Answer:
-3+15i
Step-by-step explanation:
Apply complex arithmetic rule: \(\left(a+bi\right)\left(c+di\right)=\left(ac-bd\right)+\left(ad+bc\right)i\)
\(\left(-3\cdot \:3-3\left(-2\right)\right)+\left(-3\left(-2\right)+3\cdot \:3\right)i\)
-3 * 3 -3 (-2) = -3
\(-3+15i\)
An art teacher times his students, in minutes, to see how long it takes them to paint a 12-inch canvas. He makes a box plot for the data. Paint Times
10 15 20 25 30 35 40 45 50 55
How long could a student take to paint their canvas if they are slower than 75% of the other students? 15 minutes O 25 minutes O 40 minutes 0 46 minutes
To find the answer, we need to identify the quartiles of the data set and use them to construct the box plot.
First, we need to order the data set in increasing order:
10, 15, 20, 25, 30, 35, 40, 45, 50, 55
Next, we need to find the median (Q2) of the data set. Since we have an even number of data points, we take the average of the two middle values:
Q2 = (25 + 30) / 2 = 27.5
This value represents the median of the data set.
To find Q1 and Q3, we divide the data set into two halves:
10, 15, 20, 25, 30 | 35, 40, 45, 50, 55
Q1 is the median of the lower half:
Q1 = (15 + 20) / 2 = 17.5
Q3 is the median of the upper half:
Q3 = (45 + 50) / 2 = 47.5
We can now use this information to construct the box plot:
| -------
| /
| -------
| /
|-------
| 10 20 30 40 50
Q1 Q2 Q3
The box represents the middle 50% of the data (from Q1 to Q3), while the whiskers represent the minimum and maximum values that are not outliers.
Since we want to find the paint time for a student who is slower than 75% of the other students, we need to look at the upper quartile (Q3) of the data set. 75% of the data is contained between Q1 and Q3, so a student who is slower than 75% of the other students would have a paint time greater than Q3.
Therefore, the answer is 46 minutes, which is greater than Q3 (47.5 minutes).
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26% of all college students major in STEM (Science, Technology, Engineering, and Math). If 39 college students are randomly selected, find the probability that exactly 12 of them major in STEM. Round to 4 decimal places.
The probability of exactly 12 from 39 college students majoring in STEM is \(0.1776\)
What is the probability of a specific number of STEM majors?To find the probability of exactly 12 out of 39 college students majoring in STEM, we can use the binomial probability formula.
The formula is P(X=k) = (n choose k) * p^k * (1-p)^(n-k).
Data;
n = 39, k = 12, p = 0.26, and (n choose k) = 39 choose 12 = 3,720.
Plugging in the values:
P(X=12) = 3,720 * 0.26^12 * 0.74^27
P(X=12) ≈ 0.1776
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There are 30 giraffe and 6 penguin at the zoo. Which tatement correctly compare the two quantitie?
To compare the two quantities, divide the number of giraffes by the number of penguins There are 5 times as many giraffes as penguins at the zoo.
To compare the two quantities, you need to divide the number of giraffes by the number of penguins.
30 giraffes / 6 penguins = 5
This means that there are 5 times as many giraffes as penguins at the zoo.
There are 5 times as many giraffes as penguins at the zoo. To compare the two quantities, divide the number of giraffes by the number of penguins (30/6 = 5). This means that there are 5 times more giraffes than penguins at the zoo.
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Enter the ratio as a fraction in lowest terms
15 minutes to 50 minutes
Answer:
3 minutes to 10 minutes
Step-by-step explanation:
15 : 50. Both can be divided by 5
3 : 10
A bolt manufacturer is very concerned about the consistency with which his machines produce bolts. The bolts should be 0.2 centimeters in diameter. The variance of the bolts should be 0.025. A random sample of 15 bolts has an average diameter of 0.21 cm with a standard deviation of 0.1587. Can the manufacturer conclude that the bolts vary by more than the required variance at α=0.01 level? Step 1 of 5: State the hypotheses in terms of the standard deviation. Round the standard deviation to four decimal places when necessary. A bolt manufacturer is very concerned about the consistency with which his machines produce bolts. The bolts should be 0.2 centimeters in diameter. The variance of the bolts should be 0.025. A random sample of 15 bolts has an average diameter of 0.21 cm with a standard deviation of 0.1587. Can the manufacturer conclude that the bolts vary by more than the required variance at α=0.01 level? Step 2 of 5: Determine the critical value(s) of the test statistic. If the test is twotailed, separate the values with a comma. Round your answer to three decimal places. A bolt manufacturer is very concerned about the consistency with which his machines produce boits. The bolts should be 0.2 centimeters in diameter. The variance of the boits should be 0.025. A random sample of 15 bolts has an average diameter of 0.21 cm with a standard deviation of 0.1587. Can the manufacturer conclude that the bolts vary by more than the required variance at α=0.01 level?
To determine if the bolts vary by more than the required variance, we can conduct a hypothesis test. The null hypothesis (H₀) states that the variance of the bolts is equal to or less than the required variance (σ² ≤ 0.025), while the alternative hypothesis (H₁) states that the variance is greater than the required variance (σ² > 0.025).
Next, we need to determine the critical value(s) of the test statistic. Since we are testing for variance, we will use the chi-square distribution. For a one-tailed test with α = 0.01 and 14 degrees of freedom (n-1), the critical value is 27.488.
Now, we can compare the test statistic to the critical value. The test statistic is calculated as (n-1) * s² / σ², where n is the sample size (15), s² is the sample variance (0.1587²), and σ² is the required variance (0.025).
If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the bolts vary by more than the required variance. Otherwise, we fail to reject the null hypothesis.
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To determine if the bolts vary by more than the required variance, we can conduct a hypothesis test. The null hypothesis (H₀) states that the variance of the bolts is equal to or less than the required variance (σ² ≤ 0.025), while the alternative hypothesis (H₁) states that the variance is greater than the required variance (σ² > 0.025).
Next, we need to determine the critical value(s) of the test statistic. Since we are testing for variance, we will use the chi-square distribution. For a one-tailed test with α = 0.01 and 14 degrees of freedom (n-1), the critical value is 27.488.
Now, we can compare the test statistic to the critical value. The test statistic is calculated as (n-1) * s² / σ², where n is the sample size (15), s² is the sample variance (0.1587²), and σ² is the required variance (0.025).
If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the bolts vary by more than the required variance. Otherwise, we fail to reject the null hypothesis.
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Write the quadratic equation whose roots are 3 and -5, and whose leading coefficient is 2 . (Use the letter x to represent the variable.)
The required quadratic equation is: \(2x^2 + 4x - 30\)
How to find quadratic equation?A second-order polynomial equation with just one variable, x, is referred to as a quadratic equation. with a ≠ 0 . The fundamental theorem of algebra guarantees that it has at least one solution since it is a second-order polynomial equation. The solution might be real or hard.
The quadratic equation with roots 3 and -5 and a leading coefficient of 2 can be written as:
\(2(x - 3)(x - (-5))\)
Simplifying, we get:
\(2(x - 3)(x + 5)\)
Expanding, we get:
\(2(x^2 + 5x - 3x - 15)\)
\(2(x^2 + 2x - 15)\)
So, the quadratic equation is:
\(2x^2 + 4x - 30\)
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Cherries are $2.00/ pound what is the constant of proportionality
Answer:
$2 price per pound
2 is the constant of proportionality
Step-by-step explanation:
Price of Cherries = $2 per pound
what is the constant of proportionality
If y = total cost of buying x pounds of Cherries at $2 per pound
The equation below represent the situation
y = $2 * x
y = 2x
The constant of proportionality is 2
That is, the $2 price per pound
Mia and her neighbor Lora use their garden hoses to fill the pool. Mia and lora can fill the pool in 16 hours, Lora fills the pool twice as fast as mia. How long would it take mia to fill the pool
Answer:
x = 5 1/3 hours
Step-by-step explanation:
Let
x = number of hours Mia fills the pool
y = number of hours Lora fills the pool
x + y = 16
Lora fills the pool twice as fast as mia.
y = 2x
Substitute y =2x into the equation
x + y = 16
x + 2x = 16
3x = 16
x = 16/3
x = 5 1/3 hours
x = number of hours Mia fills the pool =5 1/3 hours
which of the following is equivalent to the expression below when x >0?
Answer:
C
Step-by-step explanation:
kkgkckyxitxitzoyfoycyoc
which equation below has a proportional relationship
Answer:
Ummm where is the options ?????
Step-by-step explanation:
El denominador de una fracción es 3 unidades menor que su numerador, y la fracción es 2,1 unidades mayor que su recíproco. ¿Cuál es esta fracción si tanto su numerador como su denominador son números enteros?
The price of a share of stock started the day at $19. During the day it went down $13 up $1, and down $14 and up $4. What integer represents the price of a share at the end of the day.
Answer:
-3
Step-by-step explanation:
19-13=6+1=7-14=-7+4=-3
The integer represents the price of a share at the end of the day will be negative 3.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
The price of a share of stock started the day at $19. During the day it went down $13 up $1, down $14, and up $4.
Then the integer represents the price of a share at the end of the day will be
⇒ 19 - 13 + 1 - 14 + 4
⇒ -3
The integer represents the price of a share at the end of the day will be negative 3.
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14 = x over 3
What's the x factor?
Which region represents the solution to the given system of the equalities
The solution to the given system of inequalities is the region below the line y = (-1/3)x - 1 and to the right of the vertical line x = 3.
To determine the region that represents the solution to the given system of inequalities, we need to graph the individual inequalities and identify the overlapping region.
Let's start with the first inequality: x + 3y < -3. To graph this inequality, we can first rewrite it in slope-intercept form:
3y < -x - 3
Next, isolate y by dividing both sides of the inequality by 3:
y < (-1/3)x - 1
This inequality represents a line with a slope of -1/3 and a y-intercept of -1. We can plot this line on a coordinate plane.
Next, let's graph the second inequality: x > 3. This inequality represents a vertical line passing through x = 3.
Now, we need to determine the overlapping region between the two graphs. Since we have a strict inequality (less than) for the first inequality, the region below the line represents the solution set.
Combining both graphs, we find that the solution to the given system of inequalities is the region that lies below the line y = (-1/3)x - 1 and to the right of the vertical line x = 3.
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The question probable may be:
[x+3y_< -3
[ X_>3
Factorise the following 25x²-4y²
Answer:
(5x + 2y)(5x - 2y)
Step-by-step explanation:
This is the difference of two squares whose factorisation is
a² - b² = (a + b)(a - b)
25x² - 4y² =
= (5x)² - (2y)²
= (5x + 2y)(5x - 2y)
PLS HELP!! WILL GIVE BRAINLY!! ASAP PLS!!!!!
Answer:
The solutions are,
x=0 and x= 5
(I don't know if you have to write both of these or only one, sorry)
Step-by-step explanation:
\(x^2-3x+6=2x+6\\solving,\\x^2-3x-2x+6-6=0\\x^2-5x+0=0\\x^2-5x=0\\x(x-5)=0\\\\x=0, x-5=0\\x=0,x=5\)
So, the solutions are,
x=0 and x= 5
Adeel and shayan are given money in the ratio 4:5 if adeel has RS 1179 after the adjustment, how much did he have in the original share out
Answer:
$2652.75
Step-by-step explanation:
Let b represent the original amount shared out
The equation representing how much adeel received is
4/9 x b = RS 1179
To find b, divided both sides by 9/4
b = $2652.75
I NEED HELP PLEASE: If x and y are proportional, fill in the blank with a number in simplest form.
What is the equation of a line that contains the points (5, 0) and (5, −2)? (1 point)
Answer: \(x=5\)
Step-by-step explanation:
Because the \(x\) coordinate of both of the points is 5, the equation is \(x=5\).
y=-6/5x +4
y-= -1/5x -1
Answer: (5,-2)
Step-by-step explanation:
I'm assuming the equations are:
Y=-(6/5)x +4
y = -(1/5)x -1 [Note that I changed "y-" to just "y."]
We can solve this in one of two ways: Mathematically and Graphically.
Math:
y = -(1/5)x -1
6y = -(6/5)x -6
-(Y=-(6/5)x +4)
5y = -10
y = -2
y = -(1/5)x -1
-2 = -(1/5)x -1
-1 = -(1/5)x
5 = x
x = 5
The solution is (5,-2)
Graph:
See the attached graph. The lines intersect at (5,-2)
how many feet should be cut off to make a plank 5 7/8 feet long
Answer:
2 5/8
Step-by-step explanation:
5 7/8 + 2 5/8= 8 1/2
Answer:
3 4/8 or 3 1/2
Step-by-step explanation:
Find the lateral area of this square
based pyramid.
10
ft
10 ft
[ ? jft?
Answer:
200
Step-by-step explanation:
happy to help
The lateral area of square based pyramid is 200 square feet
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
The given square base pyramid has four faces of triangles and one square shape base
The lateral surface area of pyramid formula 4 × (1/2)bl,
b = side length of the base, and
l = slant height
Lateral surface area =2 bl
=2×10×10
=200 square feet
Hence, the lateral area of square based pyramid is 200 square feet
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Diego has two jobs. He works 3 hours at the library each day, making $8 per hour. In addition, he works at a coffee shop, making $7.50 per hour. At the coffee shop, he works more than 4 hours but less than 7 hours
each day Diego needs to make at least $70 daily to afford his living expenses.
Which of the following systems represents the constraints given in this scenario?
Let I represent the number of hours he works at the library
and c represent the number of hours he works at the coffee shop.
A: l = 3
4 < c < 7
8l + 7.50 ≥ 70
B: l = 3
4 ≤ c ≤ 7
8l + 7.50 ≥ 70
C: 1 = 3
4 ≤ c ≤ 7
7.50l + 8c ≤ 70
D: 1=3
4 < c < 7
7.50l + 8c ≥ 70
Answer:b
Step-by-step explanation:
Answer:B
Step-by-step explanation:
This diagram shows a pre-image △ABC, and its image, △A′′B′′C′′, after a series of transformations.
Select from the drop-down menus to correctly complete the statements.
ΔABC is translated by 4 units to the right to become ΔA'B'C'. Then ΔA'B'C' is reflected over the y-axis to become ΔA"B"C". Because the transformations are rigid transformations, the pre-image and image are congruent.
How to Interpret Series of Transformations?In transformations, there are different types such as translation, reflection, dilation e.t.c.
Now, the transformation from ΔABC to ΔA'B'C' is a translation by 4 units to the right because we see that the shape and dimensions are preserved and the coordinates change by the transformation rule;
(x, y) → ((x + 4), y)
The second transformation is simply a reflection over the x-axis as we see that all the y-values are negated.
Thus, the final transformation from ΔA'B'C' to ΔA"B"C" follows the transformation rule (x, y) → (x, -y)
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X =
ML =
M
N
J 6x + 2 K
25
4x - 2
P
H
L
Answer:
x = 5 , ML = 18
Step-by-step explanation:
the midsegment NP of the trapezoid is half the sum of the bases, that is
NP = \(\frac{JK+ML}{2}\)
25 = \(\frac{4x-2+6x+2}{2}\) ( multiply both sides by 2 to clear the fraction )
50 = 10x ( divide both sides by 10 )
5 = x
Then
ML = 4x - 2 = 4(5) - 2 = 20 - 2 = 18
Entrywise eigenvector analysis of random matrices with low expected rank (Abbe, Fan, Wang, Zhong).pdf
Recovering low-rank structures via eigenvector perturbation analysis is a common problem in statistical machine learning, such as in factor analysis, community detection, ranking, matrix completion, among others.
While a large variety of bounds are available for average errors between empirical and population statistics of eigenvectors, few results are tight for entrywise analyses, which are critical for a number of problems such as community detection.
This paper investigates entrywise behaviors of eigenvectors for a large class of random matrices whose expectations are low-rank, which helps settle the conjecture in Abbe et al. (2014b) that the spectral algorithm achieves exact recovery in the stochastic block model without any trimming or cleaning steps. The key is a first-order approximation of eigenvectors under the ℓ∞ norm:
\(u_{k }\)≈1/ λ (\(\frac{A u^*_{k}}{*k}\))
where {uk} and {u∗k} are eigenvectors of a random matrix A and its expectation EA, respectively. The fact that the approximation is both tight and linear in A facilitates sharp comparisons between uk and u∗k. In particular, it allows for comparing the signs of uk and u∗k even if ∥uk−u∗k∥∞ is large. The results are further extended to perturbations of eigenspaces, yielding new ℓ∞-type bounds for synchronization (Z2-spiked Wigner model) and noisy matrix completion.
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Data reduction can only be applied to rows (observations) but not to columns (variables) in a given dataset.True/False
False.
Data reduction techniques can be applied to both rows (observations) and columns (variables) in a given dataset. Data reduction techniques like Principal Component Analysis (PCA) and Factor Analysis are applied to variables in order to reduce the number of variables and extract relevant information from them. These techniques aim to identify underlying factors or components that explain the variance in the data and represent them in a lower-dimensional space. Similarly, techniques like clustering and outlier detection can be applied to observations in order to group similar observations together or identify outliers.
Therefore, data reduction can be applied to both rows and columns, depending on the analysis goals and data characteristics.
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HELP PLSSSSSSS algebra 1
Answer:
answer is x=-1/10 is the answer
HURRY TWO MINUTES PLEASE HELP
Answer:
(-1,-2)
Step-by-step explanation:
y≥-2x
y>|x+|^?
according to the graph only (-1,-1) are in the shaded area
Select all equations that are equivalent to
(6x + 2)
3
-=2(3x +14)
(Select all that apply.)
(6x + 2)
3
(6x + 2) = 2 (3x+14)
2x+3=2-(3x +14)
=-3x-12
6x + 2 = -9x-36
(6x + 2)
3
= -3x+16
Using Simplification , all the equations that are equivalent to (6x+2)/3 = 2 - (3x+14) are (6x+2)/3 = -3x - 12 and 6x + 2 = -9x - 36 , the correct option is (a) and (d) .
In the question ,
it is given that
the equation is (6x+2)/3 = 2 - (3x+14)
solving the brackets on the right side of the equation ,
(6x+2)/3 = 2 - 3x - 14
(6x+2)/3 = -3x - 12 ....option(a)
On Cross Multiplying , we get
6x + 2 = 3(-3x - 12)
6x + 2 = -9x - 36 ....option(d)
Therefore , all the equations that are equivalent to (6x+2)/3 = 2 - (3x+14) are (6x+2)/3 = -3x - 12 and 6x + 2 = -9x - 36 .
The given question is incomplete , the complete question is
Using Simplification , Select all equations that are equivalent to
(6x+2)/3 = 2 - (3x+14)
(a) (6x+2)/3 = -3x-12
(b) (6x+2) = 2 - (3x+14)
(c) 2x + 2/3 = 2 - (3x+14)
(d) 6x+2 = -9x-36
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