Multiply. Write your answer as a fraction in simplest form.

−4/9(−7/9)=

Answer:

abc- 130

ebd-130

abe-50

Step-by-step explanation:

The position value, r(t) is equals to the (t³/6)k + 2j and velocity value, v(t) is equals to ( t²/2 )k + 4i , for a(t) = tk, v(0) = 4i, r(0) = 2j.

Acceleration is defined as the rate of change of the velocity of an object with respect to time. Accelerations are vector quanty.

a = dv/dt

We have the following informations are available,

Initial velocity, v(0) = 4i

Initial position, r(0) = 2j

Acceleration at any time "t",

a(t) = tk

we have to determine the value of v(t) and r(t).

As we know, a(t) = dv(t)/dt = tk

integrating the above equation ,

v(t) = ∫tk dt = ( t²/2 )k + c

at t = 0 , v(0) = 0 + c = 4i ( since, v(0) = 4i

=> c = 4i

So, v(t) = ( t²/2 )k + 4i

Also, velocity is calculated by derivative of postion (r) with respect to time.

=> v(t) = dr(t) /dt

=> r(t) = ∫ v(t) dt

=> r(t) = ∫ ( t²/2 )k dt

integrating value of the right hand side,

r(t) = ( t³/2×3 )k +d

= (t³/6)k + d

At t = 0, r(0) = (0/6)k + d

=> r(0) = d = 2j

so, r(t) = (t³/6)k + 2j

Hence, the required position and velocity are

(t³/6)k + 2j and ( t²/2 )k + 4i.

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Answer:

Grey dice.                  White dice

Step-by-step explanation:

Flip them around, this one really got me lol

DJ received 12 requests for the hip hop song on Friday night as per the given equations.

"A system of equations is a finite set of equations for which we find the common solution."

here, we have,

According to the question,

x represents the number of hip hop songs

y represents the number of country songs

Situation 1: Number of requests for the country songs was 2 more than

4 / 3 times the number of requests of hip hop songs , represents the equation:

y = (4 / 3) x + 2                 ______(1)

Situation 2: Number of  requests for country song is 18 , represents the equation:

y = 18                             _________(2)

Substitute the value of y in equation (1) from (2) we get,

 18 = (4 /3)x +2

⇒ ( 4/ 3) x = 18 - 2

⇒ x = 12

Hence, DJ received 12 requests for the hip hop song on Friday night as per the given equations.

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The measure of FG is 16 units.

The measure of FG can be found as follows:

GE is an angle bisector.

An angle bisector is a bisector that bisect angles into two equal halves.

Therefore,

GE bisect ∠FEH

Hence,

FG = GH

FG = x + 11

GH = 3x + 1

x + 11 = 3x + 1

11 - 1 = 3x - x

10 = 2x

x = 10 / 2

x = 5

Therefore,

FG = x + 11 = 5 + 11 = 16 units

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Given the expression 2/3x-5=x-8

we need to find the value of x from the expression as shown;

collect the like terms:

2/3x-5=x-8

2/3 x - x = -8+5

Find the LCM

(2x-3x)/3 = -3

-x/3 = -3

Cross multiply

-x = -3(3)

-x = -9

Multiply both sides by -1

-1(-x) = -1(-9)

x = 9

Hence the correct value of x is 9

Given:

John's age is a multiple of 3

Let the age of this year = 3x

Last year, his age was 1 less than a multiple of 4.

So, {(3x-1) + 1 } is a multiple of 4

so, (3x) is a multiple of 4 also

And, Next year, his age will be 3 more than a multiple of 5

So, {(3x + 1 ) - 3 } is a multiple of 5

Considering the previous conditions:

The least multiple of 3 and 4 = 3 x 4 = 12

So, x = 12/3 = 4

Checking for the last condition:

Which is the multiple of 5

So, the youngest age = 12 years

By solving: Y = (-4x + 9) / 2 is the solution to the equation -4x=2y-9 for y.

To solve for y in the equation -4x=2y-9, we need to isolate y on one side of the equation.

First, we add 9 to both sides to get rid of the -9 on the right side:

-4x + 9 = 2y

Next, we divide both sides by 2 to get y by itself:

(-4x + 9) / 2 = y

This gives us our final answer:

y = (-4x + 9) / 2

To show our work, we can write it out like this:

-4x=2y-9

-4x + 9 = 2y

(-4x + 9) / 2 = y

y = (-4x + 9) / 2

Therefore, y = (-4x + 9) / 2 is the solution to the equation -4x=2y-9 for y.

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Answer:

180

Step-by-step explanation:

A 3-digit number cannot start with 0, so the leftmost digit is a choice of 6 digits out of the 7. The middle digit can be chosen from all 7 digits minus the one already used, so there are 6 choices. The right digit can be chosen from 5.

6 × 6 × 5 = .180

The number of three-digit numbers that can be formed from the digits 0, 1, 2, 3, 4, 5, and 6 is 180.

This can be calculated by finding the number of element availabe at first place which is 6 excluding 0 than for second position 6 as first number is excluded and 0 is added and for the last positon the number of possibe combination is 5 as 2 digits are already used.

The final answer is 6*6*5 = 180

so count of 3 digit numbers that can be formed by the given set of digit without repetetion allowed is  180

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The error Justin made in his calculation is "He should have added the values in the numerator before dividing by 2".

The correct answer choice is option B

(x + y + 5) / 2

Where,

x and y are his parents’ current heights in inches,

Mom’s height = 54 inches

Dad’s height = 71 inches

Substitute into the expression

(71 + 54 + 5) / 2

= 130/2

= 65 inches

Justin's work:

( 71 + 54 + 5 ) / 2

= 71 + 27 + 5

= 103 inches

Therefore, Justin should have added the numerators before dividing by 2.

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To solve this problem, we need to use the Fundamental Counting Principle which states that the total number of outcomes is the product of the number of ways each event can occur.  The state can make 11,881,376 different license plates

In this case, there are 10 possible choices for the first digit (0-9) and 26 possible choices for each of the remaining 5 letters of the alphabet. Therefore, the total number of different license plates that can be made is:
10 x 26 x 26 x 26 x 26 x 26 = 11,881,376
Another way to think about it is to use permutation. We have 10 choices for the first digit and 26 choices for each of the 5 remaining letters. Therefore, the total number of permutations is:
10P1 x 26P5 = 10 x 26 x 25 x 24 x 23 x 22 = 11,881,376
Either way, the answer is the same. So, the state can make 11,881,376 different license plates if each of its license plates contains 1 different digit followed by 5 different letters of the alphabet.

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Answer: 12 people each person would get 2 sweethers and 3 trowser

Step-by-step explanation:

the GCF of 24 and 36 is 12 then 24/12=2 and 36/12=3

Answer:

The surface area of the figure is 40 + 5π.

Step-by-step explanation:

Answer:

The Answer is A

Step-by-step explanation:

58(0.2) = 11.6 + 58 = 69.6

it's a

now have a nice DaY

Answer:

Decomposers

Step-by-step explanation:

They are breaking down waste sometimes decomposers break down other dead organisms as well.

Answer:

decomposers. hope i helped!

Step-by-step explanation:

decomposers are bacteria who eat dead things or droppings!

Answer:

-14 and -4

Step-by-step explanation:

x+y=18

xy=56 solving simultaneously, x=56/y

56/y + y = 18

Answer:

28

Step-by-step explanation:

similar triangles are proportional

and add all the sides of the bigger triangle

Answer:

Your parameter of interest is the thing that your research is focusing on. For example, if you want to find the weight of an average goat, your parameter of interest will be the weight of an average goat.

In this case, you will have two parameters of interest: percentages of children in a school district living in two-parent homes that graduated high school, and percentages of children living in single-parent homes that graduated from high school.

Hope this helps!

Based on the information, Christian would have $5525.5 of an annuity.

According to the given information, the number of coffees per week is 3 then, per month is 3x4 = 12

Each coffee is $4.5. Then monthly expenditure for coffees is 12 x 4.5 = $54

Rate of interest r = 1.6% = 1.6/100 = 0.016 and for monthly compounding r = 0.016/12 = 0.00133

n = number of payments = 8 x 12 = 96

We can use the formula for finding the future value as below

FV = C x [ ( 1 + r )n-1 ] / ( r )

FV = 54 x [ ( 1 + 0.00133 )96 – 1 ] / (0.00133)

= 54 x [ (1.13609 - 1)] / (0.00133)

= 54 x 0.13609 / (0.00133)

= 54 x 102.3233

= 5525.5

Therefore Christian would have $5525.5 of the annuity.

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25% is the larger circle area is gray.

Area of a Circle: The area of a circle is pi times the radius squared.

To calculate the area of the circle we have the formula:

A = π r²-----(1)

where

A=area

r=radius.

First, we have to analyze the given data, the large circle center o passes through d, so

Gray circle area=π*(radius)^2----(2)

The radius of the smaller circle = OD/2 substitute in (2)

Gray circle area=π*(OD/2)^2

Gray circle area=π*OD^2/4

Larger circle area=π*(radius)2    

radius of the larger circle = OD

larger circle area=π*OD^2  

To know the percentage of a large circle we have a small formula:

gray circle area/large circle area--------(3)

=π*OD^2/4/π*OD^2  

=π*OD^2/4*1/π*OD^2=1/4

=25/100

=25%

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The function for the model that gives the future value of the investment in dollars after t years is: f(t) = 2000.e⁰·°⁴²t

Give, a lump sum of $2000 is invested at 4.2% compounded continuously.

Hence we have:

P = $2000

rate of interest = 4.2%

years = t

we know that A = Pe^rt

Substitute the above values in the formula.

Amount = f(t)

f(t) = 2000.e⁰·°⁴²t

hence we get the function for the model that gives the future value of the investment is f(t) = 2000.e⁰·°⁴²t

Therefore we get the required function.

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Step-by-step explanation:

Looks like it's a scale factor?

The base of the small one is 5ft and the base of the large is 45ft. If we divide

45/5 = 9

Since the height of the small is 40ft, we can multiply by 9, the number we just found, to find the value of X.

40 x 9 = 360ft

So the frequency of individuals with red hair in population b after 10 generations of migration is approximately 0.02%.

We need to use the Hardy-Weinberg equation, which describes how the frequencies of alleles in a population will change over time.
The equation is:
p^2 + 2pq + q^2 = 1
Where:
p = frequency of one allele
q = frequency of the other allele
p^2 = frequency of homozygous dominant individuals
2pq = frequency of heterozygous individuals
q^2 = frequency of homozygous recessive individuals
In this case, the recessive trait is red hair, so we'll use q to represent the frequency of the recessive allele.
In population a, q = 0.49, so p (the frequency of the dominant allele) = 1 - q = 0.51.
In population b, q = 0.25, so p = 0.75.
After the emigrants from population a migrate to population b, the new frequency of the recessive allele in population b will be:
q' = (0.1 x 0.49) + (0.9 x 0.25) = 0.286
This is the new value of q after one generation of migration. To calculate the frequency of red-haired individuals after 10 generations, we need to use the equation:
q^10 = (0.286)^10 = 0.0002
So the frequency of individuals with red hair in population b after 10 generations of migration is approximately 0.02%.
The frequency of individuals with red hair in population b after 10 generations of migration is approximately 0.02%. This is based on the assumption that the emigrants from population a mate randomly with members of population b and that the population sizes remain constant over time.
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Answer:

3V/b = h

Step-by-step explanation:

Step 1: Write equation

V = 1/3bh

Step 2: Multiply both sides by 3

3V = bh

Step 3: Divide both sides by b

3V/b = h

The function f(x) = (4x³ - 5x - 1)/(2x² - 3x² + x - 3) does not have a horizontal asymptote.

To find the equation of the horizontal asymptote of the function f(x) = (4x³ - 5x - 1)/(2x² - 3x² + x - 3) as x approaches infinity (x → ∞), we can examine the behavior of the function when x is extremely large.

Divide each term in the numerator and denominator by the highest power of x. In this case, divide both numerator and denominator by x³:

f(x) = (4x³/x³ - 5x/x³ - 1/x³) / (2x²/x³ - 3x²/x³ + x/x³ - 3/x³)

= (4 - 5/x² - 1/x³) / (2/x - 3/x² + 1/x² - 3/x³)

As x approaches infinity, all the terms involving 1/x or 1/x² or higher powers of x become negligible. Therefore, we can ignore them and simplify the expression:

f(x) ≈ (4 - 0 - 0) / (0 - 0 + 0 - 0)

= 4/0

Since the denominator approaches zero and the numerator does not, we can conclude that the function approaches positive or negative infinity as x approaches infinity. This means that there is no horizontal asymptote for the function f(x).

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The answers are in the the vector in the form ai + bj
8) Option C: 3.825i + 1.169j
9) Option D: -7.25i + 3.381j

both questions by writing the vectors in the form ai + bj.

8) Direction angle 17°, magnitude 4:
First, convert the direction angle to radians: 17° * (π/180) ≈ 0.297 radians.
Now, calculate a and b:
a = magnitude * cos(direction angle) = 4 * cos(0.297) ≈ 3.825
b = magnitude * sin(direction angle) = 4 * sin(0.297) ≈ 1.169
The vector is 3.825i + 1.169j (Option C).

9) Direction angle 115°, magnitude 8:
First, convert the direction angle to radians: 115° * (π/180) ≈ 2.007 radians.
Now, calculate a and b:
a = magnitude * cos(direction angle) = 8 * cos(2.007) ≈ -7.25
b = magnitude * sin(direction angle) = 8 * sin(2.007) ≈ 3.381
The vector is -7.25i + 3.381j (Option D).

So, the answers are:
8) Option C: 3.825i + 1.169j
9) Option D: -7.25i + 3.381j

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Answer:

a=3,b=5

Step-by-step explanation:

\( \frac{3}{x} + \frac{5}{ {x}^{2} } \\ = \frac{3x}{ {x}^{2} } + \frac{5}{ {x}^{2} } \\ = \frac{3x + 5}{ {x}^{2} } \)

so as you got it:

\( \frac{(ax + b)}{ {x}^{2} } = \frac{3x + 5}{ {x}^{2} } \\ a = 3 \\ b = 5\)

The characteristic polynomial is λ² - 10λ + 16 = 0 and the eigenvalues of a are 8 and 2.

The given matrix is a 2x2 matrix as it is 2 rows and 2 columns.

Therefore, the characteristic polynomial can be found using the formula |A - λI| = 0

where λ is the eigenvalue and I is the identity matrix.

Also, the eigenvalues of a are the roots of the characteristic polynomial.

Hence, let us find the characteristic polynomial and the eigenvalues of a below:

Given a = 5 3 3 5Let us solve the following equation:

|A - λI| = 0

We have, A - λI = 5-λ 3 3 5-λ|A - λI| = (5-λ)(5-λ) - 3(3) = λ² - 10λ + 16 = 0

Now we can find the eigenvalues of a by solving the quadratic equation using the formula given below:

x = (-b ± sqrt(b² - 4ac)) / 2awhere a = 1, b = -10 and c = 16

Therefore,

x = (-(-10) ± sqrt((-10)² - 4(1)(16))) / 2(1)

⇒ x = (10 ± sqrt(100 - 64)) / 2

⇒ x = (10 ± sqrt(36)) / 2

⇒ x = (10 ± 6) / 2

Eigenvalues of a are:x = 8 and 2

Hence, the characteristic polynomial is λ² - 10λ + 16 = 0 and the eigenvalues of a are 8 and 2.

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