Find all values of k for which the function y=sin(kt) satisfies the differential equation y′′+19y=0. separate your answers by commas.

Answers

Answer 1

For  all values of k for which the function y=sin(kt) satisfies the differential equation y''+19y=0.

A differential equation is an equation which contains one or more terms and the derivatives of one variable (i.e., dependent variable) with respect to the other variable (i.e., independent variable) dy/dx = f(x) Here “x” is an independent variable and “y” is a dependent variable.

The given differential equation is

y'' + 19 y= 0

The following function satisfy the differential equation

y = sin(kt)

Differentiating twice with respect to t,

y'' = - k^2  sin(kt)

Putting the value in differential equation given above, we get

- k^2 sin(kt) + 19  sin(kt) = 0

k^2 = 19 ⇒ k = +/- sqrt(19).

points to know

(sin(at))'=acos(at)

and (cos(at))'=-asin(at)

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Related Questions

4 Four boys and five girls went to the movies together. Between them they
had $120 to spend. Tickets cost $8 each. How much money did they have
to buy refreshments?

Answers

48. Because 8 x 9 = 72, then subtract 120 - 72, you get 48. Hope this helps.

Mick drew the following steps using parallel lines. What is the measure of z?

Answers

Answer:

Step-by-step explanation:

The top left angle = 52⁰ - also right angle = 52⁰.  ( alternate angles of parallel l;ines).

So, x = 180 - 2(52) = 180-104

= 76 degrees.

4. For a process quality characteristics, the specification limits are 0.4037 +/- 0.0013 (that is from 0.4024 to 0.4050). The following data gives the data for 14 measurement data sets, each data set is a subgroup of 5 measurement. The value is recorded in the units of 0.0001 (that is, the specification limit will be considered 24 to 50) Based on the following data, compute Cp,Cpk,Pp and Ppk.(Use MINITAB is ok) and determine if the capability of the process. Subgroup Subgroup # 1 2 3 4 5 # 1 2 3 4 5 . 1 36 35 34 33 32 34 28 35 34 38 . 2 31 31 34 32 30 36 35 37 34 33 . 3 30 30 32 30 32 30 37 33 34 35 . 4 32 33 33 32 35 38 31 33 33 33 . 5 32 34 37 37 35 33 30 34 33 35

Answers

If the calculated Cp and Cpk values are greater than 1, the process is considered capable. If Pp and Ppk are greater than 1, the process is considered capable.

To calculate Cp, Cpk, Pp, and Ppk using MINITAB, you would need to input the data into the software and run the appropriate statistical analysis.

Cp and Cpk are measures of a process's capability, they are calculated as follows:

Cp = (USL - LSL) / (6*σ)Cpk = min(Cpu, Cpl)

Where,

USL and LSL are the upper and lower specification limitsσ is the standard deviation of the process.

Pp and Ppk are similar to Cp and Cpk, but they are calculated using the range of the data instead of the standard deviation.

Pp = (USL - LSL) / (4*R)Ppk = min(Ppu, Ppl)

Where R is the range of the data.

If the calculated Cp and Cpk values are greater than 1, the process is considered capable. If Pp and Ppk are greater than 1, the process is considered capable.

It is worth noting that Capability analysis can only be performed on stable and in-control processes. If the process is not in control, analyzing process capability is not meaningful.

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consider the following input-output table. p q r s 1 1 1 0 1 1 0 1 1 0 1 0 1 0 0 0 0 1 1 0 0 1 0 1 0 0 1 0 0 0 0 0 the output column, s, was created from the student id 21444368 using the algorithm: if id digit n (left-to-right) is an even integer, place a 0 in s, row n (top-down) if id digit n (left-to-right) is an odd integer, place a 1 in s, row n (top-down) create a similar table, but with s reflecting the result of the algorithm applied to your student id (do this on scratch paper). on the quiz essay: record your student id, id

Answers

The output column, S, of the given input-output table was created from the student ID 21444368 using an algorithm where if the student ID digit is an even integer, a 0 is placed in the corresponding row of column S, and if the student ID digit is an odd integer, a 1 is placed in the corresponding row of column S.

Student ID: 81725225

P Q R S

1 1 1 0

1 1 0 1

1 0 1 1

0 1 0 0

0 0 1 1

0 1 1 0

0 0 0 1

Student ID: 81725225

P: The first digit of my student ID is 8 so it is an even integer, therefore I place a 0 in row 1 of column P.

Q: The second digit of my student ID is 1 so it is an odd integer, therefore I place a 1 in row 2 of column Q.

R: The third digit of my student ID is 7 so it is an odd integer, therefore I place a 1 in row 3 of column R.

S: The fourth digit of my student ID is 2 so it is an even integer, therefore I place a 0 in row 4 of column S.

The resulting table is:

P Q R S

1 1 1 0

1 1 0 1

1 0 1 1

0 1 0 0

0 0 1 1

0 1 1 0

0 0 0 1

The output column, S, of the given input-output table was created from the student ID 21444368 using an algorithm where if the student ID digit is an even integer, a 0 is placed in the corresponding row of column S, and if the student ID digit is an odd integer, a 1 is placed in the corresponding row of column S. The same algorithm was applied to my student ID 81725225, resulting in the table shown above.

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convert the system to an augmented matrix. type each element of the answer in the spaces provided. 2x y

Answers

The augmented matrix of the solution to the system of equations is x = 4 and y = -1/2.

The augmented matrix of the system of equations 2x + y = 8 and 3x - y = 7 can be written as follows:

|2x + y = 8 |

|3x - y = 7 |

This can be rewritten in matrix form as:

|2 1 | |x | | 8 |

|3 -1| |y | | 7 |

To solve this system of linear equations, we can use the Gauss-Jordan elimination method. First, we add the first row to the second row to eliminate the x coefficient from the second equation:

|2 1 | |x | | 8 |

|0 -2| |y | | 1 |

Then, we can divide the second row by -2 to get the coefficient of y to be 1:

|2 1 | |x | | 8 |

|0 1 | |y | |-1/2|

Finally, we can subtract the second row from the first row to eliminate the y coefficient from the first equation:

|2 0 | |x | | 8/2|

|0 1 | |y | |-1/2|

Therefore, the solution to the system of equations is x = 4 and y = -1/2.

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#20 i need help with this question

Answers

Answer:

Step-by-step explanation:

tha answer is 69

Help I need to do corrections but they need to be turned in by 4pm today

Answers

Answer: I think it is -7 I'm not exactly sure but that's what I think please take someone else's answer just in case.

Step-by-step explanation:

Write an expression for a polynomial function whose graph intercepts the horizontal axis at -7,8 and 15

Answers

The polynomial function with the given intercepts of the hirzontal axis can be written as:

p(x) = (x + 7)*(x - 8)*(x - 15)

How to write the polynomial?

We know that a polynomial of degree N whose leading coefficient is 1 and has the zeros {x₁, x₂, ...}

Then the polynomial can be written as:

p(x) = (x - x₁)*(x - x₂)*...

Here the zeros (also called intercepts of the horizontal axis, like on this case) are {-7, 8, 15}

Then wecan write the polynomial with these zeros as:

p(x) = (x - (-7))*(x - 8)*(x - 15)

p(x) = (x + 7)*(x - 8)*(x - 15)

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Find the equation for the plane through Po(-4,-3,8) perpendicular to the following line.
x = -4+t, y=-3-3t, z= -4t, -∞

Answers

The equation of plane is x - 3y - 4z = 27.

What method can be used to determine the equation of a plane that is perpendicular to a vector?

a plane produced by the application of vectors perpendicular to a normal. The implication of this is that, given a vector a, b, c, we may deduce that all planes perpendicular to it have the form ax+by+cz=d and that any surface with this form is a plane perpendicular to a, b, c.

The equation for a plane perpendicular to a given line with direction ratios a, b, and c> and passing through a point is a(x-x1) + b(y-y1) + c(z-z1) = 0. (x1, y1, z1).

The equation of the plane traveling through the points x, y, and z on a plane perpendicular to the line whose parametric equation is provided

Equation of a plane through the point (-4,-3,8) is

a(x - 4) + b(y - 3) + c(z + 8) = 0

Since it is perpendicular to the line :

x = -4+t, y=-3-3t, z= -4t,

t = x + 4 = -y - 3 / 3 = -z/4

therefore coefficients a, b, c must be proportional to 1, - 3 & (-4) respectively.

Therefore, putting the values of a, b & c in eq.(1), we get the required equation of the plane as ;

λ(x - 4) -3 λ(y - 3) - 4λ(z + 8) = 0 (λ is a constant)

⇒ x - 4 - 3y + 9 -4z - 32 = 0

⇒ x - 3y - 4z = 27

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Find f(-5) if f(x) = |x + 1|

Answers are 4, 5, or 6

Answers

Answer:

f(-5) = 4

Step-by-step explanation:

[tex]f(x)=|x+1|\\f(-5)=|-5+1|=|-4|=4[/tex]

I’m pretty sure it’s 4 we did a test on one of these types of problems

let f (x, y) be the statement x trusts y, where the domain of discourse for both x and y is all people. (a) use quantifiers to express each of the following propositions in symbols. (i) nobody trusts ralph. (ii) everybody trusts fred. (iii) somebody trusts everybody.

Answers

The required expressions are ¬ ∃x(F(x, Ralph)), ∀xF(x, Fred), and  ∀x∃yF(x,y). Here, ¬ means negation, ∃ means existential quantifier, and ∀ means universal quantifier.

One or more variables that are defined on a particular domain are expressed by a predicate. By giving the variable a value or by quantifying it, it is possible to turn a predicate with variables into a proposition.

There are two quantifiers used in this they are (i) existential quantifier which is represented by ∃ and (ii) universal quantifier which is represented by ∀.

For, the proposition, "Nobody trusts Ralph", the quantifier is written as      ¬ ∃x(F(x, Ralph)).

For the proposition, "Everybody trusts Fred", the quantifier is written as ∀xF(x, Fred).

For the proposition, "Somebody trust everybody", the quantifier is written as ∀x∃yF(x,y).

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–35 –
–20 = N please need k to

Answers

Answer: - 15 = N

Step-by-step explanation:

2 negatives make a positive so it would be -35 + 20 = -15 Have a nice day ;)

Claire is 5 feet tall and casts a 96 inch shadow. How tall is her friend Steve if his shadow is 1.5 inches shorter than hers?

Answers

Answer:

4.725 ft

Step-by-step explanation:

well if i see this right the shadow for claire is 1.60x the person's hight

Add 4x +1

To

5x+6

Write the following as an algebraic expression. Simply if possible

Answers

Answer:

9x + 7

Step-by-step explanation:

Add 4x + 1 to 5x + 6

in an algebraic expression is:

4x + 1 + 5x + 6

To simplify, combine like terms. This means add the x terms together and add the constants (plain number- - the 1 and 6) together.

4x + 1 + 5x + 6

= 4x + 5x + 1 + 6

= 9x + 7

Sophie is a dog that loves to play catch. Unfortunately, she isn't very good, and the probability that she catches a ball is only 0.2. Let x be the number of tosses required until Sophie catches a ball. (a) Does x have a binomial or a geometric distribution? (b) What is the probability that it will take exactly two tosses for Sophie to catch a ball? P(exactly two tosses) (c) What is the probability that more than three tosses will be required? P(more than three tosses)

Answers

X has a geometric distribution because it is the number of trials (tosses) required until a success (catching the ball) occurs.

b) The probability that it will take exactly two tosses for Sophie to catch a ball is P(x=2) = (0.2)(0.8)^1 = 0.16. This is calculated by multiplying the probability of success (0.2) by the probability of failure (0.8) raised to the power of the number of trials (2-1=1)

c) To find the probability that more than three tosses will be required, we need to find the probability that Sophie does not catch the ball on the first three tosses and then catch it on the fourth toss.

This can be found by summing the probabilities of Sophie not catching the ball on the first three tosses (0.8^3 = 0.512) and Sophie catching the ball on the fourth toss (0.8^3*0.2 = 0.1024). The probability that more than three tosses will be required is P(x>3) = 1 - P(x≤3) = 1 - (0.512 + 0.1024) = 0.3856.

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Will Mark brainliest
Write an equation in point slope form for the line that passes through the given point and is perpendicular to the graph of each equation.

(3, - 2) ; y = 2/3x + 4

Answers

An equation in point slope form for the line that passes through the given point and is perpendicular to the graph of each equation is y=2/3 x²+4x

How to find the equation?

A mathematical equation is a formula that uses the equals sign ('=') to express the equality of two expressions. The meanings of the word equation and its cognates in other languages can vary slightly. For instance, an equation in English is any well-formed formula consisting of two expressions related by an equals sign, while an equation in French is defined as containing one or more variables.

step 1

y=2/3+4

y=2/3 x²+4x

y=m x+ b

step 2

y= y coordinate

m=slope

x=x coordinate

b=y intercept

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For the rectangular parking area of the shopping
center shown, which one of the following equations
says that the area is 30,000 yd² ?
A. x(4x +300) = 30,000
B. x+(4x +300)=30,00
Equation
(Type A, B, C, or D.)
says that the area is 30,000 yd².
CO
C. 2x + 2(4x + 300) = 30,000
D. x² (4x+300)² = 30,000²
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CI
RE
4x+300
TORP
COBECOBOBEE
LED
LD
ME
C
MAGI
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(0)
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7100
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Answers

For the rectangular parking area of the shopping center shown, an equation which says that the area is 30,000 yd² is: A. x(2x + 200) = 30,000.

How to calculate the area of a rectangle?

Mathematically, the area of a rectangle can be calculated by using this formula:

A = LW

Where:

A represents the area of a rectangle.W represents the width of a rectangle.L represents the length of a rectangle.

From the information provided about the rectangular parking area of the shopping center shown in the image attached below, we have the following dimensions:

Length = x

Width = 2x + 200

Substituting the given points into the area of rectangle formula, we have the following;

30,000 = x × (2x + 200)

30,000 = x(2x + 200) ⇒ (required equation).

30,000 = 2x² + 200x.

2x² + 200x - 30,000 = 0.

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What is (f/g)(x)?

f(x) = -x
g(x) = -5x + 2

Write your answer as a polynomial or a rational function in simplest form.

Answers

The rational function in the simplest form of (f/g)(x)  is x / 5x - 2.

How to solve functions?

Composite functions are when the output of one function is used as the input of another. A typical example of a composite function is (f/g)(x).

Therefore, let's solve the rational function in the simplest form.

Hence,

f(x) = -x

g(x) = -5x + 2

(f/g)(x) = f(x) / g(x)

Therefore,

(f/g)(x) = - x / -5x + 2

Hence,

(f/g)(x) = - x / - (5x - 2)

Finally,

(f/g)(x) = x / 5x - 2

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PLEASE HELP ME IT’S URGENT

Answers

The images of the points after the transformation are (6, 1), (3, 6), (5, 2) and (-8, -4)

How to determine the coordinates of the point?

r(x-axis) o T(2, -3) (4, 2)

This implies that we reflect the point (4, 2) across the x-axis and then translate it by (x + 2, y - 3)

Mathematically, this is represented as

Image = (x + 2, 3 - y)

Substitute the known values in the above equation, so, we have the following representation

Image = (4 + 2, 3 - 2)

Evaluate

Image = (6, 1)

T(2, -5) o R 90 CCW (4, 2)

This implies that we translate the point (4, 2) by (x + 2, y - 5) and then rotate it by 90 degrees counterclockwise

Mathematically, this is represented as

Image = (5 - y, x + 2)

Substitute the known values in the above equation, so, we have the following representation

Image = (5 - 2, 4 + 2)

Evaluate

Image = (3, 6)

T(1, 4) o r(y-axis) (4, 2)

This implies that we translate the point (4, 2) by (x + 1, y + 4) and then reflect it across the y-axis

Mathematically, this is represented as

Image = (x + 1, 4 - y)

Substitute the known values in the above equation, so, we have the following representation

Image = (4 + 1, 4 - 2)

Evaluate

Image = (5, 2)

r(y-axis) o T(1, 4) (4, 2)

This implies that we reflect the point (4, 2) across the y-axis and then translate it by (x + 4, y + 2)

Mathematically, this is represented as

Image = (-x - 4, y + 2)

Substitute the known values in the above equation, so, we have the following representation

Image = (- 4 - 4, 2 + 2)

Evaluate

Image = (-8, 4)

Hence, the image is (-8, -4)

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Determine constants and such that the given piecewise function is continuous for all .
F(x)= -6 if x < -1
Ax + 2. if -1 ≤ x ≤ 2
-x^2 + Bx + 14. if x > 2

Round your answers to one decimal place, if necessary.

Answers

Answer: To make the piecewise function continuous for all x, we need to make sure that the function values and the function slopes at the boundaries (-1 and 2) are the same for each piece.

For x = -1:

F(-1) = -6 (from the first piece)

F(-1) = A(-1) + 2 = -A + 2 (from the second piece)

So, to make the function continuous at x = -1, we need to set -6 = -A + 2, which gives us A = -8.

For x = 2:

F(2) = -x^2 + Bx + 14 (from the third piece)

F(2) = A(2) + 2 = 2A + 2 (from the second piece)

So, to make the function continuous at x = 2, we need to set -4 + 2B + 14 = 2A + 2, which gives us B = -5.

Now we can write the function with the constants that we found :

F(x) = -6 if x < -1

-8x + 2 if -1 ≤ x ≤ 2

-x^2 - 5x + 14 if x > 2

This function is continuous for all x and the values and slopes match at x = -1 and x = 2.

Step-by-step explanation:

If an item that originally cost $18 is decreased to $12, what is the percentage of decrease in the item?

Answers

33%
This is the answer

A sunflower is measured at the beginning of June and is 40cm tall. The sunflower
grows by 25% each month for three months. What height is the sunflower to the nearest
centimetre at the beginning of September?

Answers

Answer:

78cm  78.125

Step-by-step explanation:

Answer: 78.13

Step-by-step explanation:

you start with 40cm and find 25% of that and add it to 40cm. Or you can do 1.25x40=50 That would be July, so repeat to get 50x1.25=62.5 to get august, then again to get 62.5x1.25=78.13

#15 find the measure of angle P. I need help with this problem

Answers

The measure of ∠P is 96°.

What is an expression?

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

∠P and ∠R are alternate angles.

Alternate angles are equal.

So,

∠P = ∠R

2x = x + 48

2x - x = 48

x = 48

Now,

∠P = x + 48

∠P = 48 + 48

∠P = 96

Tus,

The value of ∠P is 96°.

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PLEASE HELP ASAP!!!


Mrs. Lopez needs 40 ounces of sweetened milk to make flans. She has 24 ounces. Which equation shows how many more ounces of sweetened milk Mrs. Lopez needs to make flans?

Answers

Answer: As Mrs Lopez required 40 ounce

Step-by-step explanation:

PLEASE HELP FOR 30 POINTS ITS A UNIT TEST!!!!!!!
The coordinates of the vertices of a polygon are shown on the graph below.


What is the name of the polygon?

hexagon

octagon

quadrilateral

triangle

Answers

Answer: Quadrilateral

Step-by-step explanation:

hexagon: 6 sides

octagon: 8 sides

quadrilateral: 4 sides

triangle: 3 sides

The quadrilateral is the only one that makes sense.

Solve the system by elimination 8x+3y=4 2x+y=2 what is the solution

Answers

The solution for the system of equations 8x + 3y = 4 and 2x + y = 2 by elimination are x = -1, y = 4

How to evaluate for the solutions of the equations by elimination

we shall write the equations as:

8x + 3y = 4...(1)

2x + y = 2...(2)

multiply equation (2) by 3 to get equation (3)

3(2x + y) = 3 × 2

6x + 3y = 6...(3)

subtract equation (1) from (3) to eliminate y

6x + 3y - 8x - 3y = 6 - 4

-2x = 2

divide through by -2

x = -1

put the value -1 for x in equation (2) to get y

2(-1) + y = 2

-2 + y = 2

y = 2 + 2 {add 2 to both sides}

y = 4

Therefore, the solution for the system of equations 8x + 3y = 4 and 2x + y = 2 by elimination are x = -1, y = 4.

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2 x – 3 y = 7
–4 x + y = –5
What is the x -value of the solution to this system of equations?

Answers

Answer:

x =  [tex]\frac{4}{5}[/tex]

Step-by-step explanation:

2x - 3y = 7 → (1)

- 4x + y = - 5 → (2)

multiplying (2) by 3 and adding to (1) will eliminate y

- 12x + 3y = - 15 → (3)

add (1) and (3) term by term to eliminate y

- 10x + 0 = - 8

- 10x = - 8 ( divide both sides by - 10 )

x = [tex]\frac{-8}{-10}[/tex] = [tex]\frac{4}{5}[/tex] (= 0.8 )

which has the lowest price per unit.

$23.35 per 6.5 lbs.
$31.60 per 8 lbs.

Answers

Per unit is referring to per lbs
Thus,
Total money needed to count per lbs

Solution:
23.35/6.5 = 467/130 = $3.59 per lbs
31.60/8 = 79/20 = $3.95 per lbs
Thus,
$23.35 per 6.5 lbs has the lowest price per unit

The monthly cost (in dollars) of a long-distance phone plan is a linear function of the total calling time (in minutes). The monthly cost for 52 minutes of calls is $14.06 and the monthly cost for 78 minutes is $17.18. What is the monthly cost for 73 minutes of calls?

Answers

Answer:

16.58

Step-by-step explanation:

as you can see from the graph, there's a monthly fixed cost on Y axis.  so you need to figure out 1: how much per minute. and 2. the monthly fixed fee.  you've got 2 scenarios = 2 equations, for 2 variables. so you can solve both.

assume: x=per min rate; m = monthly fixed cost.

1. 14.06 =52x+m

2. 17.18 =78x+m

use equation 2 minus equation 1 & you get

3.12 = 26 x.  so x = 0.12

plug this into equation 1: 14.06 =52*0.12 +m so m=7.82

now for 73 mins the cost = 73*0.12 +7.82 =16.58

The image includes the questions

Answers

Answer:

a.

b. 35/100 of 76 = 26 to 27 remained

c.
d. statistic

e. experiment

f. I don't think so

Step-by-step explanation:

Other Questions
a horseman left the village at a point with coordinates (-2, 5) and began riding along a straight road whose direction was given by the vector . then at some point he turned at a right angle; he never changed direction again until he arrived in the village at the point with coordinates (2, 11). at the point where he made the turn he buried a jar full of silver coins. unfortunately, he forgot the coordinates of the point. can you help him recover them? The common characteristic not possessed by all assets is _____.a. a future economic benefitb. economic life greater than one yearc. physical substanced. usually has greater financial value which of the following are true regarding causes of incidents?a) most incidents will have more than one causeb) there may be less obvious root cuasesc) diect cuases are the immediate and apparent actions or conditions that contribute to the incidentd) there will be one immediate cause and one less obvious cuase to every incident that you investigate Zappos creates __________ for its customers by offering a wide selection, higher levels of service, and customer-friendly return policiesA) valueB) equityC) exchangesD) demandsE) satisfaction the garden clud at central middle school is planting a flower bed. a scale drawing of the flower is shown. the scale 1 in. :2 ft At maturity, a bond issued at a premium will have ______ bonds payable balance compared to the maturity value had the bond had sold at a discount or par. I need to know the 10th term? 4. Is 3 in the domain of the function ? Why or why not? the apparent inclination of some survey respondents to avoid appearing racist or racially motivated has become known as the the term pink-collaroccupation refers to . group of answer choices a relatively low-paying, nonmanual, semiskilled position that is primarily held by women any type of occupation or position in which emotional labor is the dominant feature a working-class position such as a machine operator and a factory foreman that can only be occupied by women any occupation that was earlier dominated by women but is now dominated by men bob went out to buy some fishing equipment. he spent half of what he had plus $5 at the first store. at the second store, he spent half of what was left plus $4, and at the third store, he spent half of the remainder plus $3. he then had $5 left to put aside for bait. how much money did he start with? a pregnant patient in the first trimester has developed pregnancy complications and undergoes a medical abortion. the nurse finds from the patient's blood reports that the patient is rh negative. what is a priority action by the nurse 4. give me an assessment of the shape of the sizes/mileages that you entered in your data set. what shape do you think the data possess? attach both the stem-and-leaf display and the histrogram for the size/mileage variable for all 75 observations below your assessment of the shape Complete the table of ordered pairs for the linear equation y=3x-11 Dan Elliott uses online banking. He pays the basic monthly charge, 9 bills, and requests a printed statement. He also has ATM transactions that include 2 out of networks transactions and a cash advance of $200. 0. What are his total fees for the month ? which of the following tables best shows the expected values in the f2 generation for a chi-square goodness-of-fit test for a model of independent assortment? According to an article on The Guardian website, a British woman born in 2003 has probability 0.27 of living at least 100 years. Five high school friends all happen to be females born in 2003.Assuming that the survival of each one is independent of the others, what is the probability that at least one of them lives to be 100 years old? Which equence trace the level of anatomical organization from lower to higher complexity? A linear function passes through the points (-3, 7) and (2, -3). Part A: What is the slope of the linear function that passes through these points. Part B: What is the function rule of the linear function that passes through these points. Part C: Where does the linear function intersect the x-axis and y-axis? You see that First National Bank is willing to make you a four-year $40,000 car loan with an interest rate of 4.2%. However, the same bank will charge you 16.5% interest on a credit card that it issues. Why is the interest rate on the credit card so much higher than the interest rate on the car loan?