Answer:
The 95% confidence interval is [tex]84.83< \mu < 90.37[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 113[/tex]
The sample mean is [tex]\= x = 87.6[/tex]
The standard deviation is [tex]\sigma = 15[/tex]
Given that the confidence level is 95% then the level of significance is mathematically represented as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5\%[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table, the value is
[tex]Z_{\frac{ \alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically evaluated as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{ \sigma}{ \sqrt{n} }[/tex]
=> [tex]E = 1.96 * \frac{ 15}{ \sqrt{113} }[/tex]
=> [tex]E = 2.77[/tex]
The 95% confidence interval is mathematically represented as
[tex]\= x - E < \mu < \= x + E[/tex]
substituting values
[tex]87.6 - 2.77< \mu < 87.6 + 2.77[/tex]
[tex]84.83< \mu < 90.37[/tex]
The Venn diagram shows 3 type numbers odd even in prime
Carla drove her truck 414 miles on 18 gallons of gasoline. How many miles did she drive per gallon?
Answer:
23 miles per gallon
Step-by-step explanation:
414 miles = 18 gallons
=> 18/18 gallons = 414/18 miles
=> 1 gallon = 23 miles
So, she drove 23 miles per gallon.
if the sin 30 = 1/2, then which statement is true?
Answer:
cos 60° = 1/2 because the angles are complements.
Step-by-step explanation:
Two fraction have the same denominator, 8.the some of two fraction is 1/2.if one of the fraction is added to five times the order, the result is 2,find the number.
Answer:
1/8, 3/8
Step-by-step explanation:
Let x and y represent the two fractions. Then we are given ...
x + y = 1/2
x + 5y = 2
Subtracting the first equation from the second, we get ...
(x +5y) -(x +y) = (2) -(1/2)
4y = 3/2 . . . . . simplify
y = 3/8 . . . . . . divide by 4
x = 1/2 -3/8 = 1/8
The two numbers are 1/8 and 3/8.
Two faces of a six-sided die are painted red, two are painted blue, and two are painted yellow. The die is rolled three times, and the colors that appear face up on the first, second, and third rolls are recorded. (a) Find the probability of the event that exactly one of the colors that appears face up is red.
Answer:
12/27
Step-by-step explanation:
Step 1
We find all the total number of possible outcomes of rolling two faces of a six-sided die are painted red, two are painted blue, and two are painted yellow.
Where
R = Red
B = Blue
Y = Yellow
RRR, BBB, YYY, RBY, RYB, YBR, YRB, BRY, BYR, BBY, BBR, YYB, RRY, RRB, BYB, BRB, YRY, YBY, RYR, RBR,YRR, BRR, RBB, RYY, BYY,YBB, YYR
We have 27 Total outcomes for this 6 faced die
Step 2
The event that exactly one of the colors that appears face up is red.
RBY, RYB, YBR, YRB, RBB, RYY, BBR,
BRB, BRY, YRY, BYR, YYR
Total number of Possible outcomes where EXACTLY one of the colours that appears face up is red = 12
The probability of the event that exactly one of the colors that appears face up is red = Number of possible outcomes/ Total number of outcomes
= 12/27
Find the total amount in the compound interest account.
$10000 is compounded semiannually at a rate of 9% for 22 years.
(Round to the nearest cent.)
Answer:
$69,361.23
Step-by-step explanation:
[tex] A = P(1 + \dfrac{r}{n})^{nt} [/tex]
[tex] A = 10000(1 + \dfrac{0.09}{2})^{2 \times 22} [/tex]
[tex]A = 10000(1.045)^{44}[/tex]
[tex] A = 69361.23 [/tex]
Answer: $69,361.23
A paint machine dispenses dye into paint cans to create different shades of paint. The amount of dye dispensed into a can is known to have a normal distribution with a mean of 5 milliliters (ml) and a standard deviation of 0.4 ml. Answer the following questions based on this information. Find the dye amount that represents the 9th percentile of the distribution.
Answer:
4.464 ml
Step-by-step explanation:
Given that:
mean (μ) = 5 mm, standard deviation (σ) = 0.4 ml
The z score is a score in statistics used to determine by how many standard deviation the raw score is above or below the mean. If the z score is positive then the raw score is above the mean and if the z score is negative then the raw score is below the mean It is given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
From the normal distribution table, the 9th percentile (0.09) corresponds to a z score of -1.34
[tex]z=\frac{x-\mu}{\sigma}\\\\-1.34=\frac{x-5}{0.4}\\\\x-5=-0.536\\\\x=5-0.536\\\\x=4.464[/tex]
The dye amount that represents the 9th percentile of the distribution is 4.464 ml
Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. Find the probability that a given score is less than 1.99 and draw a sketch of the region.
Answer:
Step-by-step explanation:
To find this probability, we shall be using the z-score route
Mathematically ;
z-score = (x -mean)/SD
From the question, x = 1.99, mean = 0 and SD = 1
So z = (1.99-0)/1 = 1.99
So the probability we want to calculate is;
P(z<1.99)
This value can be obtained from the standard normal distribution table.
P(z < 1.99) = 0.9767
The sketch of the region is as shown as in the attachment.
Complete the table for the given rule.
Rule: y = 6x – 4
х. Y
1
3
10
Answer:
a y = 2
b.y = 14
c. y =56
Step-by-step explanation:
a .6 (1)- 4=2
y=2
b. 6 (3)- 4
=18-4
y=14
c. 6 (10) - 4
= 60 - 4 =56
What is the nearest 100 of 1730
Answer:
1700
Step-by-step explanation:
pls thnx and mark me brainliest
Compute the least-squares regression line for the given data set. Use a TI-84 calculator. Round final answers to four decimal places, as needed.
x 5 7 6 2 1
y 4 3 2 5 1
Regression line equation: ŷ = _______ + _______ x.
Answer:
Y = 2.843+ 0.037 X
Step-by-step explanation:
Let the equation of the straight line to be fitted to the data , be Y = a+b X where a and b are to be evaluated. The normal equations fro determining a and b are
∑Y = na +b ∑X
∑XY = a∑X + b∑X²
We now calculate ∑X, ∑Y , ∑X², and ∑XY
X Y XY X²
5 4 20 25
7 3 21 49
6 2 12 36
2 5 10 4
1 1 1 1
21 15 64 115
Thus the normal equation becomes
5a + 21b =15
21a +115b = 64
Solving these two equations simultaneously we get
105 a + 441b = 315
105a + 575b = 320
134b= 5
b= 0.037 , a= 2.843
Hence the equation for the required straight line is
Y = 2.843+ 0.037 X
average of 2721 2557 2999 2278 4339
Answer:
Step-by-step explanation:
So we know that the average of numbers is all of the numbers added up and divided by the total amount of numbers.
2721
+ 2557
-------------------
5278
.... AND SO ON.........
=14,894 is all of the number added together!!!
Then we count up the numbers= 5
14,894/5
=2978.8
I hope this helps!!!
A cylindrical grain silo, with a flat top, is 30 feet tall and has a radius of 12 feet. It is full to the top with shelled corn. If the density of shelled corn averages 45 pounds/cubic foot, what does the corn in the silo weigh to the nearest pound
Answer:
610805 pounds
Step-by-step explanation:
The volume of grain in the silo will be calculated as equal to the volume of the cylinder formed by the silo
Height of the silo [tex]l[/tex] = 30 ft
radius of the silo r = 12 ft
volume of a cylinder = [tex]\pi r^{2} l[/tex]
substituting, we have
V = 3.142 x [tex]12^{2}[/tex] x 30 = 13573.44 cubic feet
We know that density ρ = weight/volume
density of the grains in the silo = 45 pound/cubic feet
therefore,
weight of grains = density x volume
weight of grains = 45 x 13573.44 = 610804.8 ≅ 610805 pounds
Which expression is equal to (1+6i)−(7+3i) ?
Answer:
- 6+3iStep-by-step explanation:
[tex](1+6i)-(7+3i) ?\\Group\:the\:real\:part\:and\:the\:imaginary\\\:part\:of\:the\:complex\:number\\\left(a+bi\right)\pm \left(c+di\right)=\left(a\:\pm \:c\right)+\left(b\:\pm \:d\right)i\\=\left(1-7\right)+\left(6-3\right)i\\1-7=-6\\6-3=3\\=-6+3i[/tex]
Find the measure of A.
A. 50
B. 70
C. 100
D. 90
Answer:
D
Step-by-step explanation:
I don't know how to eliminate the wrong answers.
Two line segments which have one end at a diameter and the other end meeting at a common point, make a 90 degree angle.
A is made that way, so A is 90 degrees.
Answer:
Step-by-step explanation:
I believe it is 90
What is the measure of FEG?
A. 30 degrees
B. 40 degrees
C. 50 degrees
D. 70 degrees
Please include ALL work!! <3
Answer:
C. 50 degrees
Step-by-step explanation:
Because 6x + 5x = 110° and x = 10
5×10 = FEG 50°
A passenger train traveled 180 miles in the same amount of time it took a freight train to travel 120 miles. The rate of the freight train was 15 miles per hour slower than the rate of the passenger train. Find the rate of the passenger train.
Answer:
The passenger train is moving at 45 miles per hour
Step-by-step explanation:
Let the amount of time it took the two trains to travel the distance = t.
Since the two trains traveled the distance at the same time,
Rate of the passenger train =[tex]\frac{180}{t}[/tex]
Rate of the freight train = [tex]\frac{120}{t}[/tex]
Where t is in hours.
From the problem, we can see that the rate of the freight train was 15 miles per hour slower than the rate of the passenger train. Mathematically, we can represent this as
[tex]\frac{120}{t}= \frac{180}{t}-15[/tex]
from the above equation, we can now get our value for t as
[tex]\frac{120-180}{t}=-15\\\frac{-60}{t}=-15\\t=4 hours[/tex]
We have our time of travel for the two trains as 4 hours.
The rate of the passenger train can now be calculated by 180/4 = 45 miles per hour
A group of fitness club members lose a combined total of 28 kilograms in 1 week. There are approximately 2.2 pounds in 1 kilogram. Assuming the weight loss happened at a constant rate, about how many pounds did the group lose each day?
Answer:
8.8 pounds
Step-by-step explanation:
Given the following :
Combined weight loss which occurred within a week = 28 kg
Number of days in a week = 7 days
1 kilogram (kg) = 2.2 pounds
Combined weight loss in pounds that occurs within a week:
Weight loss in kg × 2.2
28kg * 2.2 = 61.6 pounds
Assume weight loss occurred at a constant rate :
Weight lost by the group per day :
(Total weight loss / number of days in a week)
(61.6 pounds / 7)
= 8.8 pounds daily
Answer:
88
Step-by-step explanation:
Found the answer and I am doing the quiz rn lel
Which of the following correlation values represents a perfect linear relationship between two quantitative
variables? Select all that apply.
A. 0
B. 9
c. -1
D. 1
E. .5
Answer:
C. -1
D. 1
Step-by-step explanation:
A perfect linear relationship is indicated by a correlation with a magnitude of 1. The sign of the correlation coefficient is the sign of the slope of the line describing the relationship. It may be positive or negative.
The appropriate choices are ...
C. -1
D. 1
Answer:
c=-1
d=1
Step-by-step explanation:
5. If W(-10, 4), X(-3,-1), and Y(-5, 11) classify AWXY by its sides. Show all work to justify your
answer.
Answer:
an isosceles right triangle
Step-by-step explanation:
The square of the length of a side can be found from the distance formula:
d^2 = (x2-x1)^2 +(y2-y1)^2
The square of the length of WX is ...
WX^2 = (-3-(-10))^2 +(-1-4)^2 = 49+25 = 74
The square of the length of XY is ...
XY^2 = (-5-(-3))^2 +(11-(-1))^2 = 4 +144 = 148
The square of the length of YW is ...
YW^2 = (-10-(-5))^2 +(4 -11)^2 = 25 +49 = 74
The sum of the squares of the short sides is equal to the square of the long side, so this is a right triangle. The squares of the short sides are equal, so this is an isosceles right triangle.
Compute each matrix sum or product if it is defined. If an expression is undefined. Explain why. Let A = (3 4 0 -4 -1 4), B = (8 1 -4 -5 2 -4), C = (1 -1 3 1) and D = (3 -2 4 5).
- 2A, B - 2A, AC, CD
Compute the matrix product -2A.
A. -2A =
B. The expression-2A is undefined because A is not a square matrix.
C. The expression-2A is undefined because matrices cannot be multiplied by numbers.
D. The expression 2A is undefined because matrices cannot have negative coefficients.
Answer:
-2A = (-6, -8, 0, 8, 2, -8)
B - 2A = (2, -7, -4, 3, 4, -12)
AC is undefined.
CD = (3, 2, 12, 5)
Step-by-step explanation:
Given the matrices:
A = (3 4 0 -4 -1 4)
B = (8 1 -4 -5 2 -4)
C = (1 -1 3 1)
D = (3 -2 4 5)
We are required to compute the following
-2A, B - 2A, AC, CD
For -2A:
-2(3 4 0 -4 -1 4)
= (-6, -8, 0, 8, 2, -8)
For B - 2A:
Because B - 2A = B + (-2A), we have:
(8 1 -4 -5 2 -4) + (-6, -8, 0, 8, 2, -8)
(2, -7, -4, 3, 4, -12)
For AC:
(3 4 0 -4 -1 4)(1 -1 3 1)
This is undefined.
For CD:
(1 -1 3 1)(3 -2 4 5)
= (3, 2, 12, 5)
the coefficient of 6x
Answer:
The coefficient is 6
Step-by-step explanation:
The coefficient is the number in front of the variable
The variable is x
The coefficient is 6
Answer:
6
Step-by-step explanation: The coefficient of this would be the real number that is in front of a variable that is not a variable like x, and that number is 6. So, the coefficient of 6x is 6.
Factor completely 6x - 18.
6(x + 3)
6(x-3)
6X (-18)
Prime
Answer:
6(x-3)
Step-by-step explanation:
the common number for 6 and 18 is 6 so if you extract that from the expression then it turns to 6(x-3) which cannot be factored further
Answer:
Option B: 6(x - 3)
Step-by-step explanation:
Simplify 6m^2-5m-3+3m+4+9m^2
Answer: 15m²-2m+1
Step-by-step explanation:
To simplify, you want to combine like terms.
15m²-2m+1
Answer:
[tex]\huge\boxed{15m^2-2m+1}[/tex]
Step-by-step explanation:
[tex]6m^2-5m-3+3m+4+9m^2\\\\\text{combine like terms}\\\\=(6m^2+9m^2)+(-5m+3m)+(-3+4)\\\\=(6+9)m^2+(-5+3)m+1\\\\=15m^2-2m+1[/tex]
Please answer quick!!! Find the range of the data set represented by this box plot.
80
76
40
56
Answer:
highest value (H)= 80
lowest value (L)= 40
range (R)=?
now using formula,
Range (R)=H-L
=80-40
=40
therefore range (R)=40
Find the missing term in the
geometric sequence.
13,[ ? ],208
Answer:
110.5
Step-by-step explanation:
208=13+(3-1)d
208=13+2d
-13. -13
195=2d
÷2. ÷2
97.5=d. (d means difference)
13(first term)+97.5=110.5
Answer: 676
Step-by-step explanation: r/13=208/r
r²=2704
r=52
13x52=676
What is the value of x for the given equation?
4 – 2(x + 7) = 3(x + 5)
X=
Answer:
-5
Step-by-step explanation:
algebra pyramid please answer !! be the first to be marked as a brainliest .
Answer:
The first pyramid:
63x
39x 24x
23x 16x 8x
The second pyramid:
162x
82x 80x
4x 78x 2x
The third pyramid:
12a+2b
9a+b 3a+b
9a b 3a
The fourth pyramid:
-19a
-5a -14a
3a -8a -6a
Step-by-step explanation:
All that an alegbra pyramid is is adding the two terms below it.
So you can see how I added the terms that lied below each number, such as in number 1: I added 23x and 16x to get me 39x, and I added 16x and 8x to get me 24.
Hope this helped!
What are the slope and y-intercept of the equation 2x - 5y = -10?
Answer:
Step-by-step explanation:
y=2/5x+2
x= 5/2y-5
hopefully this works
Given the function, Calculate the following values:
Answer:
[tex]f(-2)=33\\f(-1)=12\\f(0)=1\\f(1)=0\\f(2)=9[/tex]
Step-by-step explanation:
[tex]f(x)=5x^{2} -6x+1\\f(-2)=5(-2)^{2} -6(-2)+1\\f(-2)=5(4)+12+1\\f(-2)=20+13\\f(-2)=33[/tex]
[tex]f(x)=5x^{2}-6x+1\\f(-1)=5(-1)^{2} -6(-1)+1\\f(-1)=5(1)+6+1\\f(-1)=5+7\\f(-1)=12[/tex]
[tex]f(x)=5x^{2}-6x+1\\f(0)=5(0)^{2}-6(0)+1\\f(0)=5(0)-0+1\\f(0)=0+1\\f(0)=1[/tex]
[tex]f(x)=5x^{2}-6x+1\\f(1)=5(1)^{2}-6(1)+1\\f(1)=5(1)-6+1\\f(1)=5-5\\f(1)=0[/tex]
[tex]f(x)=5x^{2}-6x+1\\f(2)=5(2)^{2}-6(2)+1\\f(2)=5(4)-12+1\\f(2)=20-11\\f(2)=9[/tex]
