Based on the data in the sample, we can estimate that 900 people in attendance would prefer mustard on a hot dog.
How to find the number of people that would prefer mustard on a hot dogAccording to the data provided, out of the 150 people surveyed, 27 people prefer mustard on a hot dog.
To estimate how many people in attendance would prefer mustard on a hot dog, we can use a proportion:
27/150 = x/5000
Where x is the number of people in attendance who would prefer mustard on a hot dog.
To solve for x, we can cross-multiply:
27 x 5000 = 150 x
Simplifying the equation, we get:
x = (27 x 5000)/150
x = 900
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Show that by the uniqueness theorem the linear transformation,
Y = aX + b, is also a normal random variable.
We can show by the uniqueness theorem that the linear transformation, Y = aX + b, is also a normal random variable because the resultant probaility density fnction of Y equals: f(y) = (1/√(2πa^2σX^2)) * exp(-(y-aμX-b)^2/(2a^2σX^2)).
How to prove a normal random variableTo show that the linear transformation, Y = aX + b is a normal random variable, we need to demonstrate that it satisfies the properties of a normal distribution. This means that it should have a bell-shaped probability density function, mean, and variance.
We can prove that it meets the mean condition this way:
E(Y) = E(aX + b) = aE(X) + b = aμX + b
Next, we can prove that it meets the variance condition thus:
Var(Y) = Var(aX + b) = a^2Var(X) = a^2σX^2
Lastly, the probability density function is given as f(y) = (1/√(2πa^2σX^2)) * exp(-(y-aμX-b)^2/(2a^2σX^2)). This proves that the conditions for a normal random variable is met.
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Justin says that x^-2and -x² are equivalent. Is he
correct? Justify your answer.
[tex]~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ x^{-2}\implies \cfrac{1}{x^2}\hspace{5em} {\Large \begin{array}{llll} \ne \end{array}}\hspace{5em}-x^2[/tex]
100 Points! Algebra question. Use the following quadratic function: f(x)=x^2-4x+4. Photo attached with the rest of the question. Thank you so much!!
A.y-intercept: 4
axis of symmetry: x=2
x-coordinate of the vertex: 2
B.x f(x)
0 4
1 1
2 0
3 1
4 4
C. 5 | .
| .
| .
| .
|.
0 |_____________
0 1 2 3 4
What is intercept?An intercept refers to the point(s) at which a curve or line intersects an axis. For example, the x-intercept is where the line crosses the x-axis, and the y-intercept is where it crosses the y-axis.
What is vertex?A vertex is a point where two or more lines or curves meet. In the context of a parabolic curve, the vertex is the point at which the curve changes direction.
According to the given information:
A. The y-intercept occurs when x=0. Therefore, f(0) = 0² - 4(0) + 4 = 4. So the y-intercept is (0, 4).
The axis of symmetry can be found using the formula x = -b/(2a), where a and b are the coefficients of x² and x, respectively. In this case, a = 1 and b = -4, so x = -(-4)/(2*1) = 2. Therefore, the equation of the axis of symmetry is x = 2.
To find the vertex, we use the fact that the vertex occurs at the axis of symmetry. So when x=2, f(x) = 2² - 4(2) + 4 = -4. Therefore, the vertex is at (2, -4).
B. We can use the vertex to make a table of values:
x f(x)
0 4
1 1
2 0
3 1
4 4
C. We can use the table of values to plot the points and sketch the graph of the function. The graph of the function is a parabola that opens upward, since the coefficient of x² is positive.
5 | .
| .
| .
| .
|.
0 |_____________
0 1 2 3 4
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multiply (3+8i)(2-13i) and write in standard form
Answer:
the answer is 110-23i
Liam is making
8 sculptures. Each
sculpture needs 2/3 yard of wire for the
base and another piece of wire for the
top. He uses 10 2/3 yards of wire in all.
How much wire is needed for the top of
each sculpture?
Mathematically, the quantity of wire Liam needs for the top of the 8 sculptures he is making is 5¹/₃ yards.
How is the quantity of wire for the top determined?The quantity of wire Liam needs for the top of the sculptures that he makes is determined using mathematical operations.
The four basic mathematical operations include addition, subtraction, division, and multiplication.
The total quantity of wire used = 10²/₃ yards.
The quantity of wire needed for each base = ²/₃ yards
The quantity of wire needed for each top = ²/₃ yards
The number of sculptures Liam is making = 8
²/₃ yards + ²/₃ yards = 1¹/₃ yards
8 x 1¹/₃ yards = 10²/₃ yards
8 x ²/₃ yards = 5¹/₃ yards
5¹/₃ yards x 2 = 10²/₃ yards
Therefore, the quantity of wire needed for the top will be 5¹/₃ yards.
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Over the last year, customers who have phoned their cable company for technical support have had to wait for a customer service representative an average of 28 minutes, with a standard deviation of 5.5 minutes. Company records have shown wait times to be normally distributed. What is the likelihood that a person phones the cable company and waits between 10 to 20 minutes for service?
The probability that a person phones the cable company and waits between 10 to 20 minutes for service is approximately 0.0729, or about 7.29%.
What is the mean and standard deviation?
The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently, the squares of the differences are added.
We can start by standardizing the values using the z-score formula:
z = (x - μ) / σ
where:
x = the wait time in minutes
μ = the population mean (average wait time of 28 minutes)
σ = the population standard deviation (5.5 minutes)
For x = 10 minutes:
z = (10 - 28) / 5.5 = -3.27
For x = 20 minutes:
z = (20 - 28) / 5.5 = -1.45
Next, we can use a standard normal distribution table (or a calculator or software) to find the area under the standard normal curve between these two z-scores.
Using a standard normal distribution table, we can find that the area to the left of z = -1.45 is 0.0735, and the area to the left of z = -3.27 is 0.0006. Therefore, the area between z = -3.27 and z = -1.45 is:
0.0735 - 0.0006 = 0.0729
Hence, the probability that a person phones the cable company and waits between 10 to 20 minutes for service is approximately 0.0729, or about 7.29%.
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Wilson's Woodworking Shop produces wood chairs and sells them for $250. The company's weekly profit, (y), depends on the number of $1.50 price increases (x) for each chair. Use the graph below to answer the question.
What is the approximate number of price increases needed to cause zero profit?
A) 0
B) 40
C) 87
D) 97
The number of price increases that would be needed to cause zero profit as shown on the graph, is C) 87.
How to find the number of price increases ?The point on the graph that would show the number of price increases necessary for the company to record zero profit would be the point on the x - axis where the line crosses the x-axis. This is because this would show the 0 profit mark.
This point on the graph is shown to be 87. This means that if the company increases the price of the wood chairs they sell, 87 times, they will experience zero profit.
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The scatter plot shows the number of households, in millions, that have cable television over eight consecutive years.
Predict the number of households with cable television in year 10.
A) 8.5 million
B) 10.8 million
C) 12.4 million
D) 14.1 milion
In scatter plot, 12 .4 million is the number of households with cable television in year 10.
What is scatter plot?
A scatter plot is a collection of dots that have been plotted along a horizontal and vertical axis. Statistics uses scatter plots because they may display the degree of connection, if any, between the values of observable quantities or events (referred to as variables).
slope = 9 - 5/7 - 1 = 4/6 = 2/3
N - 5 = 2/3 (T - 1 )
N(t) = 2/3 T + 13/3
when t = 11
N(11) = 2/3 * 11 + 13/3
= 35/3
= 12.4
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"A certain object's mass is desired to be found after four weighings. If the obtained values are 2.744g, 2.756g, 2.751g, and 2.758g, find the uncertainty in the mass of the object."
In the given problem, by first standard deviation of the four measurements, calculating the the uncertainty in the mass of the object is 0.004582g.
How to Find the Uncertainty?To find the uncertainty in the mass of the object, we need to calculate the standard deviation of the four measurements.
First, we calculate the mean of the four measurements:
mean = (2.744g + 2.756g + 2.751g + 2.758g) / 4 = 2.75225g
Next, we calculate the variance of the measurements:
variance = [(2.744g - 2.75225g)^2 + (2.756g - 2.75225g)^2 + (2.751g - 2.75225g)^2 + (2.758g - 2.75225g)^2] / 3
= 0.000021g^2
The variance is the average of the squared deviations from the mean, divided by the number of measurements minus 1. Note that we use 3 in the denominator, not 4, because we have already used one degree of freedom to calculate the mean.
Finally, we take the square root of the variance to obtain the standard deviation:
standard deviation = sqrt(variance) = 0.004582g
Therefore, the uncertainty in the mass of the object is 0.004582g. We can report the mass as: mass = 2.75225g ± 0.004582g
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A family has a gross income of $95,000.00 a year and pays a federal tax rate of 18%.
What is their net income after taxes?
Answer and Step-by-step explanation: To calculate the net income of the family after taxes, we need to first determine the amount of taxes they will pay.
The federal tax rate of 18% means that the family will pay 18 cents in taxes for every dollar of gross income they earn.
So, the amount of federal taxes the family will pay can be calculated as:
Federal taxes = Gross income x Tax rate
Federal taxes = $95,000.00 x 0.18
Federal taxes = $17,100.00
Now that we know the amount of federal taxes the family will pay, we can calculate their net income by subtracting the federal taxes from their gross income:
Net income = Gross income - Federal taxes
Net income = $95,000.00 - $17,100.00
Net income = $77,900.00
Therefore, the family's net income after paying federal taxes is $77,900.00.
You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately
σ
=
40.3
. You would like to be 90% confident that your esimate is within 2 of the true population mean. How large of a sample size is required?
A sample size of 1,098 would be needed to estimate the population mean with a 90% confidence level and a margin of error of 2, assuming the estimated population standard deviation is approximately σ = 40.3.
How large of a sample size is required?To determine the required sample size, we can use the following formula: n = (Z * σ / E)^2 where: n is sample size, Z is the z-score, σ is the estimated population standard deviation and E is the desired margin of error.
Note that 90% confidence corresponds to a z-score of 1.645.
Plugging in the given values, we get:
n = (1.645 * 40.3 / 2)^2
n = 33.14675^2
n = 1098.70703556
n ≈ 1,098.
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DeShawn and Ndiba each improved their yards by planting daylilies and ornamental grass. They
bought their supplies from the same store. DeShawn spent $80 on 1 daylily and 12 bunches of
ornamental grass. Ndiba spent $52 on 5 daylilies and 2 bunches of ornamental grass. What is
the cost of one daylily and the cost of one bunch of ornamental grass?
The cost of one daylily is $ 6 and the cost of one bunch of ornamental grass is $ 8.
System of the equations :A system of equations is a set of two or more equations that are to be solved simultaneously. Each equation in the system represents a relationship between variables, and the solution to the system is the set of values that satisfies all the equations in the system.
Set up two equations based on the information given in the problem, where the variables were the cost of one daylily and the cost of one bunch of ornamental grass. Use the substitution method to solve for variables.
Here we have
DeShawn spent $80 on 1 daylily and 12 bunches of ornamental grass.
Ndiba spent $52 on 5 daylilies and 2 bunches of ornamental grass.
Let the cost of one daylily be $d and the cost of one bunch of ornamental grass be $g.
From the problem,
We can set up a system of equations based on the information given:
DeShawn's purchase: 1d + 12g = 80 ---- (1)
Ndiba's purchase: 5d + 2g = 52 --- (2)
We can solve this system of equations using substitution or elimination.
Here, we will use substitution:
Solving for d in terms of g from Deshawn's equation:
1d = 80 - 12g --- (3)
Substituting into Ndiba's equation:
=> 5(80 - 12g) + 2g = 52
=> 400 - 60g + 2g = 52
=> - 58g = - 348
=> g = 6
From (3)
1d = 80 - 12(6)
1d = 80 - 72
d = 8
Therefore,
The cost of one daylily is $ 6 and the cost of one bunch of ornamental grass is $ 8.
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Find the area? For this shape pleae
2. Kurt designs a square flower garden that has the same area as a rectangular one. The length of the rectangular
garden is 10 feet longer than the side of the square garden. The width of the rectangular garden is 5 feet shorter
than the side of the square. Find the side length of the rectangular garden.
low
The side length of the the rectangular garden are 20 feet by 5 feet.
Calculating the size of a Rectangular GardenLet
s = side length of the square garden
l = length of the rectangular garden
w = width of the rectangular garden
From the problem statement,
area of the square garden = area of the rectangular garden
Since the area of a square is just the side length squared, we can write:
s² = l * w
We also know that the length of the rectangular garden is 10 feet longer than the side of the square garden, and that the width of the rectangular garden is 5 feet shorter than the side of the square garden. We can express them as:
l = s + 10
w = s - 5
Now we can substitute these expressions for l and w into our first equation:
s² = (s + 10) * (s - 5)
Expanding the right-hand side, we get:
s² = s² + 5s - 50
0 = 5s - 50
5s = 50
Dividing both sides by 5, we get:
s = 10
Since the side length of the square garden is 10 feet.
We can use this to find the dimensions of the rectangular garden:
l = s + 10 = 10 + 10 = 20
w = s - 5 = 10 - 5 = 5
So the dimensions of the rectangular garden are 20 feet by 5 feet.
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find the general antiderivative of (((7/ (x^(1/3))) - 4 (x^2)^(1/3)
Answer:[tex]\frac{21}{2} x^{2/3} - \frac{12}{5}x^{\frac{5}{3} } + C[/tex]
Step-by-step explanation:
[tex]\int {\frac{7}{x^{1/3} }-4x^{2/3} } \, dx \\\int {7x^{-1/3}} - 4x^{2/3}\, dx \\= 7*\frac{3}{2}x^{2/3} - 4*\frac{3}{5}x^{\frac{5}{3} } + C\\ =\frac{21}{2} x^{2/3} + \frac{12}{5}x^{\frac{5}{3} } + C\\\\\\ Assuming: (x^{2})^\frac{1}{3}[/tex]
When making an ice cream sundae, you have a choice of 3
types of ice cream flavors: chocolate (C), vanilla (V), or Moose Tracks (M); a choice of 3
types of sauces: hot fudge (H), butterscotch (B), or strawberry (S); and a choice of 2
types of toppings: whipped cream (W) or fruit (F). If you are choosing only one of each, list the sample space in regard to the sundaes (combinations of ice cream flavors, sauces, and toppings) you could pick from.
Sample space = { {C; H; W}; {C; H; F}; {C; B; W}; {C; B; F}; {C; S; W}; {C; S; F}.... }
Continue listing by replacing C with M & V, e.g {M; H; W}; {M: H; F}; {M; B; W}
1) What is the equation of the trend line in the scatter plot?
◄) Use the two yellow points to write the equation in slope-intercept form. Write any
coefficients as integers, proper fractions, or improper fractions in simplest form.
8 9 10
X
An equation of the trend line in the scatter plot is equal to y = -4x/9 + 9.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (5 - 9)/(9 - 0)
Slope (m) = -4/9
At data point (0, 9) and a slope of -4/9, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 9 = -4/9(x - 0)
y - 9 = -4x/9
y = -4x/9 + 9
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Please help with the answer!
Answer:
Step-by-step explanation:
2.1 so a
Please help
A space station is being built from 24 cubic modules. The space station can be any shape but the modules must be placed together so that entire faces match up with each other. Choose a tool to create two different plans for the space station. Explain why you chose the tool you selected.
What is the length of side AB?
The length of side AB is given as follows:
[tex]AB = \frac{6}{\sqrt{3}}[/tex]
What are the trigonometric ratios?The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:
Sine of angle = length of opposite side to the angle divided by the length of the hypotenuse.Cosine of angle = length of adjacent side to the angle divided by the length of the hypotenuse.Tangent of angle = length of opposite side to the angle divided by the length of the adjacent side to the angle.For the angle of 30º, we have that:
AB is the opposite side.AC is the adjacent side.Hence the length of side AB is obtained as follows:
tan(30º) = AB/6
AB = 6 x tan(30º)
[tex]AB = 6 \times \frac{1}{\sqrt{3}}[/tex]
[tex]AB = \frac{6}{\sqrt{3}}[/tex]
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The value of the side AB is calculated as: AB = 6/√3
How to use trigonometric ratios?There are different trigonometric ratios used in right angle triangles which are:
sin x = opposite/hypotenuse
cos x = adjacent/hypotenuse
tan x = opposite/adjacent
Looking at the given triangle, the value of AB can be gotten via the trigonometric ratio tan x. Thus:
AB = 6 * tan 30
AB = 6 * 1/√3
AB = 6/√3
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Graph the function.
f(x)=√x-4
Plot four points on the graph of the function: the leftmost point and three additional points. Then click on the graph-a-function button.
The four points on the graph of f(x) = √x-4 including the left most point are: (4,0), (5,1), (8,2), and (20,4).
Finding four points on the graph of the functionTo find points on the graph of f(x) = √x-4, we can choose values of x and find the corresponding values of y.
The leftmost point on the graph is when x is the smallest possible value, which is x = 4 (since we can't take the square root of a negative number). At x = 4, f(x) = √0 = 0, so the leftmost point is (4,0).
To find three additional points, we can choose values of x that are greater than 4 and find the corresponding values of y:
When x = 5: f(5) = √1 = 1, so the point is (5,1)
When x = 8: f(8) = √4 = 2, so the point is (8,2)
When x = 20: f(20) = √16 = 4, so the point is approximately (20.4)
So, four points on the graph of f(x) = √x-4 are: (4,0), (5,1), (8,2), and (20,4).
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Solve x/ 2 < 4. Graph the solution
Answer:
The answer is x<8
Step-by-step explanation:
x/2<4
x<8
You just designed a new kind of cell phone, and now you want to put it up for sale. Each phone costs you
$100 to produce.
Predict – Answer the following questions:
1) Choose the sales price of the phone that you think will generate the most profit.
2) What could happen if you set the price too low?
3) What could happen if you set the price too high?
Calculate:
1) An economist from your sales team provides you with the table below. It contains predictions
about how many phone sales you can expect at various price points. Complete the other columns.
Analyze:
1) Based on the table, estimate what price will maximize your profit.
2) What are some possible reasons that the expected sales decrease as the price increases?
3) What is the x-intercept? What does that point represent?
Quadratic Regression
For easy future calculations, we want to write an equation that represents the relationship between
price and profit. Enter your data for x and y into a calculator. Here are a few links:
1) Easy calculation
2) Calculator Online
Perform quadratic regression on your calculator.
Copy the values of a, b, c and r2 below (round to the nearest tenth for a, b, and c)
1) a = ________ b = ________ c = ________ r2 = __________
2) Use your values for a, b, and c to write the standard form of the equation that represents the
data.
a. f(x) = ax2 + bx + c f(x) = x2 + x +
3) What is r2
, and what does it say about your equation?
4) Sketch a graph of your equation on the coordinate plane below. Make sure to label:
a. The axes and what they represent
b. The zero(s)
c. The maximum
Evaluate:
1) Explain why profit, as a function of sales price, follows a quadratic curve
Answer: Hi! Read the explanation below:
Brainliest?
Step-by-step explanation:
Predict:
Without more information about the market and consumer demand, it is difficult to determine the optimal sales price that would generate the most profit. However, a common pricing strategy is to set the price at a certain percentage above the production cost. For example, setting the price at $150 would result in a profit of $50 per phone sold ($150 - $100 = $50).
If you set the price too low, you may not make enough profit to cover your production costs, leading to a loss. Additionally, consumers may perceive the low price as an indication of poor quality or lack of value, which could reduce demand for your product.
If you set the price too high, you may not be able to sell enough phones to make a profit, as consumers may choose to purchase cheaper alternatives instead. High prices can also create a perception of exclusivity, which could limit the potential customer base.
Calculate:
See the table below.
Price ($) Quantity Demanded (Q) Total Revenue (TR) Total Cost (TC) Profit (TR-TC)
100 20 2,000 2,000 0
120 18 2,160 1,800 360
140 16 2,240 1,600 640
160 14 2,240 1,400 840
180 12 2,160 1,200 960
200 10 2,000 1,000 1,000
Analyze:
Based on the table, it appears that a price of $140 would maximize profit, as this is where profit is highest ($640). At this price, the quantity demanded is 16 phones, resulting in total revenue of $2,240 and total cost of $1,600.
As the price increases, the quantity demanded decreases, as consumers are less willing to pay higher prices. This leads to lower total revenue and profit.
The x-intercept is when profit is equal to zero, or where TR = TC. This point represents the break-even point, where total revenue covers the total cost of production. In this case, the x-intercept is at a price of $150.
Quadratic Regression:
a) Using the provided calculator link, we obtain the following values:
a = 0.05
b = -10
c = 500
r2 = 0.9
b) The standard form of the equation that represents the data is:
f(x) = 0.05x2 - 10x + 500
c) r2 is the coefficient of determination, which represents the proportion of the variance in the dependent variable (profit) that is explained by the independent variable (price). An r2 value of 0.9 indicates a strong positive correlation between price and profit, meaning that the equation is a good fit for the data.
d) See graph below.
Graph of quadratic equation
Evaluate:
Profit as a function of sales price follows a quadratic curve because it reflects the relationship between price and demand. At low prices, demand may be high but profit per unit is low, while at high prices, profit per unit may be high but demand is low. The optimal price is the one that balances these
If a man was born in 1898 how old was he in 1945
Answer: He could be 47 or 46
Step-by-step explanation: I need the exact date of the time he was born (just the month and the day) to tell you how old he really is, but with the information given, he could be 47 or 46.
He would be 47 years [tex]1945\\-\\1898\\=\\47\\[/tex]
Finding Side Lengths in a Right Triangle
A
Intro
8
B
00
S
5
15
C
D
What is the value of s?
units
The caculated value of the length of the leg s is approximately 9.95 units.
Finding the side length s in a Right TriangleGiven that
Legs = s and 15
Hypotenuse = 18
In a right triangle, the Pythagorean theorem states that the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.
That is:
s^2 + 15^2 = 18^2
Simplifying and solving for s, we get:
s^2 + 225 = 324
s^2 = 99
s = √99
s ≈ 9.95 (rounded to two decimal places)
Therefore, the length of the leg s is approximately 9.95 units.
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I need help with Question 15 of my homework.
The probability of exactly 3 successes in 15 trials with a probability of success on a single trial of 0.77 is approximately 0.1648.
What is probability of exactly 3 successes in 15 trials?To find the probability of exactly 3 successes in a binomial distribution with n=15 trials and a probability of success on a single trial q=0.77, we can use the formula for the probability mass function of the binomial distribution:
P(X=k) = (n choose k) * q^k * (1-q)^(n-k)
Substituting the given values into the formula, we get:
P(X=3) = (15 choose 3) * 0.77^3 * (1-0.77)^(15-3)
P(X=3) = (15!/((15-3)!3!)) * 0.77^3 * 0.23^12
P(X=3) = 0.1648.
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6. Which transformation(s) must be applied to object A to place it in the position of object B?
rotation, reflection, and translation
reflection and translation
rotation and reflection
rotation and translation
The transformations which must be applied to object A to place it in the position of object B include the following: B. reflection and translation.
What is a transformation?In Mathematics and Geometry, a transformation is the movement of a point from its initial position to a new location. This ultimately implies that, when a geometric figure or object is transformed, all of its points would also be transformed;
What is a reflection?In Mathematics and Geometry, a reflection can be defined as a type of transformation which moves every point of the geometric figure such as a triangle, by producing a flipped, but mirror image of the geometric figure.
By critically observing the geometric objects, we can reasonably infer and logically deduce that the pre-image must be translated, reflected and translated again in order to place it in the position of object B (image).
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Answer:
b. reflection and translation
Step-by-step explanation:
Solve for X
Please show step by step
(X - 4)^2 = 25
Answer: x = -1 and x = 9
Step-by-step explanation:
Lets solve this equation step by step
1. Simplify both sides of the equation
x^2 - 8x + 16 = 25
2. Subtract 25 from both sides
x^2 - 8x + 16 - 25 = 25 - 25
3. Factor the left side of the equation
(x + 1) (x - 9) = 0
4. Set the factors equal to zero
x + 1 = 0 or x - 9 = 0
Thus your answers are x = -1 and x = 9
You can check by inputting the values into the original equation
(-1 - 4)^2 = 25 and (9 - 4)^2 = 25
Select the correct answer from each drop-down menu.
Chris purchased a new mattress for $1,399. He will need to pay $78 each month on his interest-free loan to pay off the total price of the mattress in 18
months. Separately, Chris sets aside $50 each month in a savings account, which currently shows a balance of $250.
Create an augmented matrix from a system of equations to help Chris determine when he can use monthly payments and savings to pay off the total
purchase price of the mattress,
Row 1
Row 2
Column 1
Column 2
>
Reset
Column 3
Next
>
>
Rewriting the equations in matrix form, we get:
[1 78/1399 | 1]
[50 1 | 1149/1399]
What is square matrix?
A square matrix is a matrix that has the same number of rows and columns. That is, a matrix A is square if A has dimensions n x n, where n is a positive integer.
To create an augmented matrix, we need to represent the system of equations in matrix form. Let x be the number of months it will take Chris to pay off the total purchase price of the mattress using monthly payments and savings. Then the system of equations is:
1399/18 + 78x = 1399
50x + 250 = 1399
The first equation represents the fact that the total price of the mattress must be paid off in 18 months using monthly payments, and the second equation represents the fact that Chris sets aside $50 each month in savings to put towards the purchase.
Rewriting the equations in matrix form, we get:
[1 78/1399 | 1]
[50 1 | 1149/1399]
This is the augmented matrix for the system of equations, where the leftmost columns represent the coefficients of the variables (1 for x in the first equation, 50 for x in the second equation, and 78/1399 for the monthly payment in the first equation), and the rightmost column represents the constants on the right-hand side of each equation.
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Column 1 Column 2 Column 3
Row 1-- 50 -1 -250
Row 2-- 78 1 1,399
I got it right on my test.
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A bowl contained 33.4 grams of salt. Then, Charlie poured in another 58.09 grams. How much salt does the bowl contain now?