Answer:
4
Step-by-step explanation:
4
The possible values of x are:
x = -1/2 + i/2
x = -1/2 - i/2
What is a quadratic equation?A basic quadratic equation, or a second-order polynomial equation with a single variable, is represented by the equation x : ax² + bx + c = 0, where a≠0 for the variable x. As it is a second-order polynomial equation, which is ensured by the algebraic fundamental theorem, it must have at least one solution.
To find the possible values of x in equation 8x² + 4x = -1, we need to solve for x.
First, we can rearrange the equation to get:
8x² + 4x + 1 = 0
We can solve this quadratic equation using the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
where a, b, and c are the coefficients of the quadratic equation in standard form (ax² + bx + c).
In this case, a = 8, b = 4, and c = 1. Substituting these values into the quadratic formula, we get:
x = (-4 ± √(4² - 4(8)(1))) / 2(8)
x = (-4 ± √(16 - 32)) / 16
x = (-4 ± √(-16)) / 16
x = (-4 ± 4i) / 16
where i is the imaginary unit, which is defined as the square root of -1.
Therefore, the possible values of x are:
x = (-4 + 4i) / 16
x = (-4 - 4i) / 16
These values can also be simplified as:
x = -1/2 + i/2
x = -1/2 - i/2
So the possible values of x are complex numbers, specifically x = -1/2 ± i/2.
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I cannot crack this one, somebody please assist me
These [tex]N[/tex] outcomes make up the entire sample space, so
[tex]\displaystyle \sum_{k=1}^N P(e_k) = P(e_1) + P(e_2) + P(e_3) + \cdots + P(e_N) = 1[/tex]
We're given that [tex]P(e_{j+1}) = 2 P(e_j)[/tex] for all [tex]j\in\{1,2,\ldots,N-1\}[/tex], so
[tex]P(e_1) + 2 P(e_1) + 2^2 P(e_1) + \cdots + 2^{N-1} P(e_1) = 1 \\\\ \implies P(e_1) = \dfrac1{1 + 2 + 2^2 + \cdots + 2^{N-1}} = \dfrac1{2^N - 1}[/tex]
Then we can solve the recurrence relation to get the probability of the [tex]j[/tex]-th outcome,
[tex]P(e_{j+1}) = 2 P(e_j) = 2^2 P(e_{j-1}) = 2^3 P(e_{j-2}) = \cdots \\\\ \implies P(e_{j+1}) = 2^j P(e_1) \\\\ \implies P(e_j) = 2^{j-1} P(e_1) = \dfrac{2^{j-1}}{2^N - 1}[/tex]
The probability of getting this sequence of [tex]k[/tex] outcomes is then
[tex]\displaystyle P(E_k) = P(e_1) + P(e_2) + \cdots + P(e_k) = \sum_{j=1}^k \frac{2^{j-1}}{2^N-1} = \frac{2^k-1}{2^N-1}[/tex]
as required.
Some preliminary results: If [tex]S[/tex] is the sum of the first [tex]n[/tex] terms of a geometric series with first term [tex]a[/tex] and common ratio [tex]r[/tex], then
[tex]S = a + ar + ar^2 + \cdots + ar^{n-1}[/tex]
[tex]\implies rS = ar + ar^2 + ar^3 + \cdots + ar^n[/tex]
[tex]\implies S - rS = a(1 - r^n)[/tex]
[tex]\implies S = \dfrac{a(1 - r^n)}{1 - r}[/tex]
which gives us, for instance,
[tex]1 + 2 + 2^2 + \cdots + 2^{N-1} = \dfrac{1 - 2^N}{1 - 2} = 2^N-1[/tex]
A right cylinder has a radius of 5 and a height of 9. What is its surface area?
A. 45 units²
B. 140 units²
C. 90 units²
D. 70 units²
Answer:
the answer is B. 140 units²
simplify 3 + [5n - (2-n)]
Answer:
6n+1
Step-by-step explanation:
Eliminate the parenthesis by changing the symbol of each term inside
3+[5n-2+n]
Eliminate the bracket and group similar terms
5n+n+3-2
Simplify terms
6n+1
. The two bottles are similar in shape. The larger bottle holds 100 m/ of perfume. Calculate how many millilitres of perfume the smaller bottle holds.The length of the larger bottle is 10cm.the length of the smaller bottle is 5cm
Answer:
The smaller bottle holds 12.5 ml of perfume.
====================
GivenTwo bottles of similar shape;Larger bottle has volume of 100 ml;The length of larger bottle is 10 cm;The length of smaller bottle is 5 cm.To find The volume of smaller bottle.SolutionFind the scale factor, the ratio of corresponding dimensions:
[tex]k = 5/10 = 1/2[/tex]We know the volume is the function of three dimensions, therefore the ratio of volumes is the cube of the scale factor:
[tex]V_{small}/V_{large} = k^3\\[/tex]Substitute the known values and find the volume of small bottle:
[tex]V_{small}/100= (1/2)^3\\[/tex][tex]V_{small}/100= 1/8[/tex][tex]V_{small}= 1/8*100=12.5[/tex]The smaller bottle holds 12.5 ml of perfume.
The smaller bottle holds 12.5 ml of perfume.
I solved it and came with this result.
This table gives a few (x,y)(x,y)left parenthesis, x, comma, y, right parenthesis pairs of a line in the coordinate plane. xxx yyy -12−12minus, 12 141414 -2−2minus, 2 212121 888 282828 What is the xxx-intercept of the line? ((left parenthesis ,,comma ))
Answer:
(-32, 0)
Step-by-step explanation:
Answer:
(-32,0)
Step-by-step explanation:
Review the graph. Given z = , which letter represents z3?
A
B
C
D
By writing Z in polar form, we will see that:
[tex]z^3 = C[/tex]
How to get the value of Z³?
First, we can see that:
z = (-1 - i)
If we write it in polar form, we get:
[tex]z = \sqrt{2} *e^{i(\pi + \pi/4)[/tex]
If we apply the power 3, we get:
[tex]z^3 = (\sqrt{2} *e^{i(\pi + \pi/4)})^3\\\\z^3 = 2^{3/2}*e^{i*(3\pi + 3\pi/4)}\\\\z^3 = 2^{3/2}*e^{i*15\pi/4}[/tex]
Notice that:
[tex]\frac{15\pi}{4}[/tex]
Is an angle equivalent to:
[tex]\frac{15\pi}{4} - 2\pi = \frac{15\pi}{4} - \frac{8\pi}{4} = \frac{7\pi}{4} = 1.75\pi[/tex]
Because the angle is measured from the positive x-axis, this means that we will have:
[tex]z^3 = C[/tex]
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What is the current yield on a 3 year bond with 10% annual coupons, a par value of 100, and a current price of 107.87?
Based on the annual coupons on the bond and the current price, the current yield will be 9.27%.
What is the bond's current yield?This can be found as:
= Annual coupon amount / Bond price
Annual coupon:
= 10% x 100
= $10
The current yield is:
= 10 / 107.87
= 9.27%
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pls i need to pass this class i wna graduate
Answer:
[tex]\boxed{\sf x= -29.5}[/tex]
Step-by-step explanation:
[tex]\sf \sqrt{-2x+5}-3=5[/tex]
[tex]\sf \sqrt{-2x+5}=8[/tex]
[tex]\sf -2x+5=64[/tex]
[tex]\sf -2x=59[/tex]
[tex]\sf \cfrac{-2x}{-2}=\cfrac{59}{-2}[/tex]
Therefore, x = -29.5.
The Royal Fruit Company produces two types of fruit drinks. The first type is 35% pure fruit juice, and the second type is 60% pure fruit juice. The company is attempting to produce a fruit drink that contains 45% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 40 pints of a mixture that is 45% pure fruit juice?
32 pints of each of the two existing types of drink must be used to make 40 pints of a mixture that is 45% pure fruit juice.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
Let x be the pints of 60% pure fruit juice
0.60x + 0.35(40 - x) = 0.40(40)
x = 8
= 40 - 8 (pints of 35% juice)
= 32
Thus, 32 pints and 8 pints of each of the two existing types of drink must be used to make 40 pints of a mixture that is 45% pure fruit juice.
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MATH: Composition of two functions...help needed with this problem
The equation of Q(n) is [tex]Q(n) = \frac89 * (88n + 23)[/tex]
How to determine the formula of Q(n)?The functions are given as:
[tex]R(d) = \frac89 d[/tex]
[tex]P(n) = 88n + 23[/tex]
From the question, we understand that:
d = P(n)
This means that:
d = 88n + 23
Substitute d = 88n + 23 in R(d)
[tex]R(n) = \frac89 * (88n + 23)[/tex]
Also, from the question
Q(n) = R(n)
So, we have:
[tex]Q(n) = \frac89 * (88n + 23)[/tex]
Hence, the equation of Q(n) is [tex]Q(n) = \frac89 * (88n + 23)[/tex]
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PLEASE HELP QUICK ILL GIVE HIGH POINT COUNT, BRAINLIEST, FIVE STARS, AND A THANKS IF YOU ANSWER WRITE
(Please use the numbers)
Complete the Magic Square
The image is attached with the answer.
What is a Magic Square ?A magic square is a 3*3 , 4*4 ,5*5 square in which the magic sum is constant for all the columns and rows and even diagonally the sum is same.
The empty squares have been filled and the image has been attached.
The magic sum is 0.81
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Find the domain of the function y = 3 tan(2/3x)
Answer:
{x∈R | [tex]\frac{2x}{3\pi } +\frac{1}{2}[/tex], x∉Z}
Step-by-step explanation:
Given the function y=3tan(2/3x)
We know that tangent is a function that's continuous within it's domain but not continuous on all real numbers
Also, the roots of y=3tan(2/3x) is [tex]3\pi n/2[/tex] where n is an integer
Note that the domain of the function cannot be within [tex]3\pi n/2[/tex]
Therefore, {x∈R | [tex]\frac{2x}{3\pi } +\frac{1}{2}[/tex], x∉Z}
Solve the equation.
6(x−1)6/7=12
Answer:
Linear Equations In One Variable =
[6(x-1)6] / 7 = 12
[(6x - 6)6] = 84
[36x - 36] = 84
36x = 84 + 36
36x = 120
x = 120/36
x = 10/3
equation solved (Answer : 10/3)
A clinical psychologist is administering the Hamilton Rating Scale for Depression (Hamilton, 1967). The scale ranges from 0 to 52. Scoring is based on the 17-item scale and scores of 0–7 are considered as being normal, 8–16 suggest mild depression, 17–23 moderate depression and scores over 24 are indicative of severe depression (Zimmerman, Martinez, Young, Chelminski, & Dalrymple, 2013).
We have some evidence about the mean score for the Hamilton Rating Scale for Depression among the population of adolescents: μ = 6 with a standard deviation of σ =1.5. The clinical psychologist’s patient, a 14-year old girl, scores a 10 on the scale. How would you describe her score relative to the population of adolescents? (Please use your knowledge of z-scores to answer this question.)
Using the normal distribution, it is found that the girl's score of 10 is higher than 99.62% of the population.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 6, \sigma = 1.5[/tex].
Her z-score is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{10 - 6}{1.5}[/tex]
Z = 2.67
Z = 2.67 has a p-value of 0.9962.
Hence her score is higher than 99.62% of the population.
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Discriminat step by step of x^2+4x+5=0
Answer:
-4
Step-by-step explanation:
x^2+4x+5=0
a=1,b=4^1 C=5
4^2-4×1×5
-4
HELP PLEAES ASAP!!!!!
Volume is a three-dimensional scalar quantity. As per the Cavaleri's principle the volume of both the figures will be the same.
What is volume?A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.
What is Cavaleri's principle?According to Cavalieri's principle, if two figures have the same height and cross-sectional area throughout each point along that height, they have the same volume.
The height of both the objects is 16 cm, also the base area of both the objects is 96 cm². As it can be observed that for both the object there base area is the same through out their height.
Hence, as per the Cavaleri's principle the volume of both the figures will be the same.
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An event manager recorded the number of people in different age groups who attended a music concert:
A histogram titled Concert Audience is shown. The horizontal axis is labeled Age Group in years with bins 18 to 24, 25 to 31, 32 to 38, and 39 to 45. The vertical axis labeled Number of People with values from 0 to 120 at intervals of 20. The first bin goes to 80, the second goes to 120, the third goes to 40, and the last goes to 20.
Which data table accurately represents the data in the histogram?
A:
Age Group Number of People
18–24 80
25–31 120
32–38 40
39–45 20
B:
Age Group Number of People
18–24 80
25–31 200
32–38 240
39–45 260
C:
Age Group Number of People
18–24 20
25–31 40
32–38 120
39–45 80
D:
Age Group Number of People
18–24 260
25–31 240
32–38 200
39–45 80
Answer: C) Age Group Number of People:
18–24 20
25–31 40
32–38 120
39–45 80
Have a good day/night! I hoped this helped. :D
Answer:
A:
18–24: 8025–31: 12032–38: 4039–45: 20Step-by-step explanation:
You want to know the table that accurately reflects the data in the described graph.
MatchingAs presented here, this is a reading comprehension problem.
The problem statement tells you the first bin is labeled 18–24, and the graph there extends to 80. This eliminates tables C and D. Tables A and B show 80 people in the 18–24 age group.
The second bin is labeled 25–31, and the graph there extends to 120. This matches the entry in Table A.
Table A matches the graph.
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16, 13, 10 is this sequence arithmetic or geometric and determine the common difference/ ratio in simplest form
Answer:
It is arithmetic progression
Step-by-step explanation:
If wwe see, the numbers are going down by 3 each time, therfore the common difference is 3
Hii!
_________________________________________________________
[tex]\stackrel\star{\rightsquigarrow\circ\boldsymbol{\underbrace{Answer}\circ\leftharpoonup}}[/tex]
1. This sequence is arithmetic
2. The common ratio is 3.
[tex]\stackrel\star{\rightsquigarrow\circ\boldsymbol{\underbrace{Explanation.}}}\circ\leftharpoonup[/tex]
[tex]\bullet[/tex] Difference between arithmetic and geometric sequences
[tex]\twoheadrightarrow\sf Arithmetic\quad sequences[/tex] - In arithmetic sequences, we add the same amount to obtain the next term.
[tex]\twoheadrightarrow\sf Geometric\quad sequences[/tex] - In geometric sequences we multiply times the same amount to obtain the next term.
[tex]\bullet[/tex] Since we add the same amount to get the next term, the given sequence is arithmetic
[tex]\twoheadrightarrow\sf Common\;difference:-3[/tex]
[tex]\bullet[/tex] In the given sequence we add -3, or subtract 3, to obtain the next term
--
Hope that this helped! Best wishes.
[tex]\stackrel\ast{\textsl{Reach far. Aim high. Dream big.}}[/tex]
--
for
If a study determines the difference in average salary
subpopulations of mechanical engineers and civil
engineers is NOT significant, then the subpopulations
of mechanical and civil engineers are
different
salaries.
A
Guaranteed not to be earning
B
Not earning
C) Earning very
D Definitely earning
A mean is an arithmetic average of a set of observations. The correct option is B.
What is Mean?A mean is an arithmetic average of a set of observations. it is given by the formula,
Mean = (Sum of observations)/Number of observations
The average pay does not differ significantly since the average wage for subpopulations is not significant. As a result, the subpopulations of mechanical and civil engineers are Not earning different salaries.
Hence, the correct option is B.
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by what percent will the fraction change if its numerator decreased by 20 and its denominator is decreased by 60
I consider the original fraction: x/y.
If the numerator "x" increases by 20%, it can be interpreted in this way:
"x" represents 100% (the unit) and when increasing by 20% we have that the value of "x" becomes 120%
120% of "x" is [tex]\bf{\frac{120*x}{100}=1,2x }[/tex]
This is what we have left in the numerator.
By the same reasoning, in the denominator "y" remains:
100% - 40% = 60% of "and"
60% of "y" is...[tex]\bf{\frac{60*y}{100}=0.6 y }[/tex]
The new fraction is: 1,2x / 1,6y.
...simplifying by dividing top and bottom by 0.6,... 2x / y
To find out the percentage by which the original fraction has changed, we first find the relationship or ratio between the original fraction and the new fraction with the fraction quotient:
[tex]\bf{\dfrac{\frac{2x}{y} }{\frac{x}{y} }=\frac{2xy}{xy}=2 }[/tex]
... that is to say that the new fraction has doubled in relation to the original.
Therefore, the percentage of variation per increase is 100%.
Pisces04or
Soda is often packaged in cans that are supposed to contain 12 ounces. However, no
manufacturing plant is perfect and so there might be slight errors. For example, Sam's Splendid
Soda company has verified that the amount of soda in their cans has a normal distribution with
a mean of 12 ounces and a standard deviation of 0.7 ounces. Although this is made up, it's not
completely divorced from the truth.
1. You open a can of Sam's and realize there are only 11.6 oz in the can. What is the
probability that a single can will contain 11.6 ounces or less of soda? (2 points)
2. Troubled by the under-filled soda, you decide to empty out all the cans in a six pack of Sam's
Soda and find that the mean amount of soda in all the cans is 11.6 ounces. What is the
probability that six pack will have a mean of 11.6 ounces or less of soda? (2 points)
3. Not satisfied with the information you figured out in #2, you take a case (36 cans) and
empty out all the cans of Sam's Soda and find that the mean amount of soda in all the cans is
11.6 ounces. What is the probability that case will have a mean of 11.6 ounces or less of soda?
(2 points)
4. Draw three normal distributions on the same set of axes or with the same scale to show
how the probabilities decrease from one can to six cans to 36 cans even though we're looking
at "less than 11.6 ounces." (2 points)
5. Use the graphs and your own understanding of the Central Limit Theorem to write a few
sentences explaining what is happening here. (2)
The probability that a single can will contain 11.6 ounces or less of soda is 0.2843
Probability that a can contains 11.6 ounces or lessThe given parameters are:
x = 11.6
Mean = 12
Standard deviation = 0.7
Calculate the z value using:
[tex]z = \frac{x - \bar x}{\sigma}[/tex]
This gives
[tex]z = \frac{11.6-12}{0.7}[/tex]
z = -0.57
The probability is then calculated as:
P(x ≤ 11.6) = P(z ≤ -0.57)
Using the z table of probabilities, we have:
P(x ≤ 11.6) = 0.2843
Probability that a pack contains 11.6 ounces or lessIn (a), the probability that a can contains 11.6 ounces or less is 0.2843
The probability that all cans in a pack contains 11.6 ounces or less is
P(6) = 0.2843^6
P(6) = 0.00053
Probability that a case contains 11.6 ounces or lessIn (a), the probability that a can contains 11.6 ounces or less is 0.2843
The probability that all cans in a case contains 11.6 ounces or less is
P(36) = 0.2843^36
P(36) ≈ 0
Draw three normal distributionsSee attachment for the normal distributions
The happening on the graphThe summary of the graph is that, as the sample size increases the probability decreases
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Hello all! Please help me out with this.
I want to find a certain number which I will call Y. It is four times as great as another number which is two less than twenty. What is Y?
Answer:
Y=72
Step-by-step explanation:
First we set up the equation which is (20-2) times 4=Y
Then we solve, 20 minus 2 is risk since it is in the parentheses. 20 minus 2 is 18.
After that 18 times 4 is 72
Y=72
300 people went on a trip. 20% chose hiking. how many people chose hiking?
please help me asap :)
Answer:
They are not similar because corresponding sides are not proportional.
ExplainationCondition for similarity of two triangles -
The ratio of corresponding sides should be equal.
Condition for congruence of two triangle -
Any of the following -
Side side side
side angle side
angle angle
angle side angle
If “a” is a non zero constant, what is the maximum number of turns for the graph of
y = x³ + ax² - 7x+10
The maximum number of turns for the graph given by the function is; 2.
What is the maximum number of turns for the graph?It follows from the task content that the graph given is that of a cubic function. On this note, it follows that the graph has 2 turning points.
This follows from the fact that the degree of the polynomial is 3 and hence, the maximum number of turns on the graph is 2.
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16. You found a shortcut to school that saves 5 minutes off of taking the freeway. About 1 in every 10 trips
you get stuck behind a bus and it ends up taking you 20 minutes longer than the freeway. What is the expected
value of the shortcut?
Answer:
it saves 2.5 minutes
Step-by-step explanation:
The expected value of a random variable is the sum of products of possibilities and the probability of each.
Here, you have a probability of 0.9 of saving 5 minutes, and a probability of 0.1 of adding 20 minutes.
__
The expected value of the shortcut is ...
0.9(-5) +0.1(20) = -4.5 +2.0 = -2.5
The shortcut is expected to save 2.5 minutes on average.
_____
Additional comment
The probability of 0.9 comes from the 9 of 10 trips that result in a time saving.
− 11 , − 7 , 7 , − 2 , 16 , 10 , 20 , − 17 , − 10 , − 12 State the median.
Answer:
-4.5
Step-by-step explanation:
You arrange the numbers from lowest to highest value:
-17, -12, -11, -10, -7, -2, 7, 10, 16, 20
Then you find the one in the middle:
-7, -2
Because there are two in the middle, you add them and divide them by two:
(-7 + -2)/2 = -4.5
Your answer is -4.5.
Step-by-step explanation:
firstly arrange it increasingly
-2,-7,-10,-11,-17, 7,10,16,20
n=9 it is odd so we use (n+1/2 )th formula
9+1/2
10/2=5th
os it is -17
Figure ABCD is transformed to figure A prime B prime C prime D prime, as shown below:
A coordinate grid is shown from negative 5 to 0 to 5 on both x- and y-axes. A polygon ABCD has A at ordered pair 2, 3, B at ordered pair 4, 4, C at ordered pair 3, 1, D at ordered pair 2, 1. A polygon A prime B prime C prime D prime has A prime at ordered pair negative 1, 3, B prime at ordered pair negative 3, 4, C prime at ordered pair negative 2, 1, D prime at ordered pair negative 1, 1.
Which of the following sequences of transformations is used to obtain figure A prime B prime C prime D prime from figure ABCD?
The sequence of transformations used to obtain figure A'B'C'D'from figure ABCD are a reflection across the y-axis followed by a horizontal translation 1 unit right
Complete questionFigure ABCD is transformed to figure A'B'C'D', as shown below: (see attachment)
Which of the following sequences of transformations is used to obtain figure A'B'C'D'from figure ABCD?
How to determine the transformation?From the attached figure, we can see that:
ABCD and A'B'C'D' are on either sides of the y-axis.
This means that ABCD is first reflected across the y-axis.
ABCD is 2 units from the y-axis, while A'B'C'D' is 1 unit from the y-axis.
This means that the reflection is followed by a translation.
The unit of translation is:
Unit = 2 - 1
Evaluate
Unit = 1
1 represents a right translation
Hence, the sequence of transformations are a reflection across the y-axis followed by a horizontal translation 1 unit right
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How can I solve this? Thank you
The labeled angles are both equal to c by the corresponding angles theorem.
Thus, a+b=c by the exterior angle theorem.
there are 48 tables at a school.
3/8 of the tables are in the dining hall.
the rest are shaded equally between 5 classrooms.
how many tables are in the main hall
Total: 48
DIning Hall: 48(3/8)=18
so theres 30 left for the classes
30/5(#of classes)=6 per class