Katie invested $33,750 at 11.17% compounded continuously.

What will Katie's account balance be in 10 years?

Answer:

x-1 = 0  or x-7 =0

x=1                      or x=7

Step-by-step explanation:

(x-1) (x-7) =0

Using the zero product property

x-1 = 0  or x-7 =0

x-1+1 =0 +1    or x-7+7 =0+7

x=1                      or x=7

Answer:

Step-by-step explanation:

In order to answer all of these questions we need the position function and the acceleration function.  We will discuss why when we get there.

The velocity function is given; in order to find the position function we have to take the antiderivative of the velocity function.  So in order are the position, velocity, and acceleration functions below:

[tex]s(t)=\frac{1}{3}t^3-\frac{9}{2}t^2+18t+1[/tex]

[tex]v(t)=t^2-9t+18[/tex]

[tex]a(t)=2t-9[/tex]

I know the constant on the position function is 1 because the info given tells me that s(0) = 1.

For the first question, the formula to find the average velocity is as follows:

[tex]v_{avg} =\frac{s(t_{2})-s(t_{1})  }{t_{2}-t_{1}  }[/tex]

To find s(t2) and s(t1) we sub in 8 for t2 and 0 for t1 to get the following:

[tex]v_{avg}=\frac{\frac{83}{3}-1 }{8-0}[/tex]

That simplifies to

[tex]v_{avg}=\frac{10}{3}m/sec[/tex]

The second question wants the instantaneous velocity at t = 5.  We get this by subbing in a 5 for t in the velocity function:

[tex]v(5)=(5)^2-9(5)+18[/tex] and

v(5) = -2.  This means that the velocity of the particle is 2 m/sec, but it is now going in the opposite (or negative) direction.

The third question is asking for the time interval when the particle is moving to the right.  On a velocity/time graph, the x's represent the time and the y's represent the velocity.  If the "y" values are positive, then the velocity is positive and that means the object is moving to the right.  Where the "y" values are negative, that means that the velocity is negative and the object is moving to the left.  To find the answer to this problem we think about the positive and negative y values.  Because this is a parabola, I know that the places where the graph goes through the x-axis is where the velocity changes from positive to negative and back to positive.  In order to find those places where the graph goes through the x-axis I have to factor the velocity function.  When I throw that into the quadratic formula on my calculator I get that x = 3 and x = 6.  Completing the square on the velocity function gives me a vertex of [tex](\frac{9}{2},-\frac{9}{4})[/tex]

Because the y value of the vertex is negative, that means that the values of x from negative infinity to x = 3 give positive velocity values, between x = 3 and x = 6 the values of the velocity are negative, and from x = 6 to x = positive infinity the velocity is positive again.  

So to sum up question 3, the particle is moving to the right on the intervals

(-∞, 3] and [6, ∞)

The fourth question is really tricky.  It requires you to remember some of your Physics and how velocity and acceleration vectors are related.  If the acceleration and the velocity both have the same sign, whether it be positive or negative, the object is speeding up.  If the acceleration and velocity vectors have opposite signs, one positive and one negative, then the object is slowing down.  We already know that from negative infinity to 3 the velocity is positive, so let's check the acceleration values in that interval.  I only need to test one number, so let's test a(2).  

a(2) = 2(2) - 9 and a(2) = -5

-5 means the object is slowing down here since the velocity is positive and the acceleration is negative.  

Let's test the interval between 3 and 6.  Let's test a(4).

a(4) = -1

Between the interval of 3 and 6 seconds, the velocity is negative.  Since the acceleration is also negative, the object is speeding up between the time interval [3, 6].

We already found that from the left of t = 3, the object was slowing down; so it would also be slowing down to the right of t = 6.

Phew!  That's it!  We're done!

Step-by-step explanation:

-4(27)+100

-108+100

=-8

To find the 27th term in the sequence defined by the formula an = -4n + 100, you substitute 27 for 'n' in the equation. The yielded result is -8, which is the 27th term in the sequence.

In Mathematics, a sequence can be defined by an equation, where each term an is defined in terms of its place in the sequence ('n'). In the given equation, an = -4n + 100,  the nth term is determined by multiplying 'n' by -4 and then adding 100. If we want to find the 27th term of the sequence, we substitute n with 27 in the equation.

So, a27 = -4(27) + 100 = -108 + 100 = -8.

Therefore, the 27th term of the sequence is -8.

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Answer:

  ASA

Step-by-step explanation:

Angles E/R and O and the sides EO/RO between them are indicated as congruent. Hence the Angle-Side-Angle (ASA) postulate will be the one that is applicable.

OK, f is the graph and g is the table.

f(-2) > g(-2)

f(-2) means the y coordinate of the graph when x=-2.  That's y=2, so f(-2)=2

g(-2) we look up in the table, g(-2)=1

So it's true that f(-2) > g(-2)

Answer: f(-2) > g(-2)   TRUE

-----

The characteristic of an absolute value function, possibly shifted and scaled, is the distinct V shape.   Clearly f is an absolute value function; the slopes are -1 and 1 and the vertex is at (-3,1) so f(x) = |x+3|+1

g kinda also has the characteristic V shape, but it has a slope of -3  in one place and -1 in the other, so it isn't a straight line.

Answer: f(x) and g(x) are absolute value functions.   FALSE

-----

For all x, f(x) > g(x)

Presumably this means for all x in g's domain, which is only five points.  We already checked x=-2; let's do the rest.

f(-5) = 3, g(-5) = 4

So at x=-5 it's not true

For all x, f(x) > g(x)   FALSE

-----

f(x) and g(x) intersect at exactly two points.

We already know they don't at x=-5 and x=-2.  Let's check the other three.

f(-5) = 3, g(-5) = 4

f(-4) = 2,  g(-4)=1

f(-3) = 1, g(-3) = 0

f(-2) = 2, g(-2) = 1

f(-1) = 3, g(-1) = 4

This one's tricky.   All we really know about g is the points listed.   g may be a parabola where the function is continuous between the table points.   If that's true the functions intersect at exactly two points.  We don't really know that for sure so I'll go with:

Answer: f(x) and g(x) intersect at exactly two points.  FALSE

I may be marked wrong on this last one but I'm sticking with my answer.

Answer:

A and D are both true.

Step-by-step explanation:

f(x) is a quadratic. It is the graph in red. Its equation is y = (x + 3)^2

g(x) is an absolute value formula. It is the graph in blue. Its equation is y=abs(x + 3) + 1

=====================

The last statement is correct. The two figures cross at (-1.382,2.618) and (-4.618, 2.618) so D is true. But don't stop reading. You'll learn much from this question.

======================

From the right intersect point to the left intersect point, the blue graph is greater than the red one. C is false. Remember the red graph is f(x)

=====================

B is false. g(x) is a quadratic

=====================

Unfortunately I'm getting that A is true

f(-2) = 2 and

g(-2) = 1

Answer:

Option B

Step-by-step explanation:

Plot points A, B, C and line y=x on the coordinate plane (see attached diagram, blue points)

1. The reflection across the line y=x has the rule

(x,y)→(y,x)

So,

Points A', B', C' are marked in red on the diagram

2. The rotation by 90° clockwise about the origin has the rule

(x,y)→(-y,x)

So,

Answer:

A (−7, −13) → A ′(−13, −7) → A ″(7, −13);

B (12, −8) → B ′(−8, 12) → B ″(−12, −8);

C (−17, 19) → C ′(19, −17) → C ″(17, 19)

Step-by-step explanation

The coordinates of the vertices of the preimage are given.

To find the image as it reflected from the preimage across the y=x line, use the transformation rule: (x,y)→(y,x).

Apply the transformation rule to vertices A(−7,−13), B(12,−8), and C(−17,19).

A(−7,−13)→A'(−13,−7).

B(12,−8)→B'(−8,12).

C(−17,19)→C'(19,−17).

To determine the vertices of the image after the rotation of 90∘ about the origin, use the rule: (x,y)→(−y,x).

Apply the rotation rule to the vertices of △A'B'C'.

A'(−13,−7)→A''(7,−13).

B'(−8,12)→B''(−12,−8).

C'(19,−17)→C''(17,19).

Therefore,

A(−7,−13)→A'(−13,−7)→A''(7,−13)

B(12,−8)→B'(−8,12)→B''(−12,−8)

C(−17,19)→C'(19,−17)→C''(17,19)

represents the reflection of △ABC across the line y=x and its rotation of 90∘ about the origin.

Answer:

Step-by-step explanation:

Ratios of perimeters is a one-to-one measure.  From the figure on the left to the one on the right the ratio of the one-to-one measure is 45/25 which reduces to 9/5.

Area is a squared measure.  Once we have the perimeter reduced (we do), we square those perimeter measures to find the area ratio.

[tex](\frac{9}{5})^2=\frac{81}{25}[/tex]

The translation could result in:

Translation--

It is  a transformation which changes the location of the figure but the shape and size of the figures remains the same i.e. the shape and size of the figure is retained after the transformation.

It either moves the figure up or down by some units.

i.e. f(x) → f(x)+k

then the graph of the function f(x) is shifted k units up is k>0

and k units down if k<0

Similarly it may shift the figure k units to the left or to the right.

i.e. if f(x) → f(x+k)

if k<0 then the function f(x) is shifted k units to the right.

and if k>0 then the function is shifted k units to the left.

Options B, D, and E are correct. A translation could result in a figure moving up, down, and left or right.

Translation in geometry refers to moving a figure from one location to another without changing its shape, size, or orientation. It involves sliding the figure over a plane.

Let's analyze each option:

A. "A figure getting smaller" suggests a transformation involving a reduction in size or being scaled down.

B. "A figure moving up" implies a vertical translation, where the figure is shifting in the upward direction.

C. "A figure flipping upside down" suggests a reflection transformation rather than a translation. It involves a change in orientation rather than a shift in position.

D. "A figure moving left" indicates a horizontal translation, where the figure is shifting to the left.

E. "A figure moving down" signifies a vertical translation, where the figure is shifting in the downward direction.

Based on the given options, a translation can result in:

B. a figure moving up

D. a figure moving left

E. a figure moving down

Translations do not result in a figure getting smaller (Option A) or flipping upside down (Option C).

Complete question:

Which could a translation result in? Select all that apply.

A. a figure getting smaller

B. a figure moving up

C. a figure flipping upside down

D. a figure moving left

E. a figure moving down

Answer:

k =(2/3)

Step-by-step explanation:

25 ^ (3k) = 625

Replace 25 with 5^2   and 625 with 5^4

5^2^3k = 5^4

We know that a^b^c = a^(b*c)

5^(2*3k) = 5^4

5^ (6k) = 5^4

The bases are the same, so the exponents must be the same

6k = 4

Divide each side by 6

6k/6 = 4/6

k = 2/3

Possible number of permutaions that the sum is 4 on two fair dice:

1 & 3

2 & 2

3 & 1

There are only 3 ways to make a sum of 4. Each cube has 6 digits. So, 6 x 6 is 36.

Answer: 3/36 or 1/12

Answer:

1/8

Step-by-step explanation:

There's two ways you can solve this.

Method 1: Let's say you grab the socks one at a time.  The first sock you grab has a 6/16 probability of being red.  If the sock is red, then the second sock you grab has a 5/15 probability of being red, because there's one less red sock and one less sock total.  So the overall probability is:

P = 6/16 × 5/15 = 1/8

Method 2: There are ₆C₂ ways to choose 2 red socks from 6 red socks.  There are ₁₆C₂ ways to choose any 2 socks from all 16 socks.  So the probability that both socks you choose are red is:

P = ₆C₂ / ₁₆C₂ = 15 / 120 = 1/8

The probability that both socks are red is 1/8 if the drawer contains 6 red socks and 10 blue socks

It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

We have:

Total number of socks= 6+10 = 16

Total ways of selecting = C(16, 2) = 120

Ways of selecting 2 red socks from 6 = C(6, 2) = 15

The probability = 15/120 = 1/8

Thus, the probability that both socks are red is 1/8 if the drawer contains 6 red socks and 10 blue socks

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Answer:

C) -9.6

Step-by-step explanation:

1) The answer will be negative because a negative divided my a positive will always be negative and visa-versa.

2) 5 goes into 48 9 times; 5(9) = 45

3) 5 cannot go into 3 so add a 0 to make 30 and place a decimal after -9

4) 5 can go into 30 6 times; 5(6) = 30

5) The remainder is 0 and your answer is C. -9.6

Answer: The Answer is (4,-6)

Step-by-step explanation:

Answer:

  4n^3 -10n^2 +16n -10

Step-by-step explanation:

Use the distributive property to eliminate parentheses, then combine like terms.

  = 2n(2n^2 -3n +5) -2(2n^2 -3n +5)

  = 4n^3 -6n^2 +10n -4n^2 +6n -10

  = 4n^3 +n^2(-6-4) +n(10+6) -10

  = 4n^3 -10n^2 +16n -10

Answer:

x>56

Step-by-step explanation:

Ebony waited more than 56 minutes in the doctor's office. The first step is to recognize the inequality symbols.

"≥" Can be read as more than or equal to

"≤" Can be read as less than or equal to

">" Can be read as more tha

"<" Can be read as less than

In this case, Ebony waited MORE THAN which means that the correct symbol to be used is ">".

The second step is to define a variable. In this case, we're going to say that 'x' represents the time (in minutes) that Ebony waited.

Finally, let's write the inequality.

x > 56 ✔️

Answer:

x>25

Step-by-step explanation:

Answer:

55 small boxes, 65 large boxes.

Step-by-step explanation:

First, we let x = the amount of big boxes and let y = the amount small boxes. Then, we know that any combination of such will equal 120 so we say

x + y = 120

We also know that we have to fill 4900 pounds, so we can say

50x + 30y = 4900

Then, we can use either substitution or elimination. I'll do substitution. we make the first equation

x = 120 - y

And now we can plug this into our second equation

50(120 - y) + 30y = 4900

Then we distrubute

6000 - 50y + 30y = 4900

Then simplify

6000 - 20y = 4900

Subtract 6000 from both sides

-20y = -1100

then divide both sides by -20

y = 55

so there are 55 small boxes, which means we can subtract 55 from 120 to get 65 large boxes.

The truck is carrying 65 large boxes and 55 small boxes,

x + y = 120 (total number of boxes)

50x + 30y = 4900 (total weight of the boxes in pounds)

First, we can solve one of the equations for one variable and then substitute that into the other equation. Starting with the first equation:

x = 120 - y

Now substitute x in the second equation:

50(120 - y) + 30y = 4900

6000 - 50y + 30y = 4900

-20y = -1100

y = 55

Now we know there are 55 small boxes, we can go back to the first equation to find x:

x + 55 = 120

x = 120 - 55

x = 65

Therefore, the truck is carrying 65 large boxes and 55 small boxes.

Answer:

Q'(0.4,-1.7),R'(2.4,9.3), S'(-10.6,7.3)

Step-by-step explanation:

we know that

The rule of the translation is equal to

(x,y) -----> (x-7.6,y+4.3)

That means---> the translation is 7.6 units left and 4.3 units up

Find the coordinates of the vertices of the image

Q(8,-6) -----> Q'(8-7.6,-6+4.3)

Q(8,-6) -----> Q'(0.4,-1.7)

R(10,5) -----> R'(10-7.6,5+4.3)

R(10,5) -----> R'(2.4,9.3)

S(-3,3) -----> S'(-3-7.6,3+4.3)

S(-3,3) -----> S'(-10.6,7.3)

The coordinates of the vertices Q, R, and S of the image of the triangle after a translation are (0.4, -1.7), (2.4, 9.3), and (-10.6, 7.3)

Translation is a way of changing the location of an object on the xy plane.

Given the vertices of the triangle QRS as

Q(8, –6)

R(10, 5)

S(–3, 3)

If the coordinate of the vertices is translated under the rule (x–7.6, y+4.3)

For Q'

Q' = (8-7.6, -6+4.3)

Q' = (0.4, -1.7)

For R':

Q' = (10-7.6, 5+4.3)

Q' = (2.4, 9.3)

For the coordinate S'

S' = (-3-7.6, 3+4.3)

S' = (-10.6, 7.3)

Hence the coordinates of the vertices Q, R, and S of the image of the triangle after a translation are (0.4, -1.7), (2.4, 9.3), and (-10.6, 7.3)

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Answer:

D.

Step-by-step explanation:

A function, by the easy-to-understand definition, is a relation where no x values are shared.  The only set where each x value is different is in D.  All the other sets share the same x value.  Example:  Set C has coordinates (-2, 1) and (-2, 2).  The x coordinates are the same, so this isn't a function.  It is only a relation.

Answer:

14.18 units  &  4.88 units

Step-by-step explanation:

The right triangle in this problem is shown in the attached image.

Using trigonometry, the adjacent leg would be 15 Cos 19°

and the opposite leg would be 15 Sin 19°

Thus,

one leg is 15 Cos 19 = 14.18 units, and

another leg is 15 Sin 19 = 4.88 units

Answer:

For plato users the correct option is D.

Step-by-step explanation:

D. 4.9 units, 14.2 units

Answer:

B.

Step-by-step explanation:

The first number minus the 2nd number will close off the distance.

Answer:

An estimate of a population parameter that provides an interval of values

believed to contain the value of the parameter is known as the inveral estimate.

Step-by-step explanation:

Therefore, the correct answer C.

* Hopefully this helps:)) Mark me the brainliest :))

Answer:

18.1 cm

Step-by-step explanation:

Work out CD

[tex]\sqrt{16^{2}-7^{2}  } = 14.38749457[/tex] ⇒ Pythagoras Theorem

Use CD and AD to work out AC

[tex]\sqrt{14.38749457^{2}+11^{2}  } = 18.11077028[/tex] ⇒ Pythagoras Theorem

Answer:

  C.  13.78 ≤ x ≤ 18.98

Step-by-step explanation:

The rate for Company B is show as 17.4 cents per kWh. That for Company D is shown as 14.8 cents per kWh. The savings obtained by using Company D is ...

  17.4 - 14.8 = 2.6 . . . . cents per kWh

Then to find the savings a household would experience, we multiply this savings rate by the monthly usage rate of the household.

  530 kWh × $0.026/kWh = $13.78

  730 kWh × $0.026/kWh = $18.98

So for household usage between these energy values, the savings (x) using Company D will satisfy ...

  13.78 ≤ x ≤ 18.98

Answer:

x+y=45, (5,40) and ( 25,20)

Step-by-step explanation:

Here we are given the information that Gian was given 45 mins to spend on computer after dinner. Out of those 45 mins , he can either play games of watch videos.

Therefore If the time for which he watches videos is x and that of the time he spend playing game is y , there sum must be equal to 45 mins.

Hence our equation in terms of x andy will be

[tex]x+y=45[/tex]

Now let us see the graph part.

Here we see that the graph is plot on xy plane where x is taken as time taken in watching videos and y as playing games

i) on Monday , he watch 5 minutes in watching videos

Hence x=5 , we put x=5 in x+y=45 and solve it for y

5+y=45

subtracting 5 from both sides

5+y-5=45-5

y=40

Hence he spend 40 mins on playing games.

So we plot Point (5,40) for monday.

i) on Tuesday , he watch 25 minutes in watching videos

Hence x=25 , we put x=25 in x+y=45 and solve it for y

25+y=45

subtracting 25 from both sides

25+y-25=45-25

y=20

Hence he spend 20 mins on playing games.

So we plot Point (25,20) for Tuesday.

First you must distribute the 2x to the numbers inside the parentheses

(2x * x) + (2x * -1) = 3

[tex]2x^{2}[/tex] - 2x = 3

To make this a quadratic equation you can solve bring the 3 over to the left side of the equation by subtracting it to both sides

[tex]2x^{2}[/tex] - 2x - 3 = 0

Use the quadratic equation to solve this (image of the quadratic equation is below)

Remember that quadratic functions are set up like so:

[tex]ax^{2} +bx +c = 0[/tex]

That means that in this equation...

a = 2

b = -2

c = -3

^^^Plug these numbers into the quadratic equation and solve...

[tex]\frac{2+/-\sqrt{(-2)^{2}-4(2)(-3)}}{2(2)}[/tex]

[tex]\frac{2 +/-\sqrt{4+24}}{4}[/tex]

[tex]\frac{2+/-\sqrt{28} }{4}[/tex]

[tex]\frac{2+/-2\sqrt{7} }{4}[/tex]

[tex]\frac{1+/-\sqrt{7} }{2}[/tex]

Keep in mind that +/- is ±

[tex]\frac{1+\sqrt{7} }{2}[/tex]

[tex]\frac{1-\sqrt{7} }{2}[/tex]

^^^Exact answers

Approximations:

1.823

-0.823

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

  A.  $4200

Step-by-step explanation:

A "point" is 1% of the loan value, so the cost of 3 points is ...

  0.03 × $140,000 = $4,200

Hilary must bring an additional $4200 to closing.

The additional money Hilary needs to bring to closing the mortgage is given by A = $ 4,200

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

Typically, one point is equal to 1% of the total loan amount. Therefore, if Hilary is purchasing 3 points to lower her interest rate, she will need to pay an amount equivalent to 3% of her $140,000 mortgage, which is:

On simplifying the equation , we get

3% x $140,000 = $4,200

Hence , the money is $ 4,200

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Answer:

Karen spent $ 10 , Jasmine spent $20 , Maggie spent $30

When x disappears from the equation and the two sides of the equation not equal each other , then the equation has no solution

When x disappears from the equation and the two sides of the equation equal each other , then the equation has infinite solutions

Step-by-step explanation:

* Lets read the problem and solve it

- There are three sisters ⇒ Maggie , Karen , Jasmine

- Each sister bought a gift for their mom

- Maggie spent 3 times as much as Karen

- Karen spent half as much as Jasmine

- Altogether, they spent $60

- Let Jasmine spent x

∵ Karen spent half as much as Jasmine

∴ Karen spent 1/2 x

∵ Maggie spent 3 times as much as Karen

∴ Maggie spent 3 × 1/2 x = 3/2 x

∵ Altogether, they spent $60

∴ x + 1/2 x + 3/2 x = 60

∴ 3x = 60 ⇒ divide both sides by 3

∴ x = 20

* Lets find the share of each one

∵ Jasmine spent x

∴ Jasmine spent $20

∵ Karen spent 1/2 x

∴ Karen spent 1/2 × 20 = $10

∵ Maggie spent 3/2 x

∴ Maggie spent 3/2 x 20 = $30

* Karen spent $ 10 , Jasmine spent $20 , Maggie spent $30

* Lets describe what happens when an equation has no solution

- "No solution" means that there are no values of x satisfy the equation

- When x disappears from the equation and the two sides of the

 equation not equal each other , then the equation has no solution

- Ex: solve the equation 2 + 2x – 8 = 7x + 5 – 5x

∵ 12 + 2x – 8 = 7x + 5 – 5x ⇒ add the like terms

∴ 4 + 2x = 2x + 5 ⇒ subtract 2x from both sides

∴ 4 = 5 ⇒ the two sides not equal

∴ There is no value of x satisfy this equation

∴ There is no solution

* Lets describe what happens when an equation has infinite solutions

- "Infinite solutions" means all numbers are solutions.

- When x disappears from the equation and the two sides of the

 equation equal each other , then the equation has infinite solutions

- Ex: solve the equation 2x + 3 = x + x + 3

∵ 2x + 3 = x + x + 3 ⇒ add the like terms

∴ 2x + 3 = 2x + 3 ⇒ subtract 2x from both sides

∴ 3 = 3 ⇒ the two sides are equal

∴ All values of x satisfy the equation

∴ There are infinite solutions

Answer:

p ≥ 5.5 hrs

Step-by-step explanation:

Let p represent the number of hours Brandon spends practicing per week.

So he practices for atleast 5.5 hrs.

i.e p ≥ 5.5 hrs

The inequality to represent the number of hours Brandon will spend practicing this week is p ≥ 5.5 hrs.

Mathematical expressions with inequalities are those in which the two sides are not equal. Unlike to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

We have,

Brandon wants to practice his trombone for at least 5.5 hours this week.

Let p represent the number of hours Brandon spends practicing per week.

We know the sign for at least is "≥".

So, the inequality is p ≥ 5.5 hrs.

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Answer:

  D)  0.08

Step-by-step explanation:

The pie chart shows that of the 6000 fish in the hatchery, 1/4 of them, or 1500 fish are salmon. A 5% sample of that population will be ...

  0.05 × 1500 fish = 75 fish

If 6 of these have dangerous levels of mercury, the probability of randomly choosing a contaminated fish from the test group is ...

  6/75 = 8/100 = 0.08

The probability of selecting a salmon with dangerous mercury levels can be determined using the given data.

To determine the probability of a randomly selected fish having a dangerous mercury level, we need to find the proportion of tested fish that had dangerous mercury levels. From the table, we can see that out of 120 tested salmon, 3 had dangerous mercury levels. So the probability is 3/120, which simplifies to 1/40 or 0.025. Therefore, the correct answer is option C) 0.02.

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Answer:

  D.  25%

Step-by-step explanation:

Each day, Julia's sales are 1.25 times the previous day's sales. That is, 25% more than the day before. Julia's sales are increasing 25% per day.

ANSWER:

The correct answer is D.25%

STEP-BY-STEP EXPLANATION:

f(x) = 2 * (1.25)^x

This is in the form

y = a b^x

where b is 1 plus the growth rate

b = 1.25 = 1+growth rate

1.25 = 1 + growth rate

.25 = growth rate

25% = growth rate