ...

  y = 3x +2

The blue line crosses the y-axis at y=-1, so its equation is ...

  y = 3x -1

When it comes to researching bats in captivity, we expect the sample size to be small for a few reasons.

Firstly, there may be a limited amount of time that bat keepers are able to devote to this activity due to other obligations. Secondly, we would not want to unnecessarily stress the animals by collecting too many samples. Lastly, there is a limited number of bats in captivity, so the sample size will be small.

On the other hand, there are many bats in the wild, which means that the sample size does not have to be small. Researchers can take advantage of this by collecting data from a larger sample size. However, researchers must be mindful of the impact that their research may have on the environment, and the stress that it may cause the animals.

In conclusion, the sample size for studying bats in captivity is likely to be small due to the limited amount of time that bat keepers can devote to this activity, the need to avoid unnecessarily stressing the animals, and the limited number of bats in captivity. On the other hand, a larger sample size is possible when studying bats in the wild, but researchers must be mindful of the impact of their research on the environment and the animals.

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Answer: y=-(1/4)x+5

Step-by-step explanation:

(-4,6)   (4,4)

                    [tex]\boxed {\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1} }[/tex]

x₁=-4    x₂=4    y₁=6    y₂=4

Hence,

[tex]\displaystyle\\\frac{x-(-4)}{4-(-4)}=\frac{y-6}{4-6} \\\\\frac{x+4}{4+4}=\frac{y-6}{-2} \\\\\frac{x+4}{8} =\frac{y-6}{-2} \\[/tex]

Multiply both parts of the equation by -2:

[tex]\displaystyle\\-\frac{x+4}{4} =y-6\\\\-\frac{1}{4}x -1=y-6\\\\-\frac{1}{4} x-1+6=y-6+6\\\\-\frac{1}{4} x+5=y\\\\Thus,\ y=-\frac{1}{4} x+5[/tex]

The sales tax percentage of cookie jar is 1.6% .

           (sales tax / total cost of the item) x 100 = sales tax rate

To find the sales tax percentage:

Here given,

Total cost = $1.62

Gross price = $1.60

Tax amount = $1.62 - $1.60

                    = $0.02

By substracting the tax amount from total cost,

$1.62 - $0.02

= $1.6

The sales tax percentage = 1.6%.

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Answer:

A. Same-side interior angles

Step-by-step explanation:

Same-side interior angles are angles that has same-side interior angles sum up to 180 degrees. So, the answer is A.

Answer: A. Same side interior angles

Step-by-step explanation:

because they are inside the parralel lines and they are on the same side of the line going across them

The details of the angles in the diagram used to prove the congruency of the triangles ΔABC ≅ ΔCDA  indicates;

Statements                                               [tex]{}[/tex]   Reasons

1.  ∠D ≅ ∠B                                             [tex]{}[/tex]  1. Given

∠ACB ≅ ∠CAD

2. Therefore; ∠ACD ≅ ∠CAB               [tex]{}[/tex]  2. Angle sum property of a triangle

3.  [tex]\overline{AC}[/tex] ≅ [tex]\overline{AC}[/tex]                             [tex]{}[/tex]               3. Reflexive property

4. ΔABC ≅ ΔCDA   [tex]{}[/tex]                                4. ASA congruency rule

Therefore, the completed flowchart is presented as follows;

∠D ≅ ∠B                   [tex]{}[/tex]              ∠ACB ≅ ∠CAB                [tex]{}[/tex][tex]\overline{AC}[/tex] ≅ [tex]\overline{AC}[/tex]

∠ACB ≅ ∠CAB                       Angle sum property        Reflexive prop

Reason; Given

            [tex]{}[/tex]                             ΔABC ≅ ΔCDA

                                        [tex]{}[/tex]

What are congruent triangles?

Triangles are congruent if the three sides on both triangles are congruent or if two angles and a non included side in one triangle are congruent to two angles and a non included side of the other triangle

The details of the reasons used to prove the ΔABC ≅ ΔCDA are as follows;

Angle sum property of a triangle

The angle sum property of a triangle indicates that the sum of the three interior angles of a triangle is 180°

Reflexive property

Reflexive property of congruency states that a geometric figure is congruent to itself.

ASA congruency rule

The Angle-Side-Angle, ASA, congruency rule states that the if two angles and a non included side of one triangle are congruent to two angles and a non included side of the other triangle, then both triangles are congruent

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Answer:

Step-by-step explanation:

2x - 3(6x - 3) = 25

2x - 18x + 9 = 25

-16x + 9 = 25

-16x = 16

x = -1

y = 6(-1) - 3 = -6 - 3 = -9

(-1, -9)

there are 15 different ways to form a committee of 6 people from the department if the number of men in the committee is less than the number of females in the committee by combination.

There are 15 different ways to form a committee of 6 people from the department if the number of men in the committee is less than the number of females in the committee. This is because the number of possible combinations of 6 people with varying numbers of men and women is equal to the number of combinations of 6 people with 1 more female than male, plus the number of combinations of 6 people with 1 more male than female (which is equal to the number of combinations of 6 people with 1 more female than male).

Mathematically, this can be expressed as:

Number of combinations = (number of 6-person combinations with 1 more female than male) + (number of 6-person combinations with 1 more male than female)

Number of combinations = (6C4 x 5C2) + (6C5 x 5C1)

Number of combinations = 15

Therefore, there are 15 different ways to form a committee of 6 people from the department if the number of men in the committee is less than the number of females in the committee.

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Answer:

graph C

Step-by-step explanation:

if x ≥ 0

2x + 1 < 5

2x < 5 - 1

2x < 4

2/2 x < 4/2

x < 2

0≤ x < 2

if x < 0

2 (-x) + 1 < 5

-2x < 5 - 1

-2x < 4

-2/-2 x > 4/-2

x > -2

-2 < x < 0

final solution

-2 < x < 2

By complex and real number properties, the resulting electric resistance is equal to R' = 47 / 270 + i 4 / 45 ohms.

Complex numbers are numbers of the form z = a + i b, where a, b are real numbers. The first component is the real component and the second one is the complex one. In this problem we find the case of a combination of two electric resistances described by two complex numbers. This expression must be simplified by means of real number and complex number properties:

R' = 1 / R₁ + 1 / R₂

If we know that R₁ = 4 + i 6 and R₂ = 2 - i 4, then the resulting electric resistance is:

1 / (4 + i 6) + 1 / (2 - i 4)

(4 - i 6) / [(4 + i 6) · (4 - i 6)] + (2 + i 4) / [(2 - i 4) · (2 + i 4)]

(4 - i 6) / (16 - i² 36) + (2 + i 4) / (4 - i² 16)

(4 - i 6) / (16 + 36) + (2 + i 4) / (4 + 16)

(4 - i 6) / 52 + (2 + i 4) / 20

(2 - i 3) / 27 + (1 + i 2) / 10

47 / 270 + i 4 / 45

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Tom’ mot recent book earned 10*4 time a much money a hi firt book. then The amount that Tom’s most recent book earn is 10^7.

How to illustrate the exponent?

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.

Since Tom’s most recent book earned 10*4 times as much money as his first book which was 10³.

The total amount of the recent book will be:

= 10⁴ × 10³

= 10^(4 + 3)

= 10^7

The amount is 10^7.

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The definite integral of the function f shown in the graph below, over the limits from 0 to 3.

In the given question, we have to find the definite integral of the function f shown in the graph below, over the limits from 0 to 3.

On the interval [a, b], the definite integral of a real-valued function f(x) with respect to a real variable x is written as

[tex]\int^{b}_{a}f(x)dx = f(b) - f(a)[/tex]

Any function's definite integral can be written as the upper limit of a sum or, if an anti-derivative F exists for the interval [a, b], as the difference between the values at the points a and b.

[tex]\int^{3}_{0}f(x)dx[/tex] = Area under the curve from 0 to 3

[tex]\int^{3}_{0}f(x)dx[/tex] = 1/2 ×3×12

[tex]\int^{3}_{0}f(x)dx[/tex] = 18

Hence, the definite integral of the function f shown in the graph below, over the limits from 0 to 3 is 18.

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Answer:

8 students

Step-by-step explanation:

Let's say there are x students in the theater club. We can set up the following equations to represent the information given in the problem:

We are told that there are 70 students in the theater club, so we can substitute 70 for x in the equations above to find the number of students in each show:

Therefore, there will be 8 students in the first show.

Answer:

l = S / (2*pi*r)

[tex]l = \frac{S}{2\pi r}[/tex]

Step-by-step explanation:

S = 2 pi * r * l

Then:

l = S / (2*pi*r)

l = length

pi = 3.1416

r = radius

S = surface

Answer:

x ≤ 25/7

Step-by-step explanation:

3.5x + 5.5 ≤ 18

3.5x ≤ 18 - 5.5

3.5x ≤ 12.5

x ≤ 12.5/3.5

x ≤ 25/7

Answer: Yes, they can.

Step-by-step explanation: Since quarters weigh 0.2 oz. 1 dollar weighs 0.8 oz. 0.8x150=120oz. 120ozs is about 7.5 pounds, so yes.

Answer: Yes.

Step-by-step explanation:

1.7 divided by 1.700 is 1

Answer:

$4950

Step-by-step explanation:

100-45 = 55

55% × 9000 = 4950

Answer:

Therefore, the value of "a" could be 23 or -7 in order for the two points (-5,8) and (3,a) to be 17 units apart.

Step-by-step explanation:

To find the value of "a" such that the two points (-5,8) and (3,a) are 17 units apart, we can use the distance formula to calculate the distance between the two points.

The distance formula is:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Plugging in the values for x1, y1, x2, and y2, we get:

distance = sqrt((3 - (-5))^2 + (a - 8)^2)

Simplifying the expression, we get:

distance = sqrt((8)^2 + (a - 8)^2)

distance = sqrt(64 + (a - 8)^2)

Since the distance between the two points is 17 units, we can set the expression equal to 17 and solve for "a":

sqrt(64 + (a - 8)^2) = 17

64 + (a - 8)^2 = 289

(a - 8)^2 = 225

a - 8 = 15 or a - 8 = -15

a = 23 or a = -7

Answer: 23 or -7

Step-by-step explanation:

The distance formula is:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Plugging in the values for x1, y1, x2, and y2, we get:

distance = sqrt((3 - (-5))^2 + (a - 8)^2)

Simplifying the expression, we get:

distance = sqrt((8)^2 + (a - 8)^2)

distance = sqrt(64 + (a - 8)^2)

Since the distance between the two points is 17 units, we can set the expression equal to 17 and solve for "a":

sqrt(64 + (a - 8)^2) = 17

64 + (a - 8)^2 = 289

(a - 8)^2 = 225

a - 8 = 15 or a - 8 = -15

a = 23 or a = -7

For the equation -3x - 20 to have an infinite solution, it should be equal to -3x + 20 = -3x + 20, so the blank will be + 20

Given the data in the question,

Let the equation be - 3x + 20 = - 3x blank

These situations could be turned into producing an infinite number of solutions only if the lines are coincident and have the same y-intercept.

The quantities being coincident demonstrates the equality of the expressions printed on the left and right sides.

The lines with the same slopes are equal lines.

If the lines are making equal patterns, they will be giving infinite answers as output. As we can see in the result the equations are containing infinite solutions.

So, the missing blank will be = +20 to make the equation have infinite solutions.

Therefore, the value of the blank will be +20 and the equation will be =

- 3x + 20 = - 3x + 20

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The median charge is $51. The median of a data set is also called the middle value.

Median is the value of the middle point in a data set. Here is how to find the median.

A sample of the paramedical fees:  $55, $49, $50, $45, $52, and $55. Find the median!

The number of the data is 6.

Let's sort the data form the smallest!

$45, $49, $50, $52, $55, $55

The middle part of the data is $50 and $52. The median is

($50 + $52)/2 = $102/2 = $51

Hence, the median of the data is $51.

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The Power series representation of f(x) = [tex]x^8tan^-^1x^3[/tex] is [tex]$$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^6^n^+^1^1}{2n+1}[/tex]

The Maclaurin series expansion method can be used to get the power series of such functions if the function has a composite part, such as the multiplication or quotient form.

An infinite series in mathematics known as a "power series" can be compared to a polynomial with an infinite number of terms.

The Maclaurin series will be used in this instance to expand the function:

[tex]tan^-^1x[/tex] = [tex]$$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^2^n^+^1}{2n+1}[/tex]

and for    [tex]tan^-^1x^3 = $$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{(x^3)^2^n^+^1}{2n+1}[/tex]

=>  [tex]tan^-^1x^3 = $$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^6^n^+^3}{2n+1}[/tex]  -------(i)

and f(x) = [tex]x^8tan^-^1x^3[/tex]

now we need to multiply [tex]x^8[/tex] in the above equation to get the power series expansion of f(x)

[tex]x^8tan^-^1x^3[/tex] = [tex]x^8[/tex] [tex]$$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^6^n^+^3}{2n+1}[/tex]

=> [tex]$$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^6^n^+^3^+^8}{2n+1}[/tex]

=>  [tex]$$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^6^n^+^1^1}{2n+1}[/tex]

so the expansion of f(x) = [tex]x^8tan^-^1x^3[/tex] is [tex]$$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^6^n^+^1^1}{2n+1}[/tex]

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Mariol pays $12 for a pound of cheese and a pound of sausage, and $42 for 4 pounds of cheese and 1 pound of sausage.

To solve this problem, we can apply simple algebra. Let's use the letter for the initial, C for a pound of cheese, and S for a pound of sausage.

3 C + 3 S = $36

If the sausage cost $2.00 per pound, so

3 C + 3 ($2) = $36

3 C + $6 = $36

To know the price for a pound of cheese, do as follow

3 C = $36 - $6

3 C = $30

1 C = $30 : 3 = $10

Thus, 1 pound of cheese and 1 pound of sausage would be $2 + $10 = $12

Moreover, if 4C + 1S = 4($10) + 1($2) = $40 + $2= $42

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Answer:

-------------------------------

Parallel lines have equal slopes.

Given line has a slope of m = 1/5.

Use point-slope form and the coordinates of the point (5, - 4) find the parallel line:

Correct choice is D.