Answer:
D = 0 , Dx = 4 , Dy = -6 , Dz = 2
Step-by-step explanation:
As per cramer's rule,
D = | 7 6 4 | = 0
| 3 3 3 |
| 4 4 4 |
Dx = | 10 6 4 | = 4
| 1 3 3 |
| 2 4 4 |
Dy = | 7 10 4 | = -6
| 3 1 3 |
| 4 2 4 |
Dz = | 7 6 10 | = 2
| 3 3 1 |
| 4 4 2 |
A shop has 4 types of sweets (chocolate, taffy, gummies, and cookies), 2 types of snacks (chips and crackers), and 3 types of drinks (sodas, juice, and sports drinks).
Mystery boxes are put together that randomly combine 1 sweet, 1 snack, and 1 drink.
What is the probability that a mystery box contains chocolate, chips, and juice?
Answer:
1/24
Step-by-step explanation:
1/4*1/2*1/3 = 1/24
Which of these shapes have rectangular cross sections when they are cut perpendicular to the base? Select three options.
-rectangular prism
-triangular prism
-cylinder
-cone
-square pyramid
-triangular pyramid
Answer:
A, B, and E
Step-by-step explanation:
Answer:
abe
Step-by-step explanation:
Find the slope of the line on the graph.
Write your answer as a fraction or a whole
number, not a mixed number or decimal.
Answer:
1/2
Step-by-step explanation:
Find two points on the line
(2,0) and (4,1)
The slope is given by
m= (y2-y1)/(x2-x1)
=(1-0)/(4-2)
= 1/2
Please everyone help me!
Answer:g=0 is not the solution
Step-byd-step explanation:
-1 1/2 is a negative number and 0 is not negative
Answer:
g=0
Step-by-step explanation:
happy to help ya :)
A 12cmx2cm rectangle sits inside a circle with a radius of 8cm. What isnthe area of the shaded region of the circle
Answer:
The answer would 177.06 centimeters
Question 1 of 20 :
Select the best answer for the question.
1. Divide7/15 by 3/5
OA%
O B./25
O c. 75/21
O D.21/75
Answer:
7/9
Step-by-step explanation:
7/15 ÷ 3/5
Copy dot flip
7/15 * 5/3
7/3 * 5/15
7/3 * 1/3
7/9
In the circle above, P is the center,What is the value, in degrees, of θ?
Answer:
45°
Step-by-step explanation:
There is a propiety that says "The measure of the inscribed angle is half that of the arc that the two sides cut out of the circle."
So the central angle is 90, the inscribed angle will be 90/2=45°
The first digit in any number must be 1, 2, 3, 4, 5, 6, 7, 8, or 9 because we do not write numbers such as 15 as 015. While it is reasonable to think that for most real-life data each digit occurs with equal frequency so that each digit 1, 2, ..., 9 has probability 1/9 of being the first digit, this is not true. It is a surprising phenomenon that in many naturally occurring numbers and web-based data the first digit has a probability distribution known as Benford's law.
Benford's law, also called the first-digit law, states that in lists of numbers from many (but not all) real-life sources of data, the leading digit is distributed in a specific, non-uniform way.
Specifically, for d = 1, 2, 3, 4, 5, 6, 7, 8, 9, Benford's law states P(first digit is d) = log_10(1+(1/d)) . The distribution of the first digit according to Benford's law, calculated to 3 decimal places, is shown in the table below.
Benford's law
First Digit X 1 2 3 4 5 6 7 8 9
Probability .301 .176 .125 .097 .079 .067 .058 .051 .046
Benford's Law and the Equally Likely Model benford equally likely
The law is named after physicist Frank Benford, who stated it in 1938, although it had been previously stated by Simon Newcomb in 1881. A surprising variety of data from the natural sciences, social affairs, and business obeys Benford's law.
This result has been found to apply to a wide variety of data sets, including electricity bills, street addresses, stock prices, population numbers, death rates, lengths of rivers, physical and mathematical constants, and processes described by power laws (which are very common in nature).
Numbers that are assigned, such as social security numbers and zip codes, or data with a fixed maximum, such as deductible contributions to individual retirement accounts, or randomly generated numbers, do not follow Benford's law.
The figure below shows how the distribution of the first digit of various naturally occurring and web-based data compares with Benford's law.
benford natural data web data
Figure information. Earthquakes: depth in km of 248,915 quakes, 1989-2009; source National Earthquake Information Center, United States Geological Survey. Minnesota lakes: size in acres of approx. 1100 lakes; source Wikipedia. Births: number of births in each county of the United States (approximately 3200), 2010; source: US Census Bureau. Diggs: total number of diggs for each of the top 1000 diggers at digg.com; source: socialblade.com.
Question 1:
(1a). What is the expected value of the first digit when the first digit follows Benford's law?
expected value (Use 3 decimal places).
(1b). What is the expected value of the first digit when the possible first digits are equally likely?
expected value (Use 3 decimal places).
(1c). What is the standard deviation of the first digit when the first digit follows Benford's Law?
Answer:
0.699
Step-by-step explanation:
got it on khan academy, should get brainliest thanks
Solve the system of equations by using substitution
Y=2x+3
Y=x+2
Since our first equation reads y = 2x + 3, we can substitute a 2x + 3
in for y in our second equation and then solve from there.
So we have 2x + 3 = x + 2.
Now subtract x from both sides to get x + 3 = 2.
Now subtract 3 from both sides to get x = -1.
To find y, plug -1 back into either equation.
I have chosen to plug it into the second.
So we have y = (-1) + 2 which simplifies to 1.
So our solution to this system is (-1, 1).
Fifty random shoppers at an electronics store have been interviewed and 35 of them intend to purchase a newly released smart phone. What probability distribution describes this situation and what are its mean and standard deviation of phone sales if we are concerned about 1071 shoppers that day
Answer:
We use the binomial distribution to describe this situation.
The mean number of phone sales is 749.7 with a standard deviation of 15.
Step-by-step explanation:
For each shopper, there are only two possible outcomes. Either they plan to purchase the newly released smart phone, or they do not. Each customer is independent of other customers. So we use the binomial distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Fifty random shoppers at an electronics store have been interviewed and 35 of them intend to purchase a newly released smart phone.
This means that [tex]p = \frac{35}{50} = 0.7[/tex]
What are its mean and standard deviation of phone sales if we are concerned about 1071 shoppers that day
1071 shoppers, so [tex]n = 1071[/tex]
Mean
[tex]E(X) = 1071*0.7 = 749.7[/tex]
Standard deviation
[tex]\sqrt{V(X)} = \sqrt{1071*0.7*0.3} = 15[/tex]
The mean number of phone sales is 749.7 with a standard deviation of 15.
Can anyone help me with my homework ?
2x+3y=20
7x+2y=53
Answer:
x=7, y=2
Step-by-step explanation:
Solve2x+3y=20for x:
2x+3y=20
2x+3y+−3y=20+−3y
2x=−3y+20
2x/2=-3y+20/2
x= -3/2 y
Compute 8P2 *
16
O 56
O 28
O
none of these are correct
Gordon Miller's job shop has four work areas, A, B, C, and D. Distances in feet between centers of the work areas are: A B C D A − 5 9 7 B − − 6 8 C − − − 11 D − − − − Workpieces moved per week between work areas are: A B C D A − 900 900 500 B − − 500 200 C − − − 600 D − − − − It costs Gordon $22 to move 1 work piece 1 foot.What is the weekly total material handling cost of the layout?
Answer: $600,600
Step-by-step explanation:
Total handling cost :
Workpiece moved * cost * distance
Work area A :
-, (5 × 22 × 900), (9 × 22 × 900), (7 × 22 × 500)
-, 99000, 178200, 77000
Work area B:
-, -, (6 × 22 × 500), (8 × 22 × 200)
-, -, 66000, 35200
Work area C:
-, -, -, (11 × 22 × 600)
-,-,-, 145200
Work area D:
-, -, -, -
Total weekly handling cost :
(99000 + 178200 + 77000 + 66000 + 35200 + 145200)
= $600,600
Kindly check attached picture for more explanation
if r is the radius of a circle and d is its diameter which of the following is an equivalent formula for the circumference c = 2 pie r
a C = pie d2
b C = pie rd
c C = pie d
d C = 2 pie d
Answer:
C
Step-by-step explanation:
C=2pier or pied
Answer:
a. C = 2πr
c. C= πd
both are correct
If \\(z_1=3+2i\\) and \\(z_2=4+3i\\) and are complex numbers, find \\(z_1z_2\\)
[tex]z_1z_2=(3+2i)(4+3i)=3\cdot4+2i\cdot4+3\cdot3i+2i\cdot3i[/tex]
[tex]z_1z_2=12+8i+9i+6i^2[/tex]
[tex]i^2=-1[/tex], so
[tex]z_1z_2=12+8i+9i-6=\boxed{6+17i}[/tex]
0.2x + (-0.9) + 1.7 = 9.6
0.2x + 0.8 = 9.6
X=
WHAT DOES x =
Answer:
x =44
Step-by-step explanation:
0.2x + (-0.9) + 1.7 = 9.6
Combine like terms
.2x +.8 = 9.6
Subtract .8 from each side
.2x +.8 -.8 = 9.6 -.8
.2x = 8.8
Divide each side by .2
.2x/.2 = 8.8/.2
x =44
At the beginning of year 1, Paolo invests $500 at an annual compound
interest rate of 4%. He makes no deposits to or withdrawals from the
account.
Which explicit formula can be used to find the account's balance at the
beginning of year 5? What is the balance?
Answer:
see below
Step-by-step explanation:
The way the problem is worded, we expect "n" to represent the year number we're at the beginning of. That is the initial balance is that when n=1, and the balance at the beginning of year 5 (after interest accrues for 4 years) is the value of obtained when n=5.
After compounding interest for 4 years, the balance will be ...
500·1.04^4 = 584.93
The matching answer choice is shown below.
Answer:
b
Step-by-step explanation:
A plane intersects the prism perpendicular to the base, intersecting opposite sides of the base. Which best describes the cross section?
Answer:
Step-by-step explanation:
For a rectangular prism, a plane intersecting this prism produces a two dimensional figure as its cross section and in this case the cross section is a rectangle.
For a triangular prism, a plane intersecting this prism produces a two dimensional figure as its cross section and in this case the cross section is a triangle.
New York State's "Quick Draw" lottery moves right along. Players choose between one and 10 numbers from the range one to 80; 20 winning numbers are displayed on a screen every four minutes. If you choose just one number, your probability of winning is 20/80, or 0.25. Lester plays one number fourteen times as he sits in a bar. What is the probability that all fourteen bets lose
Answer:
0.0178
Step-by-step explanation:
For computation of probability that all fourteen bets lose first we need to find out the Probability of losing in 1 bet is shown below:-
Probability of losing in 1 bet = 1 - P(winning)
= 1 - 0.25
= 0.75
With the help of probability of losing in 1 bet we can find out the Probability of losing in 8 bets which is here below:-
= Probability of losing in 1 bet ^ Number of loosing bets
= 0.75 ^ 14
= 0.017817948
or
= 0.0178
Therefore for computing the probability that all fourteen bets lose we simply applied the above formula.
If 9x+2y^2−3z^2=132 and 9y−2y^2+3z^2=867, then x+y =
Answer:
[tex]x + y = \frac{1000}{9}[/tex]
Step-by-step explanation:
Step 1: Identify the approach:
With this problem, the general solution is to try manipulate given data and transform data into a new form, in which, the desired value [tex](x + y)[/tex] is on the left side and all of other components which do not contain [tex]x[/tex] or [tex]y[/tex] are on the right side.
Step 2: Analyze:
[tex]9x + 2y^{2} - 3z^{2} = 132\\9y - 2y^{2} + 3z^{2} = 867[/tex]
Realize that in both equations, the [tex]2y^{2}[/tex] and [tex]3z^{2}[/tex] are in form of different signs. Then adding up corresponding sides of both equation can help eliminate these undesired components.
Step 3: Perform manipulation:
[tex]9x + 2y^{2} - 3z^{2} + 9y - 2y^{2} - 3z^{2} = 132 + 867[/tex]
Rearrange:
[tex](9x + 9y) + (2y^{2} - 2y^{2}) +(3z^{2} - 3z^{2}) = 132 + 867[/tex]
Simplify:
[tex]9(x + y) + 0 + 0 = 1000[/tex]
Simplify:
[tex]x + y = \frac{1000}{9}[/tex]
Hope this helps!
:)
Use technology to find the quadratic regression curve through the given points. HINT [See Example 5.] (Round all coefficients to four decimal places.) (1, 4), (3, 6), (4, 5), (5, 2)
y(x) =
Answer:
The coefficients for the quadratic regression curve are
a = (-2/3) = -0.6667
b = (11/3) = 3.6667
c = 1 = 1.0000
y(x) = -0.6667x² + 3.6667x + 1.0000
Step-by-step explanation:
Quadratic regression curve gives a general expression of
y = ax² + bx + c
And the points on the curve include
(1, 4), (3, 6), (4, 5), (5, 2)
Taking the points one at a time and substituting them into general quadratic curve expression
(1, 4), x = 1, y = 4
y = ax² + bx + c
4 = a + b + c (eqn 1)
(3, 6), x = 3, y = 6
6 = a(3²) + b(3) + c
6 = 9a + 3b + c (eqn 2)
(4, 5), x = 4, y = 5
5 = a(4²) + b(4) + c
5 = 16a + 4b + c (eqn 3)
Combining the 3 equations and solving simultaneously
4 = a + b + c
6 = 9a + 3b + c
5 = 16a + 4b + c
From eqn 1, c = 4 - a - b
Substituting this into eqn 2 and 3, we have
6 = 9a + 3b + 4 - a - b
2 = 8a + 2b (*)
5 = 16a + 4b + 4 - a - b
1 = 15a + 3b (**)
8a + 2b = 2
15a + 3b = 1
a = (-2/3), b = (11/3)
c = 4 - a - b
c = 4 - (-2/3) - (11/3)
c = 1
Hence, the coefficients for the quadratic regression curve are
a = (-2/3) = -0.6667
b = (11/3) = 3.6667
c = 1 = 1.0000
y(x) = -0.6667x² + 3.6667x + 1.0000
Hope this Helps!!!
What is the equation of the line that passes through (5, -2) and (-3, 4)?
Answer:
y = (-3/4)x + 7/4
Step-by-step explanation:
Step 1: Define general form of equation of line
An equation of a straight line on two-dimensional plane could be represented in form of: y = Mx + b, with M is slope and b is y-intercept
Step 2: Set up the system to solve for parameters of equation of line
(solve for M and b)
That equation passes 2 points, which are represented in form of (x, y), (5, -2) and (-3, 4).
Substitute these values of x and y into the original equation in step 1:
-2 = 5M + b
4 = -3M + b
Step 3: Solve the system of equations in step 2 for M and b
Subtract 1st equation from 2nd equation:
6 = -8M
=> M = -6/8 = -3/4
Substitute M back into 1st equation:
=> -2 = 5*(-3/4) + b
=> b = -2 + 15/4
=> b = 7/4
=> The equation of the line that passes through (5, -2) and (-3, 4):
y = (-3/4)x + 7/4
Hope this helps!
:)
Answer:
Y= -4/3(x-7/2)
Step-by-step explanation:
So first calculate the difference between them,
changes by 8 x units, and -6 y units.
Then substitute them into y/x to find gradient
-6/8 = -4/3
so now we have a part of the equation:
Y= -4/3(x-a)
substitute Y= -2 and x=5 (from (5,-2))
-2= -4/3(5-a)
-2= -20/3+4a/3
Multiply by 3 on both sides
-6= -20+4a
add 20 on both sides
14=4a
a=7/2
use this as the value of a
Y= -4/3(x-7/2)
2. The width of a rectangle is 12 inches less than its length. The perimeter of the rect-
angle is 56 inches. Find the length and width of the rectangle.
Answer:
[tex] P= 2*Lenght + 2*Width[/tex]
Since the perimeter is 56 inches we can solve for the lenght with this equation:
[tex] 56 in = 2*12in + 2*Length[/tex]
And solving for the length we got:
[tex] Length = \frac{56in -24 in}{2} 16 in[/tex]
So then the lenght = 16 inhes and the width of 12 inches
Step-by-step explanation:
For a rectangle of width 12 inches and lenght y inches we know that the perimeter is given by:
[tex] P= 2*Lenght + 2*Width[/tex]
Since the perimeter is 56 inches we can solve for the lenght with this equation:
[tex] 56 in = 2*12in + 2*Length[/tex]
And solving for the length we got:
[tex] Length = \frac{56in -24 in}{2} 16 in[/tex]
So then the lenght = 16 inhes and the width of 12 inches
A recent survey found that 86% of employees plan to devote at least some work time to follow games during the NCAA Men's Basketball Tournament. A random sample of 100 employees was selected. What is the probability that less than 80% of this sample will devote work time to follow games?
Answer:
4.18% probability that less than 80% of this sample will devote work time to follow games
Step-by-step explanation:
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this question, we have that:
[tex]p = 0.86, n = 100[/tex]
So
[tex]\mu = 0.86, s = \sqrt{\frac{0.86*0.14}{100}} = 0.0347[/tex]
What is the probability that less than 80% of this sample will devote work time to follow games?
This is the pvalue of Z when X = 0.8. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.8 - 0.86}{0.0347}[/tex]
[tex]Z = -1.73[/tex]
[tex]Z = -1.73[/tex] has a pvalue of 0.0418
4.18% probability that less than 80% of this sample will devote work time to follow games
2/5 of the members of a school band are 6th graders. What percent of
the students in the band are non-sixth graders?
Answer:
60%
Step-by-step explanation:
3/5 is 60%
Answer:
60%
Step-by-step explanation:
5/5 minus 2/5 is 3/5
5 divided by 3 is .6
in order to find out the percent move the decimal over to the right
What’s the correct answer for this?
Answer:
E:
Step-by-step explanation:
The equation of circles is
(x-a)²+(y-b)²=r²
Where
Center = (a,b) = (-6,-3) and r = 12
Now
The equation becomes
(x+6)²+(x+3)²=144
B
ABC is a right-angled triangle.
AC = 16 cm
Angle C = 90°
А.
size of angle B : size of angle A = 3:2
С
16 cm
Work out the length of AB.
Give your answer correct to 3 significant figures.
Answer:
19.8 cm
Step-by-step explanation:
Angle B is the complement of angle A, so we have this relation for the angles:
B/A = 3/2 = (90°-A)/A
2(90° -A) = 3A . . . . . cross multiply
180° = 5A . . . . . . . . . eliminate parentheses, add 2A
36° = A . . . . . . . . . . . divide by 5
The relations expressed by the mnemonic SOH CAH TOA remind you that ...
Cos = Adjacent/Hypotenuse
cos(A) = AC/AB
AB = AC/cos(A) = (16 cm)/cos(36°)
AB ≈ 19.8 cm
Which of the following is the slope of the line that passes through the points (-3,5) and (-3,-2)
Answer:
undefined.
Step-by-step explanation:
-2-5/-3-(-3)
-7/0
Undefined
Find the slope of the line on the graph.
Write your answer as a fraction or a whole
number, not a mixed number or decimal.
Answer:
-3/4
Step-by-step explanation:
Find two points on the line
(0,1) and (-4,4)
We can use the slope formula
m = (y2-y1)/(x2-x1)
= (4 -1)/(-4 -0)
= 3/-4
= -3/4
Assuming that $3u + 12v\neq0$, simplify $\dfrac{12u^3 + 48u^2v}{3u+12v}$.
Answer:
4u²
Step-by-step explanation:
[tex]\dfrac{12u^3 + 48u^2v}{3u+12v}=\dfrac{12u^2(u+4v)}{3(u+4v)}=\boxed{4u^2}[/tex]
Common factors cancel from numerator and denominator. The one factor that might make the expression undefined is given as non-zero, so no additional restrictions apply.