The office manager orders computer paper every 6 weeks and printer ink cartridges every 8 weeks.

QUESTION: If she places an order for both paper and ink this week, how many weeks will it be until she orders them both in the same week again?

Answer:

m = -2 and n = -3

Explanation

Given the polynomial

x^2 - 5x + 6

Rewrite as x^2 +mx + nx + 6

x^2 - 2x - 3x + 6

Compare

mx = -2x

m = -2

Similarly;

nx = -3x

n = -3

Hence m = -2 and n = -3

In the given illustration, angle 1 and angle 2 are corresponding angles.

Note that corresponding angles in parallel lines are congruent.

angle 1 measures (63 - x)

angle 2 measures (72 - 2x)

Since both angles are congruent with each other, equate the angles :

The measure of angle 1 will be :

The measure of angle 2 will be :

ANSWERS :

a. x = 9

b. angle 1 = 54 degrees

angle 2 = 54 degrees

Probability of red or green card = 3/5

Number of red cards = 3

Number of blue cards = 6

Number of green cards = 6

Total number of cards = 6 + 6 + 3 = 15

Probability of red or green card = Probability of red card + Probability of green card

Probability of red card = number of red cards/total number of cards

Probability of red card = 3/15

Probability of green card = number of green cards/total number of cards

Probability of green card = 6/15

Probability of red or green card = 3/15 + 6/15

Probability of red or green card = 9/15

In simplest term:

Probability of red or green card = 3/5

Answer:

85% but in a fraction 17/20

Step-by-step explanation:

The given system of equations is

We will substitute y in equation (2) by equation (1)

Now, add 4x to both sides

Subtract 9 from both sides

Divide both sides by 5

Substitute x by -3 in equation (1) to find y

The solution of the system is (-3, 6)

1) Considering a Normal Distribution, then we can write out the following:

Note that we're dealing with probabilities.

2) Let's find out the Z-score resorting to a table, we get:

2.2) So we can infer from 1 and 2:

Notice that this distribution refers to 120 families

Step-by-step explanation:

Chance to roll even number on one dice is 1/2 so

[tex] \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} [/tex]

Answer:

r=19

Step-by-step explanation:

15-r=-4

r=19

:]

To solve this problem, we have to compute the circumference of a circle of diameter:

Recall that the circumference of a circle is given by the following formula:

where d is the diameter.

Therefore, the circumference of the reservoir is:

SpongeBob spins the spinner to the left. What is the probability that the spinner lands on a number greater than 6?​

we know that

The total numbers in the spinner are 10

The numbers that are greater than 6 are (7,8,9 and 10)------> 4 numbers

so

To find out the probability, divide the total numbers that are greater than 6 by the total number

therefore

P=4/10

Percent

P=4/10(100)

the answer is

To simplify the expression (x-2) +(x+6), you have to follow these steps:

1.Get rid of the parentheses:

(x-2) +(x+6)

x -2 + x + 6

2. Combine like terms:

x + x - 2 + 6

2x + 4

So the answer is 2x + 4

A relationship is a function if and only if for each input, there exists only one output i.e an input cannot have two or more outputs.

We can determine which of the relationship is a function by plotting a graph of the relationship.

The only correct option is the relationship:

The graph of the function is shown below:

A) Simplification of the given Algebraic Expression is; [-⁴³/₂₄j + (-1)]/12

B) The equivalent expression to 3(−4.5b − 2.1) − (6b + 0.6) is - 19.5b - 6.9

A) We want to simplify negative one eighth j plus two thirds minus the expression five thirds j plus nine twelfths. This would be expressed as;

-1/8j + 2/3 - (5/3j + 9/12)

= -1/8j + 2/3 - 5/3j - 9/12

= -1/8j - 5/3j + (2/3 - 9/12)

= (-3j-40j / 24 + (8-9) / 12

= [-⁴³/₂₄j + (-1)]/12

B) The expression equivalent to 3(−4.5b − 2.1) − (6b + 0.6)

Expand the brackets to get;

-13.5b - 6.3 - 6b - 0.6

= -13.5b - 6b - 6.3 - 0.6

= - 19.5b - 6.9

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Given that

The equation is

and we have to convert it into the form of

Answer:

98 small drinks and 57 large drinks.

Explanation:

Let's call x the number of small drinks and y the number of large drinks.

If they sold 155 drinks, we can write the following equation:

x + y = 155

In the same way, they made $265, so

1.25x + 2.50y = 265

Because each small drink cost $1.25 and each large drink cost $2.50.

Now, we can have the following system of equations

x + y = 155

1.25x + 2.50y = 265

Solving the firs equation for y, we get:

x + y - x = 155 - x

y = 155 - x

Replacing this on the second equation:

1.25x + 2.50y = 265

1.25x + 2.50(155 - x) = 265

Then, solving for x, we ge:

1.25x + 2.50(155) - 2.50(x) = 265

1.25x + 387.5 - 2.50x = 265

-1.25x + 387.5 = 265

-1.25x + 387.5 - 387.5 = 265 - 387.5

-1.25x = -122.5

-1.25x/(-1.25) = -122.5/(-1.25)

x = 98

Finally, we can find the value of y replacing x = 98

y = 155 - x

y = 155 - 98

y = 57

Therefore, they sell 98 small drinks and 57 large drinks.

Given a quadratic equation in vertex form

In our case,

h = -10, and k= 2

Therefore the vertex is (-10, 2)

The distance from Point B (-1, 11) to line y = (-1 ÷ 3x) - 6 is 15.811.

The distance from the point B(-1 , 11) to the line y= (-1 ÷ 3x) - 6 is given by the distance formula d = (|Ax1 + By1 + C|) ÷ (√(A² + B²)).

Comparing the equation  y= (-1 ÷ 3x) - 6 with the standard forms Ax + By+ C = 0.

It is clear that the coefficient of x, A = -1 ÷ 3.

The coefficient of y, B = -1. The constant C = -6 and the points x1 = -1 and y1 = 11.

Substituting these data in the equation the distance d = (|(-1÷3)×(-1)+ (-1)×11 + (-6)|) ÷ √((-1 ÷ 3)² + (-1)² ) solving the equation the distance d becomes,

d = 15.811.

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parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone.

What is a parabola in math?

     -9(x_6)²_1

     =  -9(x-6)1

     =-9x+54

    Differentiate  x

   -9

   -9(x-6)²

   Subtract

    d/dx(-9(x-6)

    Calculate x-6

    d/dx (-9x+54)

   -9x1-1

     -9x

  =-9

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Answer:

............where is it?

The sample standard deviation of the population with confidence interval of 95% is 13.57

Standard deviation gives a value that measures how much the given value differ from the mean.

Given data form the question

95% confidence interval

population mean of a normally distributed variable is 17.3 to 24.5

population was 76

Definition of variables

confidence interval = CI = 95%

mean = X = 17.3 to 24.5

taking the average, X = 21.45

standard deviation = SD = ?

Z score = z = 1.96

from z table z score of 95%confidence interval = 1.96

sample size = n = 76

The formula for the confidence interval is given by

[tex]CI=X+Z\frac{SD}{\sqrt{n} }[/tex]   OR   [tex]X-Z\frac{SD}{\sqrt{n} }[/tex]

[tex]24.5=21.45+1.96\frac{SD}{\sqrt{76} }[/tex]

[tex]24.5-21.45=1.96\frac{SD}{\sqrt{76} }[/tex]

[tex]3.05=1.96\frac{SD}{\sqrt{76} }[/tex]

[tex]\frac{3.05}{1.96} =\frac{SD}{\sqrt{76} }[/tex]

[tex]1.5561 =\frac{SD}{\sqrt{76} }[/tex]

SD = √76 * 1.5561

SD = 13.56577

SD ≈ 13.57

The standard deviation is solved to be 13.57

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The ratio of the new scale that we are to be having is going to be 1/2

we have the ratio to be 1 grid unit / 2 ft

the new scale ratio is given as 1 grid unit / 4 ft

We have to divide the ratio of the original scale to the new scale that we have here

This would be ( 1 grid unit / 4 ft ) / ( 1 grid unit / 2 ft)

This can be written as

1/4 * 2/1

when we rewrite it we would have 2/4

= 1/2

This is 1 unit 2 feet

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Describe the transformation from the parent graph of y - 4 = – 2(x – 3)^2. Graph

both the parent graph and the transformed graph on the grid provided. Plot at least

three distinct points for each.

we have that

the parent function is

y=x^2

Is a vertical parabola open upward with the vertex at (0,0)

the transformed function

is

y-4=-2(x-3)^2

y=-2(x-3)^2+4

Is a vertical parabola open downward with vertex at (3,4)

so

The transformations are

1) Reflection over x-axis

Rule is

(x,y) ------> (x,-y)

y=x^2 ------------------> y=-x^2

2) Vertical Dilation with a scale factor of 2

Rule

(x,y) --------> (x,2y)

y=-x^2 ----------> y=-2x^2

3) Translation 3 units at right and 4 units up

Rule is

(x,y) --------> (x+3,y+4)

y=-2x^2 --------> y=-2(x-3)^2+4

see the graph to better understand the problem

There are various types of equation systems, including linear, non-linear, and multiple or single-variable systems.

A set of two linear equations with two variables is a system of linear equations.

ax + by = C

A set of two or more equations in two or more variables that includes at least one nonlinear equation is referred to as a system of nonlinear equations. A nonlinear equation can be written as ax+by+C≠0 or ax + b y + C ≠0.

The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers, and x is a variable. This equation has only one solution.

Ex: ax+b = 0

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Answer:

Explanation:

From the information given,

mean = 101

standard deviations = 14

We need to find the number of standard deviations between 73 and the mean.

Number of standard deviations = (73 - 101)/14 = - 28/14 = - 2

It is 2 standard deviations from the mean. According to the empirical rule, 95% of the population lies between 2 standard deviations of the mean. The required area is to the right of 2 standard deviations since we want to find the least score. Thus, the probability of having IQ scores are at least 73 is

We would convert to percentage by multiplying by 100

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{5}{8}p-\frac{3}{4}=4 } \end{gathered}$}}[/tex]

Add 3/4 to both sides.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{5}{8}p=4+\frac{3}{4} } \end{gathered}$}}[/tex]

Convert 4 to the fraction 16/4.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{5}{8}p=\frac{16}{4} +\frac{3}{4} } \end{gathered}$}}[/tex]

Since 16/4 and 3/4 have the same denominator, add their numerators to add them together.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{5}{8}p=\frac{16+3}{4} \longmapsto \ \ Add } \end{gathered}$}}[/tex]

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{5}{8}p=\frac{19}{4} } \end{gathered}$}}[/tex]

Multiply both sides by 8/5, the reciprocal of 5/8.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{p=\frac{19}{4}\times\left(\frac{5}{8}\right) } \end{gathered}$} }[/tex]

Multiply 19/4 by 8/5 (to do this, multiply the numerator by the numerator and the denominator by the denominator).

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{p=\frac{19\times8}{4\times5 }\longmapsto \ Multiply } \end{gathered}$}}[/tex]

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{p=\frac{152}{20} } \end{gathered}$}}[/tex]

We reduce the fraction 152/20 to its minimum expression by extracting and canceling 4.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{p=\frac{152}{20} \ \ \longmapsto \ p=\frac{152\div4}{20\div4}=\frac{38}{5} } \end{gathered}$}}[/tex]

The domain of the function for the volume of the liquid = 0 ≤ V ≤ 7.5 liters.

The domain of a function is the complete set of possible values of the independent variable.

Also a domain of a function refers to "all the values" that go into a function.

From the  graph the domain of the function of the volume of the  of liquid in the bucket is calculated as follows;

The minimum value of the volume of liquid in the bucket = 0

The maximum value of the volume of liquid in the bucket = 7.5 liters

The domain of the function for the volume (V) of the liquid = {0, 1, 2, 3, 4, 5, 6, 7.5 liters}

0 ≤ V ≤ 7.5 liters

Thus, the domain of the function or independent variables that satisfies the function include natural numbers between 0 to 7.5 liters. That is the domain of the function is {0, 1, 2, 3, 4, 5, 6, 7.5 liters}.

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The given expression is

Solving for a means that we need to isolate that variable.

First, we need to multiply the equation by 4

Second, we divide the equation by x

Therefore, the answer is

The sum of the first five terms in this series is 4 14/27.

Fractions are used to depict the components of a whole or group of items. Two components make up a fraction. The numerator is the number that appears at the top of the line. It specifies how many identically sized pieces of the entire event or collection were collected. The denominator is the quantity listed below the line. The total number of identical objects in a collection or the total number of equal sections that the whole is divided into are both displayed. A fraction can be expressed in one of three different ways: as a fraction, a percentage, or a decimal. The first and most popular way to express a fraction is in the form of the letter ab. Here, a and b are referred to as the numerator and denominator, respectively.

The first five terms

6

-6/3

6/9

-6/27

+6/81

The first thing to do is change all the fractions denominators to 81.

Sum = 6*81/81 - 6(27)/81 + 6 × 9/81 - 6 × 3/81 + 6/81

Now add

Sum = 366/81

Sum = 4 14/27

Sum = 4.5185

Recall the first term. It was increased by 6 × 81/81. Nothing is affected by the 81 over 81 in terms of value. 6 × 81/81 remains 6. It merely makes combining it with the other members of the series simpler.

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Given the expression

-2/3(9/2x + 15/2)

Open the parenthesis;

= -2/3(9/2 x) - 2/3(15/2)

= -18x/6 - 30/6

= -3x - 5

Hence the expression in its simplest form is -3x - 5