use a system of equations to solve the problem. for its sales staff, a company offers two salary options. salary option one (i1) is $386 per week plus a commission of 3 1 2 % of sales. salary option two (i2) is $200 per week plus 4 1 4 % of sales. find equations that express incomes i1 and i2 as functions of sales x.

Answer:

No Solution.

Step-by-step explanation:

-x-10y=5

-x-10y=9

--------------

-x-10y=5

-(-x-10y)=-9

------------------

-x-10y=5

x+10y=-9

----------------

0=-4

no solution

Answer:

Assuming you are looking for an expression to represent the area of the rectangle, as you didn't provide any values for the length or width, the area of the rectangle is \(x^{2} +4x\) \(un^{2} .\)

Step-by-step explanation:

          The formula for the area of a rectangle is \(a=lw\), where \(l\) represents the length of the rectangle, and \(w\) represents the width. We are given that the length of the rectangle is 4 units longer than its width, so we can set the width to be represented by the variable \(x\), and we get that the length and width are \(x+4\) and \(x\) respectively. As we are trying to find the area of the rectangle, we have to multiply the length and width of the rectangle together, which then we will get that the area of the rectangle is \(x(x+4)=x^{2} +4x\) \(un^2.\)

          If your teacher or whatever website you're using requires a specific variable, you can just replace the \(x\) in the expression to whatever you need.

Have a great day! Feel free to let me know if you have any more questions :)

We can compute various descriptive statistics such as the mean, median, mode, range, variance, standard deviation, sum of values, and sum of squared deviations.

The sample mean, also known as the average, provides information about the central tendency of the variable X. It represents the typical or average number of coupons used by the shoppers in the sample. In this case, calculating the mean of the given data would provide an estimate of the average number of coupons used over the 6-month period.

The sample standard deviation measures the dispersion or variability of the data points around the mean. It indicates how much the individual observations deviate from the mean value. A higher standard deviation implies greater variability, indicating a wider range of coupon usage among the shoppers in the sample.

By computing the sample mean and standard deviation, we can understand the average coupon usage and the degree of variability in the data. These statistics help us summarize and interpret the characteristics of the variable X, allowing us to make comparisons, identify outliers, assess the spread of the data, and make inferences about the larger population from which the sample was drawn.

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The sides of the pyramid are as follows

The sides is solved using Pythagoras theorem, perpendicular lines will be imaginarily drawn at some parts that are to enable the use of trigonometry peculiar to right triangle

AC² = 10² + 10²

AC = √(100 + 100) = 14.14 cm

height of the pyramid

h² = 20² - (14.14/2)²

h = √(400 - 49.9849) = 18.71 cm

angle between VC and the base ABCD

cos x = adjacent / hypotenuse

cos x = (10/2) / 20 = 5/20 = 1/4

x = arc cos (1/4) = 75.52 degrees

Angle AVB

= 2(90 - angle between VC and the base)

= (90 - 75.52) * 2

= 28.96 degrees

Angle AVC

let 1/2 < AVC = y

tan y = AC/2 / h

tan y = 14.14/2 / 18.71

tan y = 7.07 / 18.7

y arc tan (7.08/18.7) = 20.71

< AVC = 2 * y

< AVC = 2 * 20.71 = 41.42 degrees

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The centre line of a control chart is calculated by computing the average (mean) of the data for every period.

In control chart analysis, the centre line represents the central tendency or average value of the process being monitored. It is typically obtained by calculating the mean of the data points collected over a specific period. The purpose of the centre line is to provide a reference point against which the process performance can be compared. Any data points falling within acceptable limits around the centre line indicate that the process is stable and under control.

The calculation of the centre line involves summing up the values of the data points and dividing it by the number of data points. This average is then plotted on the control chart as the centre line. By monitoring subsequent data points and their distance from the centre line, deviations and trends in the process can be identified. Deviations beyond the control limits may indicate special causes of variation that require investigation and corrective action. Therefore, the centre line is a critical element in control chart analysis for understanding the baseline performance of a process and detecting any shifts or changes over time.

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Answer:

Step-by-step explanation:

mass of the urine lol

Number of students in the group initially is 7.

From the combination formula, C(n, r) = n!/(r!(n - r)!)

Let the number of students are in the group initially be 'n'.

The number of different committees of 4 students from n students is = C(n, 4).

When the number of students in the group increases by 1 then the total number of students becomes = n + 1

The number of different committees of 4 students from (n + 1) students is = C(n + 1, 4).

According to the question, the number of committees in both the cases are equal.

So the equation best suited for the situation is,

2C(n, 4) = C(n + 1, 4)

2n!/(4!(n - 4)!) = (n + 1)!/[4!(n + 1 - 4)!]

2n!/(n - 4)! = (n + 1)!/(n - 3)!

2n(n - 1)(n - 2)(n - 3) = (n + 1)n(n - 1)(n -2)

2(n - 3) = n + 1

2n - 6 = n + 1

2n - n = 6 + 1

n = 7

Hence the number of students are in the group is 7.

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Linear Interpolation Calculator is a free online tool that shows the interpolated point for specific coordinates, also termed as online calculator.

It allows users to interpolate (interpolation is a mathematical technique for estimating any value between two known points) data points between the sets(two sets) of points or coordinates.

Take the two known points and calculate the value of the point that lies between them. This has been used in as many engineering applications as estimating the value of a point on a graph or table. This calculator helps in estimating the value of a point that lies between two known points on a line.

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The sum of degrees is not equal to twice the number of edges, there is no graph that satisfies the given conditions with 7 vertices and degrees 1, 1, 2, 3, 3, 3, and 6.

There exists a graph with 7 vertices and degrees 1, 1, 2, 3, 3, 3, and 6, we can use the Handshaking Lemma.

The Handshaking Lemma states that the sum of the degrees of all vertices in a graph is equal to twice the number of edges in the graph. In other words:

Sum of degrees = 2 × Number of edges

Let's calculate the sum of degrees using the given degrees:

Sum of degrees = 1 + 1 + 2 + 3 + 3 + 3 + 6 = 19

Now, let's calculate the maximum number of edges possible in a graph with 7 vertices

Max number of edges = (n × (n - 1)) / 2

where n is the number of vertices.

For n = 7, the maximum number of edges is:

Max number of edges = (7 × (7-1)) / 2

Max number of edges = 7 × 6/2

Max number of edges = 21

According to the Handshaking Lemma, the sum of degrees is equal to twice the number of edges.

Sum of degrees = 2 × Number of edges

19 = 2 × 21

19 ≠ 42

Since the sum of degrees is not equal to twice the number of edges, there is no graph that satisfies the given conditions with 7 vertices and degrees 1, 1, 2, 3, 3, 3, and 6.

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Answer:

\((-6 / 5)\) between the two points, given that this function is continuous.

Step-by-step explanation:

Assume that the function in this question is continuous over the interval between the two given points. Divide the change in the value of this function by the width of the interval to find the average rate of change of this function over that interval.

For example, consider a continuous function that goes through \((x_{\text{a}},\, y_{\text{a}})\) and \((x_{\text{b}},\, y_{\text{b}})\). The width of the interval between these two points is \((x_{\text{b}} - x_{\text{a}})\). Over this interval, the value of this function has changed from \(y_{\text{a}}\) to \(y_{\text{b}}\), such that the change in the value of the function is \((y_{\text{b}} - y_{\text{a}})\).

The average rate of change of this function between these two points would be \((y_{\text{b}} - y_{\text{a}}) / (x_{\text{b}} - x_{\text{a}})\).

The function in this question goes through the two points \((2,\, -1)\) and \((-8,\, 11)\). Substitute in these values to find the average rate of change of this function between these two points:

\(\begin{aligned} (\text{avg. rate of change}) &= \frac{y_{\text{b}} - y_{\text{a}}}{x_{\text{b}} - x_{\text{a}}} \\ &= \frac{11 - (-1)}{(-8) - 2} \\ &= \frac{12}{-10} \\ &= -\frac{6}{5}\end{aligned}\).

Louis total distance of 8/5 km. Louis rose his bicycle a total distance of 8/5 km.

Louis rose his bicycle a total distance of 1/2 km + 3/4 km + 7/10 km.

To find the total distance, we need to find a common denominator for the fractions: 2, 4, and 10.

The least common denominator is 20.

So, 1/2 km can be written as 10/20 km, 3/4 km can be written as 15/20 km, and 7/10 km remains the same.

Adding these fractions together, we have:

10/20 km + 15/20 km + 7/10 km = 32/20 km

Simplifying this fraction, we get:

32/20 km = 8/5 km

Therefore, Louis rose a total distance of 8/5 km.

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Louis rode a total distance of 8/5 km or 1 and 3/5 km

Louis rode his bicycle a total of 1/2 km to school, 3/4 km to a ball field, and 7/10 km back home. To find the total distance Louis traveled, we need to add up these three distances.

First, let's add 1/2 km and 3/4 km. To add fractions with different denominators, we need to find a common denominator. The least common multiple of 2 and 4 is 4.

Converting 1/2 to have a denominator of 4, we get 2/4. Now we can add 2/4 + 3/4, which equals 5/4.

Next, we need to add 5/4 km and 7/10 km. To add fractions with different denominators, we need to find a common denominator. The least common multiple of 4 and 10 is 20.

Converting 5/4 to have a denominator of 20, we get 25/20. Now we can add 25/20 + 7/10, which equals 32/20.

To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 4. Dividing 32/4 and 20/4, we get 8/5.

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Answer:

-8, 0, and -12

Step-by-step explanation:

Using -7 would get you 8. Using -5 would get you 4

Answer:

if it's not 5 then P would be 5/6 bc there is only 5 more left if you take out 1.

Two-step equations are simple but have one critical rule — you must use the inverse order of operations. When you're able to (partly) put aside what you've learned about PEMDAS and the order of operations, you can solve for the variable of any two-step equation.

Now, According to the question:

Since the purpose of solving two-step equations is to determine the value of x, the multiplication or division of the coefficient attached to x must be the last step. Because of this, you must use inverse operations to solve two-step equations. This means adding and subtracting first, then multiplying and dividing. Adding and subtracting are usually the last steps in the order of operations, while multiplication and division are early steps.

Let's use this inverse order to solve for variable x in this two-step equation example:

4x + 13 = 37

Using inverse operations, the first step to solving this two-step equation example is to subtract 13 from 37. The left-hand side will now equal 4x and the right side will equal 24

4x = 24

Let's solve for x by dividing by 4. The value of the variable x will now be...

x = 6

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To compare the two quantities, divide the number of giraffes by the number of penguins There are 5 times as many giraffes as penguins at the zoo.

To compare the two quantities, you need to divide the number of giraffes by the number of penguins.

30 giraffes / 6 penguins = 5

This means that there are 5 times as many giraffes as penguins at the zoo.

There are 5 times as many giraffes as penguins at the zoo. To compare the two quantities, divide the number of giraffes by the number of penguins (30/6 = 5). This means that there are 5 times more giraffes than penguins at the zoo.

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Answer:

A

Step-by-step explanation:

Have a great summer :)

In summary, the quadratic function f whose graph matches the points (-7,0) and (-3,4) is:
f(x) = -0.5x^2 + 2.5x + 14

To find the quadratic function f whose graph matches the given points (-7,0) and (-3,4), we can start by using the standard form of a quadratic equation, y = ax^2 + bx + c.
We can use the two given points to form a system of equations:
0 = a(-7)^2 + b(-7) + c
4 = a(-3)^2 + b(-3) + c
Simplifying these equations, we get:
49a - 7b + c = 0
9a - 3b + c = 4
We can then solve for one of the variables, such as c:
c = -49a + 7b
c = -9a + 3b - 4
Setting these two equations equal to each other, we get:
-49a + 7b = -9a + 3b - 4
Simplifying, we get:
40a = 4b - 4
10a = b - 1
We can substitute this value of b into one of our original equations, such as:
0 = a(-7)^2 + b(-7) + c
0 = 49a - 7(10a + 1) + c
0 = 29a - 7 + c
c = 7 - 29a
So now we have the values of a, b, and c, and we can write the equation for f:
f(x) = ax^2 + bx + c
f(x) = a(x^2) + (b - 1)x + (7 - 29a)

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The mean number of hours Hannah studied for her chemistry final in the last few days is 12 hours. To find the mean of the hours Hannah studied, you need to add up all the hours and then divide by the number of hours she studied. In this case, she studied for 8 days, so the mean can be calculated as follows: (13 + 12 + 11 + 10 + 7 + 14 + 12 + 17) / 8 = 12.5

Therefore, the mean of the hours Hannah studied for her chemistry final in the last few days is 12.5.
The given list of hours studied is: 13, 12, 11, 10, 7, 14, 12, 17.
First, let's add up these numbers: 13 + 12 + 11 + 10 + 7 + 14 + 12 + 17 = 96 hours.
There are eight days in total (as there are eight numbers in the list). Now, divide the total hours (96) by the number of days (8) to find the mean: Mean = 96 / 8 = 12 hours.

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Answer:

A, D, and E

Step-by-step explanation:

Inequalities help us to compare two unequal expressions. The correct options are 2 and 3.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

The inequality for the red portion is,

slope, m = (-2/-4) = 1/2

y-intercept is 2.

y ≤ (1/2)x + 2

The inequality for the blue portion is,
slope, m = (5-0)/(3-0.5) = 2

y-intercept is -1.

y > 2x - 1

Hence, the correct options are 2 and 3.

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The dimensions of the rectangle will be 16 inches long and 7 inches wide,

Let W be the rectangle's width and L its length.

The area of the rectangle is the multiplication of the two different sides of the rectangle. Then the rectangle's area will be

Area of the rectangle = L × W square units

The length of a rectangular poster is 2 more inches than two times its width. The area of the poster is 112 square inches. Then the equations are given as,

LW = 112           ...1

L = 2W + 2       ...2

From equations 1 and 2, then we have

(2W + 2)W = 112

2W² + 2W - 112 = 0

W² + W - 56 = 0

W² + 8W - 7W - 56 = 0

W(W + 8) - 7(W + 7) = 0

(W + 8)(W - 7) = 0

W = 7, -8

Neglect - 8 because of negative signs. Then the length is given as,

L = 2 x 7 + 2

L = 14 + 2

L = 16

The dimensions of the rectangle will be 16 inches long and 7 inches wide,

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The inequalities are y ≥ (2/3)x + 1 and y < (-1/4)x + 2 and (−6, −3) satisfied the inequality.

A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.

In other words, inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.

As per the given phrase,

y is greater than or equal to two-thirds times x plus 1 ⇒ y ≥ (2/3)x + 1

y is less than negative one-fourth times x plus 2 ⇒ y < (-1/4)x + 2

Substitute, point (−6, −3)

-3 ≥ (2/3)(-6) + 1

-3 ≥ -3  

Substitute in second inequality,

-3 < (-1/4)(-6) + 2

-3 < 7/2

Hence "The inequalities are y ≥ (2/3)x + 1 and y < (-1/4)x + 2 and (−6, −3) satisfied the inequality".

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From the diagram of the CD plate shown, the area that can be used for label is:

A =( πr^2) - (πr^2)'

To find the area of a circle, you can use the following formula:

A = πr^2

where:

A is the area of the circle

π is a mathematical constant approximately equal to 3.14159

r is the radius of the circle

In the case of the CD,

The area of the label can be gotten by

Subtracting the area of the smaller circle, from the area of the big circle.

Area of big circle A = πr^2

Area of small circle A' = πr^2

Therefore

Area of label =A-A'

=A = (πr^2) - (πr^2)'

Once you know the value of the radius, simply substitute it into the formula and solve for the area.

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When corals are stressed by changes in state such as temperature, light, or nutrients, they expel the mutual algae living in their tissues, causing them to turn completely white.

Warmer water temperatures can outcome in coral bleaching. When water is too warm, corals will expel the algae (zooxanthellae) living in their tissues causing the coral to turn fully white.

This is called coral bleaching. When a coral bleaches, it is not late. Corals can hold on to a bleaching event, but they are under more stress and are subject to humanity.

contrast of satellite data from the previous 20 years confirmed that thermal stress from the 2005 event was greater than the previous 20 years combined.

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a) Population of city in 2015 = 640000

b) Population of city in 2019 = 777924

Population-growth happens when an initial population increases by the same percentage or factor over equal time increments or generations.

Given,

Population of city in 2017 (P) = 705600

Rate per annum r = 5% = 0.05

a) Population of city in 2015 (p) = ?

Time difference 2015 and 2017 = 2 years

Population of city in 2017

P = p(1 + r)ⁿ

705600 = p(1 + 0.05)²

p = 705600/1.05²

p = 705600/1.1025

p = 640000

b) Population of city in 2019 = ?

Time difference 2017 and 2019 n = 2 years

Population of city in 2019

= P(1 + r)ⁿ

= 705600(1+0.05)²

=  705600(1.05)²

= 705600 × 1.1025

= 777924

Hence, 640000 is population of city in 2015.

777924 is population of city in 2019

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Answer:

There is no graph

Step-by-step explanation:

*I see

*I think

*I think before I speak

*I say " There is no graph

I try to make people laugh when they mess up a little, we all mess up

Answer:

0.125 m²

Step-by-step explanation:

The area of a rectangle is the product of its length and breadth. Therefore:

area of the rectangle = length (l) × breadth (b) = 1 m².

l × b = 1

A triangle is cut off from that rectangle along a line connecting the midpoints of two adjacent sides, therefore the base of the triangle = length of rectangle/2 and the height of triangle = breadth of rectangle/2.

Area of triangle = 1/2(base × height) = \(\frac{1}{2}*\frac{l}{2}*\frac{b}{2}=\frac{1}{8}lb\)

since lb = 1:

Area of triangle = \(\frac{1}{8}*1=0.125m^2\)

Answer:

\( \frac{ {x}^{ - 2} {y}^{ \frac{1}{2} } }{ \sqrt{36x {y}^{2} } } = \frac{ \sqrt{y} }{ {x}^{2} \sqrt{36x {y}^{2} } } = \frac{ \sqrt{y} }{6 {x}^{2}y \sqrt{x} } = \frac{1}{6 {x}^{ \frac{5}{2} } {y}^{ \frac{1}{2} } } = \frac{1}{6} {x}^{ - \frac{5}{2} } {y}^{ - \frac{1}{2} } \)

\( \frac{1}{6} \times - \frac{5}{2} \times - \frac{1}{2} = \frac{5}{24} \)