The solutions of the quadratic equation x³+ 16x -3x² = 48 are 3, –4i, 4i
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
A mathematical statement with two expressions that have the same value and the sign "equal to" between them is called an equation.
We are given the quadratic equation as;
x³+ 16x -3x² = 48
Subtract 48 from both sides;
x³+ 16x -3x² - 48= 48 -48
x³+ 16x -3x² - 48= 0
Factor left side of equation.
(x - 3)( x² + 16) = 0
Therefore, the roots are 3, –4i, 4i
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Estimate. Then tell if your estimate is an overestimate or underestimate
The numbers that will be estimated based on the information will be 550 + 298 which gives an estimation of 850. This is an overestimation.
What is an estimation?You must approximate (eliminate or round off) the decimals to obtain whole numbers before you can use the whole numbers to find the product of two decimals using estimation.
The estimate is erroneous if only factors with even numbers are taken into account. The estimate is understated if only factors are rounded down.
In this case, 550 + 298: 298 is nearly 300 so an estimate is:
= 550+300
= 850
This is an overestimation.
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Complete question
Solve an estimation of your choice. Then tell if your estimate is an overestimate or underestimate
What is the simplified expression for 2 power 2 multiplied by 2 power 3 over 2 power 4
Answer:
ANS:- 2
Step-by-step explanation:
= (2^2)(2^3/2^4)
= (4)(8/16)
=(4)(1/2)
=4/2
= 2
University Car Wash built a deluxe car wash across the street from campus. The new machines cost $267,000 including installation. The company estimates that the equipment will have a residual value of $24,000. University Car Wash also estimates it will use the machine for six years or about 12,000 total hours. Actual use per year was as follows: Year Hours Used 1 3,000 2 1,200 3 1,300 4 2,700 5 2,500 6 1,300 Required: 1. Prepare a depreciation schedule for six years using the activity-based method. (Do not round your intermediate calculations.)
The depreciation schedule for the new machines of University Car Wash, using the activity-based method, is as follows:
Year Initial Cost Depreciation Accumulated Net Book Value
Expense Depreciation
1 $267,000 $60,750 $60,750 $206,250
2 $267,000 $24,300 $85,050 $181,950
3 $267,000 $26,325 $111,375 $155,625
4 $267,000 $54,675 $166,050 $100,950
5 $267,000 $50,625 $216,675 $50,325
6 $267,000 $26,325 $243,000 $24,000
What is a depreciation schedule?A depreciation schedule is a table that shows the annual depreciation expense, the accumulated depreciation over the years, and the net book value of each asset, including the initial cost.
An activity-based method of depreciation uses the machine hours or other activity bases used to determine each year's depreciation expenses.
Cost of machines = $267,000
Residual value = $24,000
Depreciable amount = $243,000 ($267,000 - $24,000)
Estimated useful life = 6 years or 12,000 total hours
Hourly depreciation rate = $20.25 ($243,000/12,000)
Year Annual Depreciation Expense
1 $60,750 (3,000 x $20.25)
2 $24,300 (1,200 x $20.25)
3 $26,325 (1,300 x $20.25)
4 $54,675 (2,700 x $20.25)
5 $50,625 (2,500 x $20.25)
6 $26,325 (1,300 x $20.25)
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The fox population in a certain region has a continuous growth rate of 6 percent per year. It is estimated that the population in the year 2000 was 25100.
(a) Find a function that models the population
t
years after 2000 (
t
=
0
for 2000).
Your answer is
P
(
t
)
=
(b) Use the function from part (a) to estimate the fox population in the year 2008.
Your answer is (the answer must be an integer)
The function is f(x) = 25100(1 + 0.06)ˣ and the estimate fox population in the year 2008 is 40,0005.
What is an exponential function?It is defined as a function that rapidly increases and the value of the exponential function is always a positive. It denotes with exponent y = a^x
where a is a constant and a>1
It is given that:
The fox population in a certain region has a continuous growth rate of 6 percent per year
f(x) = a(1 + r)ˣ
f(x) = 25100(1 + 0.06)ˣ
Plug x = 8 years
f(8) = 25100(1 + 0.06)⁸
f(8) = 40,0005
Thus, the function is f(x) = 25100(1 + 0.06)ˣ and the estimate the fox population in the year 2008 is 40,0005.
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2/125x10,13+2/27x10,13
The value of the expression 2/125x1013 + 2/27x1013 is 91.248.
How to illustrate the expression?It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.
The expression will be Illustrated as:
2/125x1013 + 2/27x1013
= (0.016 × 1013) + (0.0740741 × 1013)
= 16.208 + 75.04
= 91.248
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Complete question
2/125x1013 + 2/27x1013
3) A restaurant requires customers to pay a 15% tip for the server. Your family spends
$65 on the meal.
a) How much money do you need to pay the server?
Answer: You would leave $9.75 for the tip.
Step-by-step explanation:
15% of 65 is 9.75, so when you add 15% to 65 you get 74.75. In total you would be paying $74.75 but you would leave a $9.75 tip for the server.
Ziva bought 6 ⅘ balls of thread for a sweater, but she only ended up using 8 6/12 balls. What fraction of the thread did Ziva use?
Is this how we solve it?
8 6/12 by - 6 4/5 = A
Hope this helps
i think that's how we are supposed to do the problem can someone do a walk through for me with variables so i can find it on my own i just need help. I was trying to find a tutor cause I'm confused. But is that how were supposed to do it cause tutor.com isn't working.
Most likely we have to simplify and then subtract it? I hope that's how you solve it!
nvm i think i got it
Draw the graph of y = 2x − 3 for values of x from 0 to 4.
!! Please help
Solve the system using substitution
x + 3y = 3
3y - 2x = 12
Tennis balls with a diameter of 2.6 inches are sold in cans of three.
The can is a cylinder. What is the volume of the space NOT occupied
by the tennis balls? (Assume the tennis balls touch the can on all
sides, top and bottom.) Round to the nearest tenth and show all steps
and reasoning.
How can you tell if a formula represents Length, an Area, or Volume? What do you look for in
the formula?
Explain how you could get a formula for the volume of the
16 cm
solid.
Find the diagonal of the box, AD, using the Pythagorean
Theorem twice - 1. To find BD and 2. To find AD.
AB = 12 in
BC= 18 in
CD = 4 in
Show all steps for findin the diagonal of the box above using the formula instead of the
Pythagorean Theorem twice.
0
9
Diagonal of a box of
dimensions a, b, c
a2 + b2+c2 = d2
The volume of the solid is combined of a cone, cylinder, and hemisphere is
329.7 cubic cm.
What are the formulas for the volume of a cone, cylinder, and half of a sphere?The volume of a cone is (1/3)πr²h.
The volume of a cylinder is πr²h.
The volume of half a sphere or a hemisphere is (1/3)πr³.
The given figure has a volume combined of a cone, cylinder, and hemisphere.
∴ The volume of the solid is = (1/3)π(3)²×5 + π(3)²×(8) + (2/3)π(3)³ cubic cm.
= (47.1 + 226.08 + 56.52) cubic cm.
= 329.7 cubic cm.
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Prob-1A random sample of 21 glass sheets is obtained and their thicknesses are measured. The sample mean is x= 3.12 mm and sample standard deviation is S = 0.14 mm. Construct a 95% two-sided confidence interval for the mean glass thickness.
For the typical glass thickness of 3.12 mm, the 95% two-sided confidence interval will be (3.067,3.173).
What is confidence interval?An area created using fixed-size samples of data from a population (sample space) that follows a particular probability distribution is known as a confidence interval. A selected population statistic is built into the interval with a specified probability. An estimate's level of uncertainty is described by a confidence interval, which is a range of numbers.
Here,
mean x=3.12 mm
Standard deviation s=0.14 mm
number of sample n=21
two-sided confidence interval,
=x±tₐ÷₂(s/√n)
a=1-0.95
a=0.05
t₀.₀₅,₂₀=1.725
=3.12±1.725*(0.14/√21)
=3.12±1.725*(0.14/4.58)
=3.12±1.725*0.0306
=3.12±0.053
=(3.067,3.173)
The 95% two-sided confidence interval for the mean glass thickness of 3.12 mm will be (3.067,3.173).
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based on the spss output what cna you concllude about the relationship between degree attainment and age dbrn for men
There is sufficient statistical evidence at 5% level of significance that there is relationship between degree attainment and AGEKDBRN for women.
What is ANOVA model for men?
To ascertain whether there are any statistically significant differences between the means of three or more independent (unrelated) groups, the one-way analysis of variance (ANOVA) is used.
An n-way ANOVA allows a researcher to employ more than two independent variables (with n being the number of independent variables you have). For instance, any disparities in IQ scores can be investigated concurrently by country, gender, age group, ethnicity, etc.
Relationship between degree attainment and AGEKDBRN for women
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A movie theater has a seating capacity of 283. The theater charges $5 for children, $7 for students, and $12 of adults. There are half as many adults as there are children. If the total ticket sales was $2,042, How many children, students, and adults attended?
children attended.
students attended.
adults attended.
Binary form can be represented as
a A B C A
b A B
c A B A
d A B A C B A
The binary form can be represented as AB or AABB. So the write option is b.
One of the four different kinds of number systems is the binary number system. When used in computer programmes, binary numbers are solely represented by the digits 0 (zero) and 1. (one). Here, the base-2 numeric format is used to express the binary numbers.
Because the binary system is directly implemented in electronic circuits using logic gates, nearly all modern computers and computer-based gadgets employ it internally. A bit is used to describe each digit.
The binary form is a set of alphabetical character that is used to describe a musical piece using two sections of equal length. It can be represented as AB or AABB. So the write option is b.
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4x²-17x+ k = 0 has the reciprocal roots.
Answer: k=4
Step-by-step explanation:
4x²-17x+k=0
Divide both parts of the equation by 4:
[tex]\displaystyle\\\frac{4x^2}{4}-\frac{17x}{4}+\frac{k}{4}=0\\\\x^2-\frac{17}{4} x +\frac{k}{4} =0\\[/tex]
Let one of the roots of this equation be α
Then the other root of this equation is 1/α
Hence,
[tex]\displaystyle\\\alpha (\frac{1}{\alpha })=\frac{k}{4} \\\\\frac{\alpha }{\alpha }= \frac{k}{4} \\\\1=\frac{k}{4}[/tex]
Multiply both parts of the equation by 4:
4=k
Thus, k=4
18. A new college entrance exam scores designed so that for a reference population they are
distributed normally, with mean 650 and standard deviation 125. Based on this
information:
a. What percentage of students in the reference population scored above 775?
b. Between what two scores did the middle 95%of the reference population score?
c. Out of every 1,000 people in the reference population, approximately how many
scored below 525?
a. The percentage of students in the reference population scored above 775 is of: 16%.
b. The middle 95% of scores were between 400 and 900.
c. Approximately 160 students scored below 525.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation in this problem are given as follows:
[tex]\mu = 650, \sigma = 125[/tex]
Then the proportion of students who scored above 775 is one subtracted by the p-value of Z when X = 775, hence:
Z = (775 - 650)/125
Z = 1.
Z = 1 has a p-value of 0.84.
1 - 0.84 = 0.16, hence the percentage is of:
0.16 x 100% = 16%.
By the Empirical Rule, the middle 95% of scores are within 2 standard deviations of the mean, hence:
650 - 2 x 125 = 400.650 + 2 x 125 = 900.The proportion of students who scored below 525 is the p-value of Z when X = 525, hence:
Z = (525 - 650)/125
Z = -1.
Z = -1 has a p-value of 0.16.
Then the amount out of 1000 students is of:
0.16 x 1000 = 160 students.
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What is the slope of the line on this graph?
Enter your answer in the box.
Answer: 6 units
Step-by-step explanation:
There are two ways to do this. You can either choose 2 points on the graph and find the rise/run, or you can plug them in the formula. Let's choose the two points that are dotted. (1,5) and (0,-1)
Let's first do rise/run.
From (0,-1) to (1,5) the rise is 6 units, and the run is 1 unit. So we just divide that. 6/1 which means the slope is 6 units.
We can also use the formula: m = y2 - y1 / x2 - x1
(0,-1) will be our first coordinate and (0,-1) will be our second coordinate. So 0 is x1 and -1 is y1, 1 will be x2 and 5 will be y2. Now we just plug in the numbers
m=5-(-1)/1-0
m=5+1/1-0
m=6/1
m=6 units
So in both ways we get that the slope is 6 units.
A quadratic function y=f(x) is plotted on a graph and the vertex of the resulting parabola is (-6, 5) What is the vertex of the function defined as g(x)=f(-x)-2
The vertex of a parabola is the point on the graph where the parabola reaches its highest or lowest point. In the case of a quadratic function, the vertex is always of the form (h, k), where h is the x-coordinate of the vertex and k is the y-coordinate of the vertex.
The function g(x) = f(-x) - 2 can be obtained from the function f(x) by replacing all instances of x with -x and then subtracting 2 from the result. This transformation will flip the parabola over the y-axis and shift it down by 2 units.
The vertex of the parabola resulting from the function g(x) will be the point where the parabola reaches its highest or lowest point after this transformation. Since the parabola is flipped over the y-axis and shifted down by 2 units, the vertex of the resulting parabola will have the same x-coordinate as the original vertex (-6) and a y-coordinate that is 2 units lower than the original y-coordinate (5 - 2 = 3).
Therefore, the vertex of the function g(x) = f(-x) - 2 is (-6, 3).
welcome to this website
I hope this helps
1/4 + X - 1/3=2/3+3+1/4
Answer: x=4
Step-by-step explanation:
Answer:
Step-by-step explanation:
x = 4
3.5.PS-15
Question Help
Reasoning Kareem cannot decide which of two washing machines to buy. The selling price of each is $480. The first is
marked down by 50%. The second is marked down by 30% with an additional 20% off. Find the sale price of each washing
machine. Use pencil and paper. Explain why Kareem should buy the first washing machine rather than the second if the
machines are the same except for the selling price.
The sale price of the first washing machine is $
(Round to the nearest dollar as needed.)
Answer:
$240the sale price on the first machine is lowerStep-by-step explanation:
Two washing machines are offered at $480, with one marked down 50% and the other marked down 30% and another 20% off. You want to know why the first machine has a better price, and what that price is.
First machineThe price after a 50% markdown is ...
$480 × (1 -50%) = $480 × 0.50 = $240 . . . first machine sale price
Second machineThe price after a 30% markdown is ...
$480 × (1 -30%) = $480 × 0.70
After the additional 20% markdown, the price is ...
($480×0.70) × (1 -20%) = $480 × 0.70 × 0.80
= $480 × 0.56 ≈ $269
Better dealThe first machine is a better deal, because The 50% markdown is off the original price.
The 30% markdown on the second machine is off the original price, but the additional 20% is off the reduced price. Hence the total markdown is not as great as on the first machine.
Help me with this question pleaseeee
Answer:
option b .....is answer
How do I solve this?
The required probability is 0.8437 that a dart hitting the board will land in the unshaded area.
The total area of the board = 8 x 8 = 64 square inches
The area of the shaded region = 15 square inches
The probability of landing in the shaded region is the ratio of the unshaded area to the total area.
The unshaded area = 64 - 15 = 54 square inches
So, the required probability is:
P(unshaded) = 54/64 = 0.8437
Thus, the required probability is 0.8437 that a dart hitting the board will land in the unshaded area.
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With enough variables, it is possible to get an R2 value close to 1, even if the variables have no particular meaning in the model
A)True
B)False
With enough variables, it is possible to get an R2 value close to 1, even if the variables have no particular meaning in the model - True
If the model has a significant number of variables, it is still possible to obtain an R-squared value that is near to 1, even if the variables have no particular significance. R-squared is a metric used to evaluate how well a model fits data; it has a range from 0 to 1, with 1 denoting a perfect fit.
A high R-squared value does not, however, guarantee that the model fits the data well or that the variables it uses are significant. To ensure that the model accurately represents the underlying relationships in the data, it is crucial to carefully analyze the meaning and relevance of the variables included in the model, as well as other evaluation metrics like residual plots and cross-validation.
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The following stem and leaf plot shows the average high temperatures during each month in the state of Ohio. Use the data to answer questions 7-8.
7) What is the minimum temperature?
A) 38
B) 31
C) 91
D) 67
Answer:
B) 31
Step-by-step explanation:
Given a stem and leaf plot, you want to identify the minimum value.
OrderingThe values in a stem and leaf plot are ordered with the smallest stems at the top, and the smallest leaves to the left. The smallest value on the plot will be the one at upper left.
Minimum valueThe minimum value on this chart has a "stem" of 3 and a "leaf" value of 1. That is the representation of the data value 31.
The minimum temperature shown on the chart is 31.
which statement describes the end behavior of the function ? f(x)= x2-4/x2-9
The Video “The Math and Magic of Origami”describes several examples in which scientists and engineers use origami to solve problems. Which of the following is NOT one of the applications described?
The option that is not one of the application described is C. Building a bridge.
What role does origami play in engineering?Origami created through mathematical interpretation and computation is known as mathematical origami, and it has resulted in the modeling of numerous novel origami-based structures outside of the realm of the arts. Furthermore, mathematical origami inspires the creation of new structures and mechanisms in engineering.
Origami-inspired engineering has been used in NASA space equipment, the development of better heart stents, and even DNA folding in microbiology.
Origami-based designs are the use of the ancient art of origami to solve various engineering problems. Regardless of the scale at which they are implemented, origami-based designs are always defined by the laws that govern their geometrical properties at any scale.
Furthermore, for large flat structures, origami allows for the reduction of dimensions while ensuring simple deployment this is especially useful for solar arrays in space applications.
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The Video "The Math and Magic of Origami" describes several examples in which scientists and engineers use origami to solve problems. Which of the following is NOT one of the applications described?
A.A heart stent
B. A space telescope
C. Building a bridge
D. Air bags in cars
A function is shown. ƒ (x) = 2x − 9
-
What is the value of ƒ (−4) ?
Answer: To find the value of ƒ (−4), we substitute −4 for x in the function ƒ(x) = 2x − 9:
ƒ(−4) = 2(−4) − 9
Performing the multiplication and addition, we get:
ƒ(−4) = −8 − 9
Thus, the value of ƒ(−4) is equal to −17.
Answer: ƒ (−4) = -17
Step-by-step explanation:
To find the value of ƒ (−4) we will substitute all values of x for -4 in the original function and simplify.
ƒ (−4) = 2x - 9
ƒ (−4) = 2(-4) - 9
ƒ (−4) = -17
Suppose you get $1000 from your uncle. you deposited that money in a bank and added $15 per month.
Write an equation to model how much money you have deposited after m months. Let s be the amount you have deposited.
What equation would you solve to figure out how many months it would take to save $10,000 dollars?
How many months would it take to save $10,000?
Answer:
s = 1000 + 15m
Save $10,000 equation: 10,000 + 15 m
Months it takes to save = 600 months
Step-by-step explanation:
You first deposit the $1000 your uncle gave you and then, each month, you add $15. So the first month the account will have,
1000 + 15
After the second month, it will have,
1000 + 15 + 15
And so on. Therefore, the equation that models your savings s after m months is,
s = 1000 + 15m
If we want to find how many months it will take to save $10,000 we have to solve the equation for s = 10,000:
10,000 = 1000 + 15m
To solve it, subtract 1000 from both sides of the equation,
10,000 - 1000 = 1000 - 1000 + 15m
9000 = 15m
And divide both sides by 15,
9000/55 = 55m/55
600 = m
It will take 600 months to save $10,000.
Find the equation of the linear function represented by the table below in
slope-intercept form.
X
-2
1
4
7
y
6
-6
-18
-30
Answer:
Step-by-step explanation:
the answer c which is 3,280
IJ is a midsegment of triangle MLN. What is the length of segment IJ?
The length of segment IJ is 6 units.
What is a line segment?
A line segment in geometry has two different points on it that define its boundaries. A line segment is sometimes referred to as a section of a line that links two places. The difference between a line and a line segment is that a line has no endpoints and can go on forever in either direction.
Given that IJ is a midsegment of △LMN.
The line segment IJ is parallel to NL.
Thus the length of IJ is half of NL.
Therefore,
2 × IJ = LN
2 (x + 3) = 3x
2x + 6 = 3x
Subtract 3x from both sides:
-x + 6 = 0
x = 6.
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