Section 5.2-4 Graph the following system of equations and find the solution. Plot the solution on the graph. Enter your answer as (x,y). -2x-3y = 0 x+3y = 3 1 2 3 4 5 -1 -2 -3 -4 -5 1 2 3 4 5 -1 -2 -3 -4 -5 Clear All Draw: LineDot Solution =

A 90% confidence interval for the proportion of cell phone owners aged 18 - 24 who have an Android phone is 0.503 < p < 0.397.

In the given question,

We have to construct a 90% confidence interval for the proportion of cell phone owners aged 18 - 24 who have an Android phone.

A 90% confidence interval for the proportion of cell phone owners aged 18 - 24 who have an Android phone is

..............< p <...............

We have to construct the 90% confidence interval.

From the given question we know that among 240 cell phone owners aged 18 - 24 surveyed, 108 said their phone was an android phone.

So the total number of cell phone owners aged 18 - 24 is 240.

So n=240

From them 108 have an android phone.

So x=108

Estimation of sample proportion([tex]\hat p[/tex]) = x/n

Now putting the value

Estimation of sample proportion([tex]\hat p[/tex]) = 108/240

Estimation of sample proportion([tex]\hat p[/tex]) = 0.45

Now the construct a 90% confidence interval for the proportion of cell phone owners aged 18 - 24 who have an Android phone

C.I. = [tex](\hat p \pm z_{\alpha /2}\sqrt\frac{\hat p(1-\hat p)}{n}})[/tex]

As we know that

[tex]\hat p=0.45[/tex]

Now finding the value of [tex]z_{\alpha /2}[/tex]

We have to find the 90% confidence interval. We can write 90% as 90/100 = 0.90

So [tex]\alpha[/tex] = 1-0.90

So [tex]z_{\alpha /2}=z_{0.10 /2}[/tex]

[tex]z_{\alpha /2}=z_{0.05}[/tex]

From the standard z table

[tex]z_{0.05}[/tex] = 1.645

Now putting the value in the

C.I. =  [tex](\hat p \pm z_{\alpha /2}\sqrt\frac{\hat p(1-\hat p)}{n}})[/tex]

C.I. = [tex](0.45 \pm 1.645{\sqrt\frac{0.45(1-0.45)}{240}})[/tex]

Simplifying

C.I. = [tex](0.45 \pm 1.645{\sqrt\frac{0.45\times0.55}{240}})[/tex]

C.I. = [tex](0.45 \pm 1.645{\sqrt\frac{0.2475}{240}})[/tex]

C.I. = [tex](0.45 \pm 1.645\sqrt{0.001031})[/tex]

C.I. = [tex](0.45 \pm 1.645\times0.0321)[/tex]

C.I. = [tex](0.45 \pm 0.053)[/tex]

We can write it as

C.I. = {(0.45+0.053),(0.45-0.053)}

C.I. = (0.503,0.397)

Hence, a 90% confidence interval for the proportion of cell phone owners aged 18 - 24 who have an Android phone is

0.503 < p < 0.397.

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The average of a set is computed as follows:

In this case,

Answer:

-8, -5, -2, 1, 4

Explanation:

The given sequence is an arithmetic sequence -8, -5, -2 ....

The nth term of the sequence is expressed as;

Tn = a+ (n-1)d

a is the first term = -8

d is the common difference = -5 -(-8) = -2-(-5)

d = -5+8 = -2+5 = 3

Get the 4th term;

n = 4

T4 = -8+(4-1)*(3)

T4 = -8+3(3)

T4 = -8+9

T4 = 1

Get the 5th term:

n = 5

T5 = -8 + (5-1)*3

T5 = -8+4(3)

T5 = -8 + 12

T5 = 4

Hence the next two terms of the sequence are 1 and 4

If we use the variable t to represent the number of hours skating, the fixed price is $5 and the variable price is $3 per hour, that is, we have a variable cost of 3t.

So the final cost (variable C) is the sum of the fixed and variable costs:

Note that the slope is expressed as :

From the given, the slope is 2/3

So it means that from the point (2,1)

You need to rise 2 units upward and run 3 units to the right

It will be look like this :

Next step is to connect these two points by drawing a line.

That's it, the line is in blue line.

He needs 2/3 cup of sugar . But he can only find 1/2 cup measures.

tan (Q) = opposite/ adjacent

tan (55º) = PR/ 4.9

________________________

1.43 = PR/ 4.9

PR= 1.4* 4.9 = 6.9

Answer

6.9

______________________________________

Can you see the updates?

Do you have any questions regarding the solution?

____________________

PR= tan (55)* 4.9 = 6.997925 ≅ 7

_________________________________

The correct option is negative 23 over 14 times j plus negative 1 over 15

Given,

The expression negative one seventh j plus two fifths minus the expression three halves j plus seven fifteenths

The expression; -1/7j + 2/5 - 3/2j + 7/15

negative one seventh j = - 1/7j

two fifths = 2/5

three halves j = 3/2 j

seven fifteenths = 7/15

Now,

Substitute the values;

- 1/7j + 2/5 - 3/2j - 7/15

- 1/7j - 3/2j + 2/5 - 7/15

-2j - 21j /14 + 6  7 /15

-23j/14 + -1/15

Therefore,

The correct option is negative 23 over 14 times j plus negative 1 over 15

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The amount Rebecca has put into fixed savings each month to cover her annual expenses for life insurance, auto insurance and real estate taxes is $ 194.

Given that:-

Amount invested in life insurance = $ 255

Number of payments in life insurance = 4

Amount invested in real estate taxes = $ 455.35

Number of payments in real estate taxes  = 2

Amount invested in auto insurance = $ 66.21

Number of payments in auto insurance = 6

We have to find the amount Rebecca has put into fixed savings each month to cover her annual expenses for life insurance, auto insurance and real estate taxes.

Hence,

Total amount put by Rebecca in a year = 255*4 + 455.35*2 + 66.21*6 = 1020 + 910.70 + 397.26 = $ 2,327.96

Amount put by Rebecca in a month = 2327.96/12 =  $ 193.997 ≈ $ 194

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We want to know how many brownmies did Fred and his family eat together.

We will call to the total of the brownies by 1. On this case, after Fred ate 1/3 of the brownies, he will have:

This means that he has left 2/3 of the brownies. After his family ate 1/6 of the brownies:

This means they will have left 1/2 of the tray of brownies, and that they ate half of it.

The shape of the pizza is circular. This means that the total angle possible is 360 degrees.

Since the pizza have 12 equal slices

Then each slice will represent

Therefore, If you decide to eat 4 four slices, then

you will eat

Answer = 120 degrees

From the graph provided we can determine two points which are;

For the equation of the line given in slope-intercept form which is;

We would begin by calculating the slope which is;

We can now substitute the values shown above and we'll have;

Now we have the slope of the line as 3/2, we can substitute this into the equation and we'll have;

We now have the equation as;

We now have the y-intercept as -3. The equation now is;

The graph of this is now shown below;

We shall now draw lines to indicate the 'rise' and 'run' of this graph.

ANSWER

Observe carefully that the "Rise" is the movement along the y-axis (3 units), while the "Run" is the movement along the x-axis (2 units).

This clearly defines the slope of the equation that is;

You have the following function:

the x coordinate of the vertex is given by:

in this case, a = 2 and b = -4. Replace these values into the previous expression and simplify:

next, replace the previous values of x into the function g(x):

then, the vertex is (1,-18)

In order to graph, calculate another point for any value of x, for instance, for x = 0:

g(0) = 2(0)^2 - 4(0) - 16

6x - 9y - 7x + -6y

To simplify the expression add the like terms

The like terms are the terms which have the same variable and same degree

6x, -7x are like terms

-9y, -6y are like terms

So let us add them

(6x + -7x) + (-9y + -6y)

6 + -7 = -1

6x + -7x = -x

-9 + - 6 = -15

-9y + -6y = -15y

(6x + -7x) + (-9y + -6y) = -x + -15y

Remember (+)

Explanation

where x is the number of days since the start of the job

and f(x) is the rate of change

Step 1

a)find the total expenditure if the job takes 12 days

so, as x represents the number of days, just replace and calculate

let x= 12

so

a) 51.1

Step 2

now, let's find the total spent on the job from the 10 to 20th day

a) find the x value ( number of days since the job started)

x= 20 days-10dys= 10

so

x= 10

The points of the graph of a function f(x) have the form (x,f(x)). This means that the values of f(0) and f(2) are the y-values of the points in the graph that have 0 and 2 as their x-values. If you look at the graph you'll notice that the points (0,1) and (2,4) are part of the graph which implies that:

Then we get:

Then the answer is option C.

We know,

1 liter=1000 milliter.

So, millilters in 1/5 liters​ is,

Therefore, there are 200 milliters in 1/5 liters.

The amount of money that Johnny makes now = $282,508.38

Annual payment is the type of payment that is done every 12 month and by the end of the year.

The initial annual payment received by Johnny= $111,180

The new career pays the rate of 154.1% more that is;

( 154.2% of $111,180 ) + $111,180 Which is;

= (154.1/100 × 111,180) + $111,180

= (17,132,838/100) + $111,180

= $ 171,328.38 + $111,180

= $282,508.38.

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Explanation:

To know how much ice pop mixture can each mold hold, we need to calculate the volume of the mold.

The volume of a cone is equal to

Where r is the radius and h is the height of the cone. Replacing r = 2 cm and h = 15 cm, we get:

Therefore, the answer is

A. 20

The given expression is

We just have to multiply.

We need the actual question. I can write the compounded interest accrued value equation for this, but if no question about number of years the deposit is kept, there is no question to be solved. Please continue the formulation of the question. What is it we need to find? what amount of money she needs to collect?

The formula for accrued value with compounded interest would be written as:

with the information on the account, we can write it as:

but we cannot do anything with it unless you give:

1) the time to keep the account collecting interest,

OR

2) the total amount of money she needs to obtain.

What is the value of that new bicycle she wants?

Well, you have the equation needed. If you don't give me more info on what is needed, I cannot help you solve the equation. We need an extra piece of information.

The information now provided is that the person wants to keep the savings account for 2 years. So we use t = 2 in the equation above to obtain the answer:

At the end of the two years she will have a total of $832.32

Answer:

[tex] \sf x=-1.25 [/tex]

[tex]\sf--------------------------------------------------------------------- [/tex]

Step-by-step explanation:

4x = -5

Divide both sides by 4 to single out the variable

4x/4 = -5/4

x = -1.25

The rational expression is given as,

Performing the division and multiplication in the given rational expression,

The rational expression after using the indicated operation we get,

Because we have the same denominator we can do the subtraction

Paul did well the representation of the fractions in the diagram, but the operation that he made as we can see is wrong because the result is 9/10

The pair of complex numbers whose sum is -4 and whose product is 53 is illustrated as -b² - 4b - 53 = 0.

Let the numbers be represented as a and b.

Therefore a + b = -4 .....i

a × b = 53 ........... ii

From equation I, a = -4 - b

Put this into equation ii

ab = 53

(-4 - b)b = 53

-b² - 4b = 53

Equate to 0

-b² - 4b - 53 = 0

The value can be found using the Almighty formula

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The value of

The core concept of mathematics' calculus is functions. The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

g(n) = n² − 4, h(n) = n − 5

g(n).h(n)

= (n² − 4).(n-5)

= n³ - 5n² - 4n + 20

and, g(x) = 4x + 4, f(x) = x³ − 1

(gof)(x)

=g(f(x))

=g(x³-1)

= 4(x³-1) + 4

= 4x³ - 4 + 4

= 4x³

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The scale factor from the drawing to the room is 1 to 30. Then, multiply the dimensions of the drawing by 30 to obtain the real dimensions of the room. Then, use the real values to find the area of the room.

Since the length is labeled 2 inches, the real length of the room is:

Since the width is labeled 4.5 inches, the real with of the room is:

1 foot is equal to 12 inches. Then, divide the dimensions by 12 to find the measurements in feet:

Multiply the width and the length to find the area of the room:

Therefore, to the nearest whole number, the area of the game room is 56ft^2.

The value of x = 40°

To solve for x, we will use an illustration:

When two lines intersect, the angles opposite each other are vertical angles. Vertical angles are equal.

The angles marked in magenta are equal.

The angle by the right in magenta colour will also be 52°.

The sum of angles in a triangle = 180°

x° + 52° + 88° = 180°

x + 140 = 180

subtract 140 from both sides:

x + 140 - 140 = 180 - 140

x = 40°

shoe box = 1 cubic foot = 1 * 1 * 1

1 Layer: 6 shoe boxes -> Layer lenght = 6 feet, layer depht = 1 foot

Box height = 4 feet

Box volume = 6*4*1 = 24 feet

McKenzie wants to determine which ice cream option is the best choice.

Part (a)

Volume of Scoop:

A scoop of ice cream is considered a perfect sphere and has a 2-inch diameter.

The volume of the sphere is given by

Where r is the radius.

We know that radius is half of the diameter.

So, the volume of a scoop of ice cream is

Therefore, the volume of a scoop of ice cream is 4.19 in³

Volume of Cone:

A cone has a 2-inch diameter and a height of 4.5 inches.

The volume of a cone is given by

Where r is the radius and h is the height of the cone.

We know that radius is half of the diameter.

So, the volume of a cone of ice cream is

Therefore, the volume of a cone of ice cream is 4.71 in³

Volume of Cup:

A cup, considered a right circular cylinder, has a 3-inch diameter and a height of 2 inches.

The volume of a right circular cylinder is given by

Where r is the radius and h is the height of the right circular cylinder.

We know that radius is half of the diameter.

So, the volume of a cup of ice cream is

Therefore, the volume of a cup of ice cream is 14.13 in³

Part (b)

Now let us compare the various given options and decide which option is the best value for money

Option 1:

The price of one scoop in a cup is $2

The volume of one scoop of ice cream is 4.19 in³

Option 2:

The price of two scoops in a cup is $3

The volume of one scoop of ice cream is 4.19 in³

Option 3:

The price of three scoops in a cup is $4

The volume of one scoop of ice cream is 4.19 in³

Option 4:

The price of half a scoop in a cone is $2

The volume of one scoop of ice cream is 4.19 in³

The volume of one cone of ice cream is 4.71 in³

Option 5:

The price of a cup filled with ice cream is $4

The volume of a cup is 14.13 in³

As you can see, the option 5 (a cup filled with ice cream) has the highest rate (volume/$)

This means that option 5 provides the best value for money.

Therefore, McKenzie should choose "a cup filled with ice cream level to the top of cup" for the best value for money.