The quadratic equation 8x² + 16x + 3 = 0 can be solved by using the quadratic formula.
The given quadratic equation is : 8x² + 16x + 3 = 0
Comparing this equation with ax² + bx + c = 0 we get :
a = 8 , b = 16 and c = 3
Now we will use the quadratic formula:
[tex]{\displaystyle x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}}[/tex]
Now we will substitute the values in this formula to find the values of x that satisfy the quadratic equation.
[tex]{\displaystyle x={\frac {-16\pm {\sqrt {16^{2}-4\times8\times3}}}{2\times8}}}\\\\{\displaystyle x={\frac {-16\pm {\sqrt {160}}}{16}}}\\\\[/tex]
The values for x that satisfy the equation are the roots or zeros of both expressions on the left-hand side of the equation. In a quadratic problem, there can only be two possible solutions.
A problem is said to have a double root if there is only one solution. One real double root, two complex solutions that appear to be complex conjugates of one another, two real solutions, or two real solutions if all the coefficients have real values are the only options.
Hence the values of x are : [tex]-\frac{4-\sqrt{10}}{4}[/tex] and [tex]-\frac{4+\sqrt{10}}{4}[/tex].
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which is an example of a categorical random variable? a. the weight of a package of meat b. the length of the display shelf where the meat is displayed c. the color of a piece of meat d. the number of steaks sold by a supermarket
A six-sided die is rolled, with the potential results being 1, 2, 3, 4, or 6. Gender and illness status are examples of categorical random variable data. A, B, AB, or O correspond to a person's blood type. A voter's potential choice for a political party, e.
What is categorical random variable data?A categorical distribution, also known as a generalized Bernoulli distribution or a multinoulli distribution[1], is a discrete probability distribution used in probability theory and statistics to describe the potential outcomes of a random variable that can fall into one of K different categories, with the probability of each category being true being specified separately. Although numerical labels are frequently used to describe the distribution, there is no inherent ordering to these results (e.g. 1 to K). The most typical distribution over a K-way event is the K-dimensional categorical distribution; any other discrete distribution over a size-K sample space is a special instance.The only restriction on the parameters indicating the probability of each potential event is that they must all fall between 0 and 1.Hence, the example is . the color of a piece of meat
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The difference between 2 times an angle's
supplement and 120 is 30. Find the measure of
the angle.
Answer:
105
Step-by-step explanation:
An elevator can carry 28 adult or 30 children at one time during the course of the day the elevated acre carries a full passenger load 74 times all passengers were adults how many more people would the elevator carry then if all passengers were adults
The number of people the elevator would carry more if all passengers were children would be = 148 extra people.
What is an elevator?An elevator is defined as the machine that is being installed in tall buildings which helps to transport individuals either to slower level or a higher level of the building.
The number of adults the elevator can carry at a time = 28 adults.
The number of children the elevator can carry at a time = 30 children.
During the course of the day the total capacity of the elevator= 28 × 74 = 2,072.
The number of people the elevator would carry more if all the passengers where children would be;
30 × 74 = $2,220
2,220 - 2,072 = 148 extra people.
Therefore, the number of people the elevator would carry more if all passengers were children would be = 148 extra people.
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PLEASE HELP ASAP
What are the steps to writing the equation of a line, parallel
given line through a given point? Parallel lines have the _____ slope. Perpendicular lines have ____.
Answer:
parallel- same slope so the slope is 5, the slope will also be 5
perpendicular- reciprocal slope (if a whole # like 5, it goes to -1/5)
Step-by-step explanation:
a government agency wished to estimate the proportion of drivers aged 16-24 who have been involved in a traffic accident within the last year. the agency wished to make the estimate within one percentage point and at 90% confidence. find the minimum sample size required, using the information that, several years ago, the proportion was 0.12.
The required minimum sample size is 2875
Given that,
A government organization wanted to determine how many drivers between the ages of 16 and 24 had recently engaged in an accident. The agency wanted to make the estimate with a 90% confidence level and within one percentage point.
From the standard normal table, the z-critical value at 90% confidence is 1.65.
The information represent E = 0.01, p = 0.12 and z. =1.65 for finding sample size.
n = (Zc / E )² x P(1-P)
= (1.65 2x0.12(1 - 0.12)0.01
= 2874.96 ~ 2875
Hence, 2875 is the necessary number of samples, minimum.
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Are the slopes 0/3 and 9/0 perpendicular? Explain
The slopes 0/3 and 9/0 are not perpendicular .
In the question ,
the two slopes are given ,
the value of slope 1 (m₁) = 0/3
the value of slope2 (m₂) = 9/0 .
We know that the two slopes m₁ and m₂ are perpendicular is
m₁ × m₂ = -1 .
So , for the given values ,
On substituting the values of m₁ and m₂ ,
we get ,
= (0/3) × (9/0) ≠ -1
Since the product of the two given slope is not equal to -1 .
the slopes are not perpendicular .
Therefore , The slopes 0/3 and 9/0 are not perpendicular .
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the function when x = 3: b(x) = -2x-4
Answer: b(3)=-10
Step-by-step explanation:
Is this what you meant?
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The time taken by the rocket to reach its maximum height is 1.25 seconds and the maximum height is 32 feet.
Given equation:
h(t) = -16t^2+40t+7 and initial velocity is 40 feet per second and launching pad is 7 feet tall.
a = 1
t = -b/2a
= -40/2*-16
= -40/-32
= 40/32
= 1.25 seconds
h(2.5) = -16(1.25)^2+40*1.25+7
= -1.5625*16+50+7
= -25+57
= 32 feet.
Therefore The time taken by the rocket to reach its maximum height is 1.25 seconds and the maximum height is 32 feet.
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Your broker charges you 2.5% commission on the market value of bonds you buy or sell. if you wish to buy a par value $1,000 bond from cuyahoga county with a market rate of 86.681, approximately how much will you owe your broker? a. $25.00 b. $21.67 c. $89.18 d. $27.17
The amount to be paid to the broker is 2167.025. Therefore option b is correct.
Percentage:
A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction. All of something is 100 percent, half of it is fifty percent, and none of something is zero percent. To determine a percentage, you divide the portion of the whole by the whole itself and multiply by 100.
Here we have to find the amount to pay to the broker.
The given values are:
Market rate = 86.681
The commission charges by broker = 2.5%
The broker has to pay = 86.681 × 2.5% × 1000
= 86.681 × 2.5/100 × 1000
= 86681 × 0.025
= 2167.025
Therefore the amount paid to the broker is 2167.025.
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Answer:
B
I got it right
Step-by-step explanation:
Is 4x + 7y divisible by 2?
⇒ Is 4x + 7y divisible by 2?⇔ This question simply is asking you if there is a possibility that you can take out the highest common factor of 2 in the expression 4x+7y.
⇒ We cannot take out the highest common factor of 2 in this expression since there is the term 7y that has the coefficient 7 which is NOT divisible by 2. the expression 4x+7y
cannot be written in the form a(b+c)
⇒∴ 4x + 7y is not divisible by 2
If you want me to clarify more in this question please say so as soon possible so that I can make time for you.
Convert the following
Answer:
Step-by-step explanation:
1.
4,000 mm to km = 0.004
4,000 mm to m = 4
4,000 mm to cm = 400
2.
12,000 km to m = 12000000
12,000 km to cm = 1.2e+9
12,000 km to mm = 1.2e+10
3.
5,800 m to km = 5.8
5,800 m to cm = 580000
5,800 m to mm = 5800000
4.
2 mm to km = 2e-6
2 mm to m = 0.002
2 mm to cm = 0.2
5.
40,108 to m = 40108000
40,108 to cm = 4010800000
40,108 to mm = 40108000000
each quiz in a course contains 15 questions. how many different ways could the questions on a given quiz be ordered?
The no. of ways could those question be ordered is 1307674368000 ways A combination is what?
When selecting components from a collection using the combination method, the sequence of selection is unimportant, in contrast to permutations. In simpler scenarios, the number of combinations can be counted.
The act of combining n objects into k groups, one at a time, without repetition Repetition-allowed combinations are usually referred to as k-selection or k-combinations with repetition.
Given
that, Total no of question in quiz is 15 The no. of ways could those question be ordered is 15! ways = 1307674368000 ways The number of possible ways for those questions is 1307674368000.
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If x²y - 3x = y³ – 3, then at the point (-1,2), dy/dx=
now, the assumption in this implicit differentiation is that "y" is really a function in x-terms, whilst "x" is just a simple variable
[tex]x^2y-3x=y^3-3\implies \stackrel{product~rule}{\left( 2xy + x^2\cdot \cfrac{dy}{dx} \right)}-3=\stackrel{chain~rule}{3y^2\cdot \cfrac{dy}{dx}} \\\\\\ 2xy-3=3y^2\cdot \cfrac{dy}{dx}-x^2\cdot \cfrac{dy}{dx}\implies 2xy-3=\cfrac{dy}{dx}(3y^2-x^2) \\\\\\ \left. \cfrac{2xy-3}{3y^2-x^2}=\cfrac{dy}{dx} \right|_{(-1,2)}\implies \cfrac{2(-1)(2)-3}{3(2)^2-(-1)^2}\implies -\cfrac{7}{11}[/tex]
Constant Speed Quick Check
Constant Speed Quick Check
Volunteers put together 40 school-supply kits in 8 minutes. At this rate, how many could they put together in 30 minutes
Solve this problem using a unit rate. (1 point)
O 150 school-supply kits
O 10.67 school-supply kits
O 6 school-supply kits
O 9,600 school-supply kits
6 school-supply kits can be put together in 30 minutes.
What do you mean by the Unitary method?
By using the unitary technique, we may determine the value of a single unit and, using that value, get the value of the necessary number of units.
According to the questions,
By applying the unitary method,
40 school supply kits can be put together in 8 minutes.
∴1 school supply kit can be prepared in (8/40) minutes
∴30 school supply kits can be prepared in (30/5) minutes
Hence,
6 school-supply kits can be put together in 30 minutes.
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The cost of the Gas is 11p for each unit
there is also a fixed charge of £25.57
calculate the cost of the gas
you must show your working
The cost of the gas will be equal to £67.81 p.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that,
Initial gas reading = 8247
Final gas reading = 8631
The total consumed gas is given by,
Final gas reading - Initial gas reading → 8631 - 8247 = 384
Since the cost of gas is 11p per unit we have, the total cost of the gas consumed is given by
Cost of consumed gas = Units of gas consumed × Unit cost of gas
= 384 × 11p = 4224 p
100 p ≡ £ 1
4224 p = £42.24 p
The total cost of the gs is obtained by adding the fixed charge to the cost of gas consumed as follows,
£25.57 + £42.24 = £67.81 p
The cost of the gas = £67.81 p
The complete question is given below,
The gas meter readings at the beginning and end of a period were: 8247 = 8631 the cost of the gas is 11p for each unit. there is also a fixed charge of £25.57. calculate the cost of the gas. you must show your working
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task 13: are the expressions equivalent? Simplify to prove, if the two expressions are not equal write the correct equivalence. #5: x(x+y+2) and x²+xy+2x #6: 2x(x+3) and 2x+6 distribute the following. 1. 3(x+2) 2. 4(y-1) 3. x(x+6) 4. x(y+4) 5. 3x(x+y-1)
Answer:
Step-by-step explanation: watch the video
alexander was studying the effect of playing rock music on plant growth. one of the plants was exposed to rock music for 24 hours a day for a period of 6 weeks. data on the growth of the plant was collected at the end of each week and plotted in a graph. based on the data, which would be the most reasonable measurement at the end of an 8 week period?
Eight decimeters are the most logical measurement after eight weeks, according to the statistics.
A line is described as a collection of points that stretches in both directions indefinitely. It has a single-length dimension. Collinear points are points that are located on the same line. Two points form a line, which is shown below an arrowhead.
If a line intersects two spots [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], then the line's equation,
y - [tex]y_1[/tex] = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex](x - [tex]x_1[/tex])
It is evident from the above graph that the line goes through points (0,0) & (1,1). Consequently, the trend line's equation is
y - 0 = [tex]\frac{1 - 0}{1 - 0}[/tex](x - 0)
y = x
To determine the most acceptable measurement after 8 weeks, change x = 8 in the equation above.
y = 8
After eight weeks, 8 decimeters are the most realistic measurement.
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The question is -
Alexander was studying the effect of playing rock music on plant growth. One of the plants was exposed to rock music 24 hours a day for 6 weeks. Data on the growth of the plant was collected at the end of each week and plotted in a graph, with time in weeks on the X-axis and height in decimeters on the Y-axis. Based on the data, which would be the MOST reasonable measurement at the end of 8 weeks?
A) 2 decimeters
B) 6 decimeters
C) 8 decimeters
D) 16 decimeters
let s be the total amount heidi spent for scarves. each of the 4 scarves that she bought cost the same. write an expression for the cost of each scarf
The expression for the cost of each scarf is s/4.
According to the question,
We have the following information:
Let s be the total amount Heidi spent for scarves. each of the 4 scarves that she bought cost the same.
Now, the cost of 1 scarf can be easily found by dividing the total cost of the scarves by the number of scarves.
(If we would have to find the cost of 15 scarves then first we would have used division and then multiplication.)
So, we have the following expression:
4 scarves = s
Cost of one scarf = s/4
Hence, the expression for the cost of each scarf is s/4.
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There are 40 coins in a roll of nickels .there are 50 coins in a roll of dimes and 20 coins in a roll of half -dollars.alondra has 3 rolls of coins. she has a total of 90 coins. make an organized list to show all the combinations of coin rolls. what coins does alondra have?
Answer:
she has 2 half dollors and 1 dimes
Step-by-step explanation:
2 half dollors means 2x20=40 coins
1 dimes means 1x50=50 coins
when you total it you get 50+40=90
so it is 3 rolls and it totally has 90
The solutions of the equation x^2 - 6x + d = 0 are both integers. d is a prime number. Find d
The solutions of the equation x^2 - 6x + d = 0 are both integers and d is a prime number is 5.
How to determine the value of d?From the information, the solution of the equation x^2-6x+d=0 are integers
To find d, the numbers which can be added or subtracted to get -6 is needed which when multiplied will give a prime number
In this case - 5- 1 = -6
And when multiplied (-5×-1) will give +5 which is a prime number.
Therefore, x^2-6x+5=0
This illustrates that d is 5.
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a coin is altered so that the probability that it lands on heads is less than 1 2 12 and when the coin is flipped four times, the probability of an equal number of heads and tails is 1 6 16. what is the probability that the coin lands on heads?
The probability that the coin lands on heads is D = (3±√3)/6
Probability is a branch of mathematics that studies the likelihood of a random event occurring. For example, when a coin is tossed into the air, the possible outcomes are Head and Tail.
Let x be the probability of flipping heads. As a result, the probability of flipping tails is 1- x.
The probability of flipping two heads and two tails is equal to the number of ways to flip it multiplied by the product of the probabilities
(4+2)x2(1-x)2 = 1/6
6x2(1-x)2 = 1/6
x2(1-x)2 = 1/36
x(1-x) = ±1/6
As for the desired probability x, both x and 1 - x are nonnegative, we only need to consider the positive root, hence
x(1-x) = 1/6
6x2 – 6x +1 = 1/6
Using the quadratic formula, we can determine that the roots of this equation are
(3±√3)/6
Therefore the probability that the coin lands on heads is D = (3±√3)/6
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the center for medicare services reported that there were 295,000 reported appeals for hospitalization and other medicare part a services. for this group, 40% of the first round appeals were successful. suppose ten first round appeals were just received. the results follow a binomial distribution. what is the probability exactly two of the appeals was successful? enter answer to four decimal places.
The probability exactly two of the appeals were successful is 0.9536
We are given that 40% of first-round appeals were successful (The Wall Street Journal, October 22, 2012), and suppose ten first-round appeals have just been received by a Medicare appeals office.
This situation can be represented through Binomial distribution as;
[tex]P(X=r)={}^{n}C_{r}(p)^r(1-p)^r[/tex] where [tex]x=0,1,2,3.....[/tex]
where, n = number of trials (samples) taken = 10
r = number of success
p = probability of success which in our question is % of first-round
appeals that were successful, i.e.; 40%
So, here X ~ Binom(n=10 , p=0.40
Probability that at least two of the appeals will be successful = P(X>=2)
P(X >= 2) = 1 - P(X = 0) - P(X = 1)
= 1 - [tex]^{10}C_{0}(0.40)^0(1-0.40)^{10-0}-^{10}C_{1}(0.40)^1(1-0.40)^{10-1}[/tex]
= 1 - 0.00605 - 0.0403
= 0.9536
Hence, the probability exactly two of the appeals were successful is 0.9536
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Round 41.86632 off each number
to two (2) Decimal Place
Answer:
2 d.p = 41.87
Step-by-step explanation:
41.86/632
check whether its below or above 5 then round it to the nearest number
2 d.p = 41.87
Answer: 41.87
Step-by-step explanation:
41.86632 to 2 dp is 41.87
given p (1,3) q(8,-4), r(2,9) and s(7,y). find y such that pq || rs
By secant line formula, the missing value of the point S is equal to 4.
How to determine the missing coordinates of a point related to two parallel line segments
Two line segments are parallel if and only if both line segments have the same slope. Slopes can be determined by secant line formula, defined below:
m = Δy / Δx
Where:
Δx - Change in the variable x. Δy - Change in the variable y.Then, the missing value of the variable y in the point S is:
(- 4 - 3) / (8 - 1) = (y - 9) / (7 - 2)
- 7 / 7 = (y - 9) / 5
- 1 = (y - 9) / 5
- 5 = y - 9
y = 4
The missing value of the variable y is 4.
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In November's Math Meet, the Little Monsters of Beast Academy solved $\frac{1}{5}$ of the problems. In March's Math Meet, they solved $\frac23$ of the problems. (There might be different numbers of problems asked in November and March.)
In total, the Little Monsters solved $13$ of $30$ problems over both Math Meets. How many problems were asked at March's Math Meet?
The Little Monsters of Beast Academy completed 15 problems during the math meet in March.
How to calculate the total number of issues resolved in MarchThe issue is a simultaneous equation involving two equations and two unknowns.
These are the equations that are created:
Let the quantity of questions that the students at the Beast Academy have answered in
March be xNovember be yThe Little Monsters of Beast Academy successfully completed $frac1/5$ of the problems in the November = y/5
In Math Meet. they resolved $frac23$ = 2x/3 problems i
Hence:
y/5 + 2x/3 = 12
x + y = 30
When the equation is solved,
x = y = 15
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Find the area of the Polyogon below.
A =
12
14.49
Answer: 695.52
Step-by-step explanation:
The area of each triangle is [tex]\frac{1}{2}(12)(14.49)[/tex].
There are 8 triangles in the figure, so the area is [tex]8(1/2)(12)(14.49)=695.52[/tex].
A company orders 15 boxed lunches from a deli for $175.50. If each boxed lunch costs
the same amount, how much do 5 boxed lunches cost?
Answer: $58.50
Step-by-step explanation:
We will set up a proportion to help us solve.
[tex]\displaystyle \frac{15\; \text{boxed lunches}}{\$175.50} =\frac{5\; \text{boxed lunches}}{\$x}[/tex]
Next, we will cross-multiply.
15 * x = 175.5 * 5
15x = 877.5
x = $58.50
a salesman keeps 20% of his sales as a commission. how much does he have to sell to earn $1,000?
Answer:
He has to sell 5000 to earn $1000
Step-by-step explanation:
1000/0.2 = 5000
Describe the relationship between the point B (5,-3) and the point A (5,3) in terms of reflections.
Answer:
The point does not lie in the solution sets of the given system of inequalities
Step-by-step explanation:
We need to check whether the point (1,-5) is a solution to the system of inequality
We substitute x=1 and y=-5 into the top inequality:
. This is true
We substitute x=1 and y=-5 into the bottom inequality:
. This is false.
Since the point does not satisfy both inequalities, it is not a solution to the system of inequalities.
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