100 POINTS!!!

2. Millicent's password for a website is a 5-digit number. The digits are the prime factors of 2,205 listed from least to greatest. What is Millicent's password?

33577

D 35577

B 33557

A 33357

Answer:

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

Multiply the second equation by 9 and subtract from the first one:

Answer:

[tex]\left(\; \boxed{1}\:,\boxed{-1}\;\right)\; \textsf{and}\;\left(\; \boxed{7}\:,\boxed{-1}\;\right)[/tex]

Step-by-step explanation:

Given system of conics:

[tex]\begin{cases}(x-4)^2+(y+1)^2=9\\\\\dfrac{(x-4)^2}{9}+\dfrac{(y+1)^2}{81}=1\end{aligned}[/tex]

Multiply the second equation by 81:

[tex]\implies \dfrac{81(x-4)^2}{9}+\dfrac{81(y+1)^2}{81}=81[/tex]

[tex]\implies 9(x-4)^2+(y+1)^2=81[/tex]

Rearrange to make (y + 1)² the subject:

[tex]\implies (y+1)^2=81-9(x-4)^2[/tex]

Substitute into the first equation and simplify:

[tex]\implies (x-4)^2+81-9(x-4)^2=9[/tex]

[tex]\implies -8(x-4)^2=-72[/tex]

[tex]\implies (x-4)^2=9[/tex]

Solve for x:

[tex]\implies \sqrt{ (x-4)^2}=\sqrt{9}[/tex]

[tex]\implies x-4=\pm3[/tex]

[tex]\implies x=4\pm3[/tex]

[tex]\implies x=1, 7[/tex]

Substitute the found values of x into the first equation and solve for y:

[tex]\begin{aligned}x=1 \implies (1-4)^2+(y+1)^2&=9\\(-3)^2+(y+1)^2&=9\\9+(y+1)^2&=9\\(y+1)^2&=0\\y+1&=0\\y&=-1\end{aligned}[/tex]

[tex]\begin{aligned}x=7 \implies (7-4)^2+(y+1)^2&=9\\(3)^2+(y+1)^2&=9\\9+(y+1)^2&=9\\(y+1)^2&=0\\y+1&=0\\y&=-1\end{aligned}[/tex]

Therefore, the solution to the given system of conics is:

The vertex of the parabola is (-1,-1)

What is vertex of parabola?

The vertex of a parabola is the highest point or the lowest point, also known as the maximum or minimum of the parabola. The vertex is the point of intersection of the parabola and its line of symmetry.

The vertex is the maximum or minimum point of a parabola.

The vertex is the point where the parabola changes direction.

Here, the point where the parabola changes it direction is (-1,-1).

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The inequality represented by the graph in slope intercept form is

A graph is a pictorial representation of data and the graph presented represents inequality data

The graph shows a linear function written in the slope intercept form  form as

y = mx + c

where slope, m calculated as

c = intercept

x = input variables

y = output variables

calculation of slope

The points used for the slope is gotten from the graph as (2. 0)  (0, -4)

m = (y₂ - y₁) / (x₂ - x₁)

substituting the values

= ( -4 - 0 ) / ( 0 - 2 )

= -4 / -2

= 2

y intercept, c

this is a point where the graph cuts the y axis

c = -4

The graph contains

this gives the idea to use less than or equal to written with the symbol ≤

hence the equation is written using y = mx + c and substituting the values

y ≤ 2x - 4

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5 is the difference between the two numbers 12 and 7.

Given,

In the question;

The difference between 3 times a number and 7 is 5.

Write and solve an equation to determine the number.

Now, According to the question:

Let's assume the unknown number to be x,

so three time the number would be 3x.

The difference between 3 times a number (3x) with 7 is 5, so we can write it as:

3x - 7 = 5

Now we can solve this equation to the find x (the unknown number).

3x = 5 + 7

3x = 12

x = 12/3

x = 4

Therefore 3x= 12

So, 5 is the difference between the two numbers 12 and 7.

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The number of minute talk's, text message's and picture message's are 128, 72 and 15 respectively.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have Enrique who has a pay-per-use plan on his cell phone. It costs $0.10 per minute talk, $0.20 per text message, and $0.25 per picture message. His total bill last month was $30.95. The total number of text and picture messages sent was 87. The cost for the use of minutes was $1.60 less than the cost of the text messages

Assume that [x], [y] and [z] represents the number of minute talk's, text message's and picture message's respectively. Then -

0.1x + 0.2y + 0.25z = 30.95         ..[1]

y + z = 87           ..[2]

0.1x = 0.2y - 1.6     ...[3]

We can write Eq[1] as -

0.2y - 1.6 + 0.2y + 0.25z = 30.95  

z = 87 - y

0.2y - 1.6 + 0.2y + 0.25(87 - y) = 30.95  

Solving, we get y = 72.

So z = 87 - 72 = 15

and

0.1x = 0.2 x 72 - 1.6

0.1x = 14.4 - 1.6

x = 128

Therefore, the number of minute talk's, text message's and picture message's are 128, 72 and 15 respectively.

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The equations that represent the proportional relationships between the variables are as follows:

     Problem                   Variables to use          Equation

1. Tyler swimming         Time / Distance          D = 1.25t

2. Factory production   Total quantity, Q,         Q = 3s + 8p

                                      and Sparkling / Plain

3. Paint mixture            Blue / White Paints  6q = 1.5b + 5w

An equation models a mathematical statement in which two or more expressions (involving numbers, variables, and operands combined) are equated using the equation symbol (=).

Speed = 5 m/4s

= 1.25 m/s (5/4)

Swimming equation: D = 1.25t

Where D = distance and t = time spent.

Given the speed and time, we can find the swimming distance covered by Tyler.

Bottles of sparkling water = 3

Bottles of plain water = 8

Ratio = 3:8

Production equation, Q = 3s + 8p

Where Q = total quantity, s = sparkling water, and p = plain water

Blue paint = 1 ½ quarts

White paint = 5 quarts

Ratio = 1.5:5

Production equation, 6q = 1.5b + 5w

Where 6q = 6 quarts, b = blue paint, and w = white paint

Thus, using the equations, we can use the known variables to find the unknown variables.

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The addition of w, 9 and 4 is (w+13).

According to the question,

We have the following information:

We need to add w, 9 and 4.

We already know that a variable can only be added or subtracted from the terms having the same variables. For example, 8x can only be added to 5x but not 5y.

So, in this case, w is the variable and it can not be added to any other term because the other two are whole numbers.

Now, the whole numbers can be easily added.

So, we have the following expression:

w+9+4

w+13

Hence, the addition of w, 9 and 4 is (w+13).

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The initial population of the bacterial population at time t = 0, can be found to be 1,406.25.

The size of the bacterial population after 3 hours is 720,000.

The doubling period of the bacterial population is said to be 20 minutes. The number of doubling periods in 120 minutes is:

= 120 / 20

= 6 doubling periods

The initial population is:

= Population at 120 minutes / 2 ^ number of doubling periods

= 90,000 / 2⁶

= 1,406.25

The bacterial population at 3 hours is:

= Bacterial population at t = 0 x 2 ^ number of doubling periods in 3 hours

= 1,406.25 x 2 ^ (180 minutes in 3 hours / 20)

= 1,406.25 x 2⁹

= 720,000

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Answer:

m∠1 = 26°

Step-by-step explanation:

Interior angles of a triangle sum to 180°, not 360°.

Therefore, the correct calculations to find the measure of angle 1 are:

[tex]\boxed{\begin{aligned}115^{\circ}+39^{\circ}+m \angle 1 &=180^{\circ}\\\\154^{\circ}+m \angle1 & = 180^{\circ}\\\\m \angle1 & = 26^{\circ}\end{aligned}}[/tex]

Answer:

Step-by-step explanation:

The Horizontal asymptote of y = 3.10 represents that the average cost per unit will approach $3.10 as the number of units produced increases.

Hope this helps!

Have a great day!!

The Linear equation used is x -y = 1; to find the age of Isabelle's age.

What is Linear Equation?

An equation is said to be linear if the maximum power of the variable is consistent Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, whereas B is a constant. A linear equation with two variables has the conventional form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present. A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

A linear equation is an algebraic equation in which each term has an exponent of 1, and which, when plotted on a graph, always yields a straight line. It is called a "linear equation" for this reason.

Let the age of Ben be x;

Let the age of Amara be y;

According to the question:

It is given that:

Ben is one year younger than Amara. That means we have to form a linear equation such that Amara is one year older than Ben.

So,

We have assumed the Age of Ben is x;

we have assumed the Age of Amara is y;

So, According to the question,

Framing the linear equation,

x -1 =y;

⇒x -y = 1;

Hence, We can find the age of Isabelle using the linear equation: x -y = 1;

where x is ben's age;

where y is Amara's age.

Therefore, The Linear equation used is x -y = 1; to find the age of Isabelle's age.

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The average change in the otter's position each minute is -24.5 ft per minute and the otter goes deeper.

What is average change?

The ratio of "change in the function values" to "change in the interval endpoints" is referred to as the average rate of change of a function f(x) over an interval [a, b].

Here, we have

Sea level changes by -73.5 ft in 3 minutes

So, we apply the average change formula, and we get

= -73.5/3

= - 24.5 ft per minute

And the otter goes deeper because - 24.5 < 0

Hence, the average change in the otter's position each minute is -24.5 ft per minute and the otter goes deeper.

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The explanation is above

Answer:

THE CORRECT ANSWER IS 1.9824 x 10^7

Step-by-step explanation:

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Based on the information given the variance of their​ weights is 119.9200 kg².

What is variance?

The statistical assessment of the variation in numbers within a data collection is known as variance. In more detail, variance assesses how far apart each number in the collection is from the mean (average) and, consequently, from each other. This symbol is frequently used to represent variation: σ².

Main body:

n=sample size=10

Standard deviation=10.9508 kg

Using this formula

Variance=(Standard deviation)²

Let plug in the formula

Variance=(10.9508 kg)²

Variance= 119.9200 kg²

Hence the variance of their​ weights is 119.9200 kg².

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Answer:

x-int=-40

y-int=15

Step-by-step explanation:

we have points 0,15 and -40,0 on the line.

It is as easy as the y-int being 15 and the x-int being -40!

the y-int will always be= (0,#)

the x-int will always be (#,0)

Answer:

x > -2

Step-by-step explanation:

3x - 10 < 4x - 8

Collect like terms

3x - 4x < 10 - 8

-1x < 2

Divide both sides by -1

-1x/-1 < 2/-1

x > -2

An equation of the line that passes through the point (−6,−8) and is parallel to the line x−2y=6 is y=x/2-5.

Given that, an equation of the line that passes through the point (−6,−8) and is parallel to the line x−2y=6.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

We know that, the slope of a line parallel to given line is m1=m2.

Here, x−2y=6

⇒ 2y=x-6

⇒ y=x/2-3

So, slope = 1/2

The slope of a line parallel to the given line = 1/2

Now, put m=1/2 and (x, y)=(-6, -8) in y=mx+c and solve for c

-8=1/2(-6)+c

⇒ c=-8+3

⇒ c=-5

Thus, y=x/2-5

Therefore, an equation of the line that passes through the point (−6,−8) and is parallel to the line x−2y=6 is y=x/2-5.

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The seal's new position relative to the surface of the ocean is 47 meters below.

It is important to note that that question has to do with elevation which is the change in position with regards to the sea or ocean level.

In this case, the harbour seal dives 35 metres below the ocean's surface and then it dives down an additional 12 metres

The new position will be;

= -35 - 12

= -47

This implies that it's 47 meters below the ocean surface.

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The answer to the questions from 4 through 12 are below:

4. z³ + 5z + 3z² + 1 - 4 - 2z²

= z³ + 5z² + 5z + - 3

5. Perimeter of the square = Addition of all the sides

= (2d - 3) + (3c) + (2d - 3) + (3c)

= 2d - 3 + 3c + 2d - 3 + 3c

= 4d + 6c - 6

6. Perimeter of the triangle = Addition of all the sides

= (4a - 2b) + (9a - 4) + (7a + 3)

= 4a - 2b + 9a - 4 + 7a + 3

= 20a - 2b - 1

7. Perimeter of a square = 4 × side length

= 4 × 10x

= 40x

8. Perimeter of a rectangle = 2(length + width)

= 2{(2x + 7) + (3x + 8y)}

= 2(2x + 7 + 3x + 8y)

= 2(5x + 8y + 7)

= 10x + 16y + 14

Simplify the following

9. 3a + a² + 5(a - 2)

= 3a + a² + 5a - 10

= a² + 8a - 10

10. 8(v + w) + 7(v + 2w)

= 8v + 8w + 7v + 14w

= 15v + 22w

11. 4c² + 6(c + c²) - 2c

= 4c² + 6c + 6c² - 2c

= 10c² + 4c

12. z³ + 5(z + 3) + 4(2 - 2z²)

= z³ + 5z + 15 + 8 - 8z²

= z³ - 8z² + 5z + 23

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Answer:

C

Step-by-step explanation:

6/9 simplified is 2/3

Hope this helps

Answer:

-5/4

Step-by-step explanation:

slope

[tex]\frac{y2-y1}{x2-x1}\\\\ \frac{2-(-3)}{-4-0}=\frac{5}{-4}\\ \\slope = \frac{-5}{4}[/tex]

Answer:

$4.90

Step-by-step explanation:

He already has $13.70 (7.40+6.30) saved up so you have to subtract that from 18.60 to find the total Ace needs to save up.

18.60-13.70=4.90

To check your answer, you can add 7.40, 6.30, and 4.90 and see if you get a total of 18.60.

Check: 7.40+6.30+4.90=18.60

When you have a square pyramid, the plane section that will produce a trapezoid is B. A cut parallel to the vertical axis, directly through the vertical axis

It is defined in geometry as a shape with a square base with equal side lengths and all of the square's joints at the top that are perpendicular to the center of the square.

Geometry, as we know, is the branch of mathematics concerned with the size, shape, and orientation of two-dimensional figures. A trapezoid, also known as a trapezium, is a closed, flat shape with four straight sides and one pair of parallel sides.

It's parallel sides are known as the bases, and its non-parallel sides are known as the legs. A trapezoid can have parallel legs as well.

In this case, the cut parallel to the vertical axis, directly through the vertical axis will produce the trapezoid.

In conclusion, the correct option is B.

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When a six sided dice through with the coin all the possible outcomes  are as follows

H-1 H-2 H-3 H-4 H-5 H-6

T-1 T-2 T-3 T-4 T-5 T-6

Probability that she gets an outcome of tails and 2 = 1 / 12

Isabelle flips a fair coin and rells a fair six-sided dice.

Coin has two face H or T

Dice has six face hat is 1, 2, 3, 4, 5, 6  

When a six sided dice through with the coin all the possible outcomes  are as follows

H-1 H-2 H-3 H-4 H-5 H-6

T-1 T-2 T-3 T-4 T-5 T-6

So there are total 12 outcomes possible when a six sided dice through with the coin.

Probability that she gets an outcome of tails and 2 = event occur / total number of events = 1 / 12

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The require angle of x is 52.4°

Given is a quadrilateral

The given diagonal divides the quadrilateral in two parts

the first part is a right angled triangle

Thus to find the side BD

we will use the Pythagoras theorem ;

So according to this theorem

AB² + AD² = BD² [ because BD is the hypotenuse ]

Given AB = 8 cm and AD = 6 cm

8² + 6² = BD²

this implies 64 + 36 = BD²

100 = BD which implies BD = 10 cm

To find x

we know that in triangle BCD

BD = 10 cm and CD = 13 cm

tan theta = [tex]\frac{13}{10}[/tex]

this means theta = [tex]tan^{-1}[/tex] [tex]\frac{13}{10}[/tex]

theta = 52.4°

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Answer:

39.07

use pythagros to find bd then use the sine rule substitute in the values

bd=10

beacuse a²+b²=c²

substitute in 8²+6²=c²

The real​ after-tax interest​ rate is -0.0096%, if the inflation rate rises to 4%

The real interest rate is the interest rate received by an investor, saver, or lender after adjusting for inflation. The Fisher equation, which indicates that the real interest rate is roughly the nominal interest rate minus the inflation rate, can be used to define it more explicitly.

For example, if an investor could lock in a 5% interest rate for the future year and expected a 2% increase in prices, they would receive a 3% real interest rate.

Because different investors forecast different levels of future inflation, the expected real interest rate is not a single number. Because the inflation rate during the life of a loan is unknown at the outset, inflation volatility represents a risk.

Given,

The income tax rate is 50%

After tax rate=Nominal return×(1- tax rate)

=0.06(1-0.5)

=0.03=3%

Inflation rate raises to 4% then,

=(1+ rate interest)/(1+Inflation rate)-1

=(1+0.03)/(1+0.04)-1

=-0.0096%

The real​ after-tax interest​ rate is -0.0096%.

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The proportional equation between y and x^2 is:

y = 3*x^2

We know that y is directly proportional to x^2, then we can write:

y = k*x^2

Where k is the constant of proportionality.

We also know that when x = 10, the value of y is 300, replacing that in the above equation we get:

300 = k*(10)^2

Now we can solve this for k:

300 = k*100

300/100 = k

3 = k

Then the equation is:

y = 3*x^2

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Using the probability of adults of having tattoo, critical value is 1.76 and margin of error is 0.0353 and a 95% confidence interval for the proportion of all adults that have a tattoo is (0.2347, 0.3053)

In the given question,

In a poll of 489 adults, 132 of then said they have a tattoo.

We have to find critical value and margin of error, and then construct a 95% confidence interval for the proportion of all adults that have a tattoo.

From the question

Total number of adults = 489

The adults that have tattoo = 132

So the proportion in the sample is

p = 132/489

p = 0.269

p ≈ 0.27

Now finding the proportion of adults not having tattoo.

q = 1−p

q = 1−0.27

q = 0.73

Now finding the critical value(z).

The value of z from the standard table for 95% confidence interval.

We can write 95% as 0.95

Z = [tex]z_{\alpha /2}[/tex]

Z = [tex]z_{0.95 /2}[/tex]

Z = [tex]z_{0.475}[/tex]

From the standard table of z

Z = 1.96.

Now finding the margin error.

Margin Error(E) = [tex]Z\times\sqrt{\frac{pq}{n}}[/tex]

As we know that Z = 1.96, p = 0.27, q = 0.73, n = 489

Now putting the value

E = [tex]1.76\times\sqrt{\frac{0.27\times0.73}{489}}[/tex]

Simplifying

E = [tex]1.76\times\sqrt{\frac{0.1971}{489}}[/tex]

E = [tex]1.76\times\sqrt{0.000403}[/tex]

E = 1.76×0.0201

E = 0.0353

Now finding a 95% confidence interval for the proportion of all adults that have a tattoo.

Confidence Interval = p−E< P < p+E

Confidence Interval = 0.27−0.0353< P < 0.27+0.0353

Confidence Interval = 0.2347< P < 0.3053

Hence, critical value is 1.76 and margin of error is 0.0353 and a 95% confidence interval for the proportion of all adults that have a tattoo is (0.2347, 0.3053)

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