This requires finding the number of small sweaters the company made last week
Number of small sweaters the company produced last week is 372
Total sweaters made = 1,612
Let
Small sweaters = 3x
Medium sweaters = x
Large sweaters = 3(3x) = 9x
Total = small + medium + large
1,612 = 3x + x + 9x
1612 = 13x
Divide by 13
x = 1612/13
Medium sweaters = x = 124
Small sweaters = 3x
= 3(124)
= 372
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Claims from Group A follow a normal distribution with mean 10,000 and standard deviation 1,000. Claims from Group B follow a normal distribution with mean 20,000 and standard deviation 2,000. All claim amounts are independent of the other claims. Fifty claims occur in each group. Find the probability the total of the 100 claims exceeds 1,530,000.
Answer:
0.0287 = 2.87% probability the total of the 100 claims exceeds 1,530,000.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
n instances of a normal variable:
For n instances of a normal variable, the mean is [tex]n\mu[/tex] and the standard deviation is [tex]s = \sigma\sqrt{n}[/tex]
Sum of normal variables:
When two normal variables are added, the mean is the sum of the means, while the standard deviation is the square root of the sum of the variances.
Group A follow a normal distribution with mean 10,000 and standard deviation 1,000. 50 claims of group A.
This means that:
[tex]\mu_A = 10000*50 = 500000[/tex]
[tex]s_A = 1000\sqrt{50} = 7071[/tex]
Group B follow a normal distribution with mean 20,000 and standard deviation 2,000. 50 claims of group B.
This means that:
[tex]\mu_B = 20000*50 = 1000000[/tex]
[tex]s_B = 2000\sqrt{50} = 14142[/tex]
Distribution of the total of the 100 claims:
[tex]\mu = \mu_A + \mu_B = 500000 + 1000000 = 1500000[/tex]
[tex]s = \sqrt{s_A^2+s_B^2} = \sqrt{7071^2+14142^2} = 15811[/tex]
Find the probability the total of the 100 claims exceeds 1,530,000.
This is 1 subtracted by the p-value of Z when X = 1530000. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{1530000 - 1500000}{15811}[/tex]
[tex]Z = 1.9[/tex]
[tex]Z = 1.9[/tex] has a p-value of 0.9713
1 - 0.9713 = 0.0287
0.0287 = 2.87% probability the total of the 100 claims exceeds 1,530,000.
Derive
Somebody could help me?
check that
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The edge roughness of slit paper products increases as knife blades wear. Only 2% of products slit with new blades have rough edges, 3% of products slit with blades of average sharpness exhibit roughness, and 4% of products slit with worn blades exhibit roughness. If 25% of the blades in the manufacturing are new, 60% are of average sharpness, and 15% are worn, what is the proportion of products that exhibit edge roughness
Answer:
The proportion of products that exhibit edge roughness is 0.029 = 2.9%.
Step-by-step explanation:
Proportion of products that exhibit edge roughness:
2% of 25%(new blades).
3% of 60%(average sharpness).
4% of 15%(worn). So
[tex]p = 0.02*0.25 + 0.03*0.6 + 0.04*0.15 = 0.029[/tex]
The proportion of products that exhibit edge roughness is 0.029 = 2.9%.
What are the solutions to the equation?
x3 – 6x2 – 9x + 54 = 0
Answer:
x = -3 or x = 3 or x = 6
Step-by-step explanation:
x3 – 6x2 – 9x + 54 = 0
There is no common factor to factor out. There are 4 terms. We try factoring by grouping. Factor a common factor out of the first two terms. Factor a common factor out of the last two terms.
x^2(x - 6) - 9(x - 6) = 0
x - 6 is a common factor, so we factor it out.
(x^2 - 9)(x - 6) = 0
x^2 - 9 is the difference of 2 squares, so we factor it.
(x + 3)(x - 3)(x - 6) = 0
x + 3 = 0 or x - 3 = 0 or x - 6 = 0
x = -3 or x = 3 or x = 6
Answer:
x=6 x=3 x=-3
Step-by-step explanation:
x^3 – 6x^2 – 9x + 54 = 0
Factor by grouping
x^3 – 6x^2 – 9x + 54 = 0
x^2(x-6) -9(x-6 ) =0
Factor out x-6
(x-6)(x^2 -9) =0
Notice x^2 -9 is the difference of squares
(x-6)(x-3)(x+3) = 0
Using the zero product property
x-6 =0 x-3 =0 x+3 =0
x=6 x=3 x=-3
What is
the solution to the system of equations graphed below?
Work out the length x. 14 cm 7 cm Х
Answer:
If you want the area of something with the sides 14cm and 7cm then it would be 98 cm.
Step-by-step explanation:
Area = length * width
Area = 14 cm * 7 cm
Area = 98 cm
Please Help!!! Whoever helps first and gets it correct gets Brainliest!
Answer:
Step-by-step explanation:
You have three data points. Equation of the line passing through (30,2), (45,2.75), and (60,3.50):
y = 0.5x + 0.5
It takes 0.5 hour to clean up.
The starting salaries of individuals with an MBA degree are normally distributed with a mean of $40,000 and a standard deviation of $5,000. What percentage of MBA's will have starting salaries of $34,000 to $46,000
Answer:
The correct answer is "76.98%".
Step-by-step explanation:
According to the question,
⇒ [tex]P(34000<x<46000) = P[\frac{34000-40000}{5000} <\frac{x- \mu}{\sigma} <\frac{46000-40000}{5000} ][/tex]
[tex]=P(-1.2<z<1.2)[/tex]
[tex]=P(z<1.2)-P(z<-1.2)[/tex]
[tex]=0.8849-0.1151[/tex]
[tex]=0.7698[/tex]
or,
[tex]=76.98[/tex]%
Perform the following series of rigid transformations on ∆ABC: Translate ∆ABC by moving it 5 units to the right and 2 units up. Draw the line y = -x, and reflect ∆A'B'C' across the line. Rotate ∆A''B''C'' counterclockwise about the origin by 270°.
Answer:
The answer is below
Step-by-step explanation:
Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.
If a point A(x, y) is translated a units right and b units up, the new point is at A'(x + a, y + b).
If a point A(x, y) is reflected across the line y = -x, the new point is at A'(-y, -x).
If a point A(x, y) is rotated counterclockwise by 270 degrees, the new point is at A'(y, -x).
Let us assume that triangle ABC has vertices at A(-6, -1), B(-3, -3) and C(-1, -2).
If it is moved 5 units to the right and 2 units up, the new point is at A'(-1, 1), B'(1, -1) and C'(3, 0). If it is reflected across the line y = -x, the vertices are at A"(-1, 1), B"(1, -1) and C"(0, -3). If it is then rotated counterclockwise about the origin by 270°, the new point is at A'"(-1, -1), B"'(1, 1), C"'(3, 0)
Muhammad lives twice as far from the school as Hita. Together, the live a total of 12 km
from the school. How far away drom the school does each of them live?
Answer:
Muhammad lives 8 km away from the school.
Hita lives 4 km away from the school.
Step-by-step explanation:
First of all, find a number that, when you double that number and add both numbers, you will get 12. That number is 4. So double 4 and get 8. Then add both to get 12.
Find the probability of 3 success for the binomial experiment with 7 trial and the success probability of 0.3. Then find the mean and standard deviation. Write the formula substitute
the values.
Answer:
[tex]P(x=3)=0.2269[/tex]
Mean=2.1
Standard deviation=1.21
Step-by-step explanation:
We are given that
n=7
Probability of success, p=0.3
q=1-p=1-0.3=0.7
We have to find the probability of 3 success for the binomial experiment and find the mean and standard deviation.
Binomial distribution formula
[tex]P(X=x)=nC_xp^{x}q^{n-x}[/tex]
Using the formula
[tex]P(x=3)=7C_3(0.3)^3(0.7)^{7-3}[/tex]
[tex]P(x=3)=7C_3(0.3)^3(0.7)^{4}[/tex]
[tex]P(x=3)=\frac{7!}{3!4!}(0.3)^3(0.7)^{4}[/tex]
[tex]P(x=3)=\frac{7\times 6\times 5\times 4!}{3\times 2\times 1\times 4!}(0.3)^{3}(0.7)^{4}[/tex]
Using the formula
[tex]nC_r=\frac{n!}{r!(n-r)!}[/tex]
[tex]P(x=3)=0.2269[/tex]
Now,
Mean, [tex]\mu=np=7\times 0.3=2.1[/tex]
Standard deviation, [tex]\sigma=\sqrt{np(1-p)}[/tex]
Standard deviation, [tex]\sigma=\sqrt{7\times 0.3\times 0.7}[/tex]
Standard deviation, [tex]\sigma=1.21[/tex]
michael has an average of 68% in his 3 papers but that is below the pass mark of 70%. what must be his least score in the fouth paper to enable him pass?
Answer:
His least score for him in the fourth paper has to be 76.
Step-by-step explanation:
Given that Michael has an average of 68% in his 3 papers but that is below the pass mark of 70%, to determine what must be his least score in the fouth paper to enable him pass the following calculation must be performed:
(70 x 4) - (68 x 3) = X
280 - 204 = X
76 = X
Therefore, his least score for him in the fourth paper has to be 76.
Samir estimates the value of Three-fifths times 16.1. Which estimate is reasonable?
3
9
12
15
Answer: 9
Step-by-step explanation:
[tex] \frac{3}{5} \times 16.1 = 9.66[/tex]
solve above question
HELP PLEASE I CANNOT FAIL PLEASE!!!!!!!
Which statement correctly compares the two functions?
A.
They have the same y-intercept and the same end behavior as x approaches ∞.
B.
They have the same x- and y-intercepts.
C.
They have the same x-intercept but different end behavior as x approaches ∞.
D.
They have different x- and y-intercepts but the same end behavior as x approaches ∞.
Answer:
B
Step-by-step explanation:
they have the same intercepts
Dodi bicycles 14mph with no wind. Against the wind, Dodi bikes 10mi in the same time it takes to bike 20mi with the wind. What is the speed of the wind?
Answer:
4.67 mph
Step-by-step explanation:
Speed with no wind = 14 mph
Let wind speed = w mph
Thus;
Speed with wind = 14 + w
Speed against the wind = 14 - w
Now, we are told that against the wind he bikes 10 miles.
Thus, from; time = distance/speed, we have;
Time = 10/(14 - w)
Also, we are told he biked 20 miles with the wind. Thus;
Time = 20/(14 + w)
We are told the times he used in both cases are the same.
Thus;
10/(14 - w) = 20/(14 + w)
Divide both sides by 10 to get;
1/(14 - w) = 2/(14 + w)
Cross multiply to get:
1(14 + w) = 2(14 - w)
14 + w = 28 - 2w
w + 2w = 28 - 14
3w = 14
w = 14/3
w = 4.67 mph
it’s question number 3 and i know the answer but i need someone to explain to me how to get the answer the answer is B. pls can hurry i need the explanation soon
Answer:
2+6=8
Step-by-step explanation:
Start at 2
Then since we are adding 6 move 6 units to the right
Work out giving ur answer as a mixed number
Answer:
6 11/12
Step-by-step explanation:
4 1/6 + 2 3/4
Get a common denominator of 12
4 1/6 *2/2 + 2 3/4 *3/3
4 2/12 + 2 9/12
6 11/12
find the length of side x
Answer:
x=8
Step-by-step explanation:
Need help due tomorrow
Answer:
[tex]Given:[/tex] Δ ABC ≈ ΔDEF
[tex]therefor:[/tex] A(ΔABC)/A(ΔDEF)=(BC)²/(EF)²
⇒ 34/A(ΔDEF)=9²/(13.5)²
⇒34/A(ΔDEF)=81/182.25
⇒A(ΔDEF)=34×182.25/81
⇒Area of ΔDEF=76.5 cm²
----------------------------------
Hope it helps...
Have a great day!!!
A. If x:y= 3:5, find = 4x + 5 : 6y -3
Answer:
17 : 27
Step-by-step explanation:
x=3
y=5
4(3)+5 : 6(5)-3
= 12+5 : 30-3
= 17 : 27
Please help …………………….
9514 1404 393
Answer:
(-3, 3)
Step-by-step explanation:
The blanks are trying to lead you through the process of finding the point of interest.
__
The horizontal distance from T to S is 9 . (or -9, if you prefer)
The ratio you're trying to divide the line into is the ratio that goes in this blank:
Multiply the horizontal distance by 2/3 . (9×2/3 = 6)
Move 6 units left from point T.
The vertical distance from T to S is 6 .
Multiply the vertical distance by 2/3 . (6×2/3 = 4)
Move 4 units up from point T.
__
Point T is (3, -1) so 6 left and 4 up is (3, -1) +(-6, 4) = (3-6, -1+4) = (-3, 3). The point that is 2/3 of the way from T to S is (-3, 3).
Evaluate the expression 3√64
Answer:
4
Step-by-step explanation:
We want the cubed root of 64
(64)^(1/3)
(4*4*4) ^ (1/3)
4
Unless this is 3 * sqrt(64)
then it would be
3 sqrt(8*8)
3 (8)
24
Solve 2x2 - 9x - 5 = 0 by factoring.
AS IN THE PICTURE...........
A two-dimensional vector has an x-component of 10.3~\text{meters}10.3 meters and a y-component of 4.30~\text{meters}4.30 meters. Calculate the angle (in degrees) that this two-dimensional vector makes with the positive x-axis.
9514 1404 393
Answer:
23°
Step-by-step explanation:
The angle a vector makes relative to the +x axis is found as ...
α = arctan(y/x) = arctan(4.30/10.3) ≈ 22.66°
The angle is about 23°.
__
Additional comment
This vector resides in the first quadrant, so no adjustment of the angle is needed. In other quadrants, 180° may need to be added or subtracted from the angle given by the arctan function to arrive at the correct value. (Some calculators and spreadsheets have an ATAN2(x, y) function that takes signs into account.)
Coordinate plane with quadrilaterals EFGH and E prime F prime G prime H prime at E 0 comma 1, F 1 comma 1, G 2 comma 0, H 0 comma 0, E prime negative 1 comma 2, F prime 1 comma 2, G prime 3 comma 0, and H prime negative 1 comma 0. F and H are connected by a segment, and F prime and H prime are also connected by a segment. Quadrilateral EFGH was dilated by a scale factor of 2 from the center (1, 0) to create E'F'G'H'. Which characteristic of dilations compares segment F'H' to segment FH
Answer:
[tex]|F'H'| = 2 * |FH|[/tex]
Step-by-step explanation:
Given
[tex]E = (0,1)[/tex] [tex]E' = (-1,2)[/tex]
[tex]F = (1,1)[/tex] [tex]F' = (1,2)[/tex]
[tex]G = (2,0)[/tex] [tex]G' =(3,0)[/tex]
[tex]H = (0,0)[/tex] [tex]H' = (-1,0)[/tex]
[tex](x,y) = (1,0)[/tex] -- center
[tex]k = 2[/tex] --- scale factor
See comment for proper format of question
Required
Compare FH to F'H'
From the question, we understand that the scale of dilation from EFGH to E'F'G'H is 2;
Irrespective of the center of dilation, the distance between corresponding segment will maintain the scale of dilation.
i.e.
[tex]|F'H'| = k * |FH|[/tex]
[tex]|F'H'| = 2 * |FH|[/tex]
To prove this;
Calculate distance of segments FH and F'H' using:
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
Given that:
[tex]F = (1,1)[/tex] [tex]F' = (1,2)[/tex]
[tex]H = (0,0)[/tex] [tex]H' = (-1,0)[/tex]
We have:
[tex]FH = \sqrt{(1- 0)^2 + (1- 0)^2}[/tex]
[tex]FH = \sqrt{(1)^2 + (1)^2}[/tex]
[tex]FH = \sqrt{1 + 1}[/tex]
[tex]FH = \sqrt{2}[/tex]
Similarly;
[tex]F'H' = \sqrt{(1 --1)^2 + (2 -0)^2}[/tex]
[tex]F'H' = \sqrt{(2)^2 + (2)^2}[/tex]
Distribute
[tex]F'H' = \sqrt{(2)^2(1 +1)}[/tex]
[tex]F'H' = \sqrt{(2)^2*2}[/tex]
Split
[tex]F'H' = \sqrt{(2)^2} *\sqrt{2}[/tex]
[tex]F'H' = 2 *\sqrt{2}[/tex]
[tex]F'H' = 2\sqrt{2}[/tex]
Recall that:
[tex]|F'H'| = 2 * |FH|[/tex]
So, we have:
[tex]2\sqrt 2 = 2 * \sqrt 2[/tex]
[tex]2\sqrt 2 = 2\sqrt 2[/tex] --- true
Hence, the dilation relationship between FH and F'H' is::
[tex]|F'H'| = 2 * |FH|[/tex]
Answer:NOTT !! A segment in the image has the same length as its corresponding segment in the pre-image.
Step-by-step explanation:
Find the length of AC
A. 377.19
B. 378.63
C. 2.89
D. 33.13
Answer:
AC = 377.19
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp /adj
tan 5 = 33/AC
AC tan 5 = 33
AC = 33/ tan 5
AC = 377.19
An experiment consists of tossing a pair of balanced, six-sided dice. (a) Use the combinatorial theorems to determine the number of sample points in the sample space S. 36 Correct: Your answer is correct. sample points (b) Find the probability that the sum of the numbers appearing on the dice is equal to 6. (Round your answer to four decimal places.)
Answer:
Sample space = 36
P(sum of 6) = 5/36
Step-by-step explanation:
Number of faces on a dice = 6
The sample space, for a toss of 2 dice ; (Number of faces)^number of dice
Sample space = 6^2 = 6*6 = 36
Sum of numbers appearing on the dice = 6
The sum of 6 from the roll of two dice has 5 different outcomes ; Hence, required outcome = 5
Total possible outcomes = sample space = 36
Probability, P = required outcome / Total possible outcomes
P = 5 / 36
Probabilities are used to determine the chances of events
The given parameters are:
[tex]n=6[/tex] --- the faces of a six-sided die
[tex]r = 2[/tex] -- the number of dice
(a) The number of sample points
This is calculated as:
[tex]Sample = n^r[/tex]
So, we have:
[tex]Sample = 6^2[/tex]
Evaluate the exponent
[tex]Sample = 36[/tex]
Hence, the number of sample points is 36
(b) The probability that the sum of 6
See attachment for the sample space of the sum of two dice.
From the sample space, there are 5 outcomes where the sum is 6.
So, the probability is:
[tex]Pr = \frac{5}{36}[/tex] --- where 36 represents the number of sample points
Divide 5 by 36
[tex]Pr = 0.1389[/tex]
Hence, the probability that the sum of the numbers appearing on the dice is equal to 6 is 0.1389
Read more about probabilities at:
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An appliance uses 120 W. If this appliance is on for 8 hours a day, how much CO2 will this produce in the month of April?
...
Calculate Energy Cost by Appliance
Multiply the device's wattage by the number of hours the appliance is used per day.Divide by 1000.Multiply by your kWh rate.hope it's helpful for you!!..pls give me brainlist !!....Which of the following could be the equation of the graph shown below?
Answer:
According to the proposed interrogate, as well as the graph provided, the correct answers to such are identified as B. Y = -2x + 5 and C. 2x + y = 4.
Step-by-step explanation:
To evaluate such, a comprehension of linear Cartesian data is required:
Slope = rise/run. If there is a negative rise, the direction of the line is proportional to the left-hand side as it exponentially grows or augments in units.
Y-intercept: The peculiar point in which the linear data observed intersects the y-axis.
X-intercept: The peculiar point in which the linear data observed intersects the x-axis.
Since this is a negative linear, all negative slopes apply.
The interrogate states, “Check all that apply.” Thus, there may be more than one correct answer, shall such be disseminated.
A. Cannot be the answer as the line should have been a horizontal line contained within quadrants I and II on the Cartesian Plane.
B. Contains a negative slope, thus is disclosed as a correct answer.
C. This configuration is denoted in “Standard Form” or “General Form”. To convert this to “Slope-Intercept Form” the following must be executed mathematically:
2x + y = 4
Y = -2x + 4 <== Slope-Intercept Form (Contains a negative slope, thus considered a correct answer.
D. Likewise, this configuration is denoted in “Standard Form” or “General Form”. To convert this to “Slope-Intercept Form” the following must be executed mathematically:
X - y = 9
-y = -x + 9
Y = x - 9 <== Slope-Intercept Form (Cannot be considered as the correct answer, given the positive slope configuration, thus is marked out).
Thus far, as evaluated, the correct answers to the proposed interrogate, as according to the linear data provided in the Cartesian Plane is acknowledged, and henceforth disseminated, as B. Y = -2x + 5 and C. 2x + y = 4.
*I hope this helps.
