Answer:
a) Range = 1.39
b) the sample variance is 0.1597
c) the sample standard deviation is 0.3996
Step-by-step explanation:
Given the data in the question;
a) Find the range.
To determine the range, we simple subtract the smallest value from the largest value. i.e
Range = largest value - smallest value
from data set; our smallest is 0.53 while our largest value is 1.92
so
Range = 1.92 - 0.53 = 1.39
b) Find the sample variance.
To determine our variance, we use the following formula;
∑([tex]X_{i}[/tex] - [tex]x_{bar}[/tex])² / n - 1 = [ ∑[tex]X_{i}[/tex]²/n-1 ] - [ [tex]\frac{n}{n-1}[/tex]([tex]x_{bar}[/tex])²]
where [tex]x_{bar}[/tex] = ∑[tex]X_{i}[/tex]/n
n is sample size = 14 so lets calculate ∑[tex]X_{i}[/tex]
∑[tex]X_{i}[/tex] = 0.99 + 1.92 + 1.23 + 0.85 + 0.65 + 0.53 + 1.41 + 1.12 + 0.63 + 0.67 + 0.69 + 0.60 + 0.60 + 0.66
∑[tex]X_{i}[/tex] = 12.55
∑[tex]X_{i}[/tex]² = 0.99² + 1.92² + 1.23² + 0.85² + 0.65² + 0.53² + 1.41² + 1.12² + 0.63² + 0.67² + 0.69² + 0.60² + 0.60² + 0.66²
∑[tex]X_{i}[/tex]² = 13.3253
so
our [tex]x_{bar}[/tex] = ∑[tex]X_{i}[/tex]/n = 12.55 / 14 = 0.8964
so our Variance will be;
= [ ∑[tex]X_{i}[/tex]²/n-1 ] - [ [tex]\frac{n}{n-1}[/tex]([tex]x_{bar}[/tex])²]
= [ 13.3253 / 14-1 ] - [ [tex]\frac{14}{14-1}[/tex] (0.8964)²]
= 1.025 - 0.8653
= 0.1597
Therefore, the sample variance is 0.1597
c) Find the sample standard deviation.
we know that standard deviation is the square root of variance;
standard deviation = √Variance
standard deviation = √0.1597
standard deviation = 0.3996
Therefore, the sample standard deviation is 0.3996
help please please please please
Answer:
sorry it's blurry I can't fix it
A division problem divides a 3-digit number by a 1 digit number. The quotient is 307 r3. What could the division problem be?
Answer:
There is no solution to this problem.
Step-by-step explanation:
The 1 digit number cannot be 1, since there would be no remainder.
The 1 digit number cannot be 2, since the remainder could be 0 or 1.
The 1 digit number cannot be 3, since the remainder could be 0, 1, or 2.
So, the 1 digit number must be greater than 3. Let's start with 4. Since the quotient is 307 (remainder 3), 4 x 307 is already more than 3 digits.
Find the perimeter and total area of the composite shape shown below. All measurements are given in inches. Use pi equals 3.14 in any formulas used
Answer:
Perimeter = 65.12 in
Area = 292.48 in^2
which agrees with the second answer choice
Step-by-step explanation:
The perimeter is going to be the addition of the sides of the rectangle external to the composite figure ( 12 + 16 + 12 = 40) PLUS the length of half of the circumference or radius 8 inches (which is pi * radius = 3.14 * 8 = 25.12 in)
Then the total perimeter is:
Perimeter = 40 in + 25.12 in = 65.12 in
The are is going to be the area of the rectangle (12 * 16 = 192 square inches) PLUS the area of the semicircle of radius 8 in (pi *radius^2 /2 = 100.48 square inches).
Therefore the total area is:
Area = 192 + 100.48 = 292.48 in^2
Graph the inequality x < -1
Answer and Step-by-step explanation:
It is in the picture.
Since x is less than -1, everything will be shaded to the left of the line that is made. The line would also be dotted since x is only less than and NOT less than or equal to.
#teamtrees #WAP (Water And Plant)
The graph shows a linear relationship. Find the slope.
The slope is ?
Answer:
-2/5
Step-by-step explanation:
(0,1)
(5,-1)
(-1 - 1)/(5 - 0)
-2/5
YOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO PLEASE HELP
Find the x-intercept(s) and the coordinates of the vertex for the parabola y=x^2-6x-7. If there is more than one x-intercept, separate them with commas.
Answer:
x = -1, 7
( x + 1 ) , ( x - 7 )
plz follow me
Question 4 of 10
If a radius of a circle bisects a chord, then it is
to that chord
O A. perpendicular
B. adjacent
C. congruent
D. parallel
SUBMIT
Answer:
If a radius of a circle bisects a chord, then it is perpendicular to that chord.
So. A. perpendicular
Similarity - Item 33751 Select the two figures that are similar to each other. help pls
Answer:
Similar: First two shapes only
Step-by-step explanation:
Triangle Similarity Theorems
There are three triangle similarity theorems that specify under which conditions triangles are similar:
If two of the angles are congruent, the third angle is also congruent and the triangles are similar (AA theorem).
If the three sides are in the same proportion, the triangles are similar (SSS theorem).
If two sides are in the same proportion and the included angle is equal, the triangles are similar (SAS theorem).
The first pair of shapes are triangles that are both equilateral and therefore have all of its interior angles of 60°. The AAA theorem is valid and the triangles are similar.
The second pair of shapes are parallelograms. The lengths are in the proportion 6/4=1,5 and the widths are in proportion 3/2=1.5, thus the shapes are also similar.
The third pair of shapes are triangles whose interior acute angles are not congruent. These triangles are not similar
Given that WXYZ is a rectangle and ZY=2x + 3, and WX=x +4, then WX=
Answer:
Step-by-step explanation:
SOLUTION:
The opposite sides of a rectangle are parallel and congruent. So, ZY = WX.
2x + 3 = x + 4
x=1
Use the value of x to find WX. WX = 1 + 4 = 5.
Find the slope of a line perpendicular to y = -3/4x + 5. show your work.
Answer:
4/3
Step-by-step explanation:
All you have to do is find the reciprocal of the slope and switch to the opposite sign.
-3/4
flip
-4/3
switch
4/3
Sorry if this doesn't really make much sense. I don't know how else to explain this.
Use the quadratic formula to find the solutions for
y = 3x^3 + 8x - 1
Answer:
Solving the equation using quadratic formula we get [tex]\mathbf{x=0.119\:or\:x=-2.785}[/tex]
Step-by-step explanation:
We need to use the quadratic formula to find the solutions for
[tex]y = 3x^2 + 8x - 1[/tex]
(Note: quadratic formula is used when x^2 is in the equation. So considering 3x^2 instead of 3x^3)
The quadratic formula is: [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
From the given equation [tex]y = 3x^3 + 8x - 1[/tex] we have a =3, b=8 and c =-1
Putting values in the formula and finding solutions:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\x=\frac{-8\pm\sqrt{(8)^2-4(3)(-1)}}{2(3)}\\x=\frac{-8\pm\sqrt{64+12}}{6}\\x=\frac{-8\pm\sqrt{76}}{6}\\x=\frac{-8\pm8.71}{6}\\x=\frac{-8+8.71}{6}\:or\:x=\frac{-8-8.71}{6}\\x=0.119\:or\:x=-2.785[/tex]
So, Solving the equation using quadratic formula we get [tex]\mathbf{x=0.119\:or\:x=-2.785}[/tex]
Zachary used the calculations shown to find how much he would spend on 16 ounces of pistachios.
6 ounces of pistachios cost $7.50
5.5 is what percent of 6.875?
Answer:
80%
Step-by-step explanation:
please answer this correctly without making mistakes
Multiply. Write your answer using the smallest numbers possible.
6 pints 1 cup times 1,156
= pints cups
Answer:
7514 pints
Step-by-step explanation:
If it is american pints/cups(one pint is two cups)
1. Multiply
6 x 2 = 12
2. Add
12 + 1 = 13
3. Multiply
13 x 1156 = 15028
4. Divide.
15028 divided by 2 = 7514
If you get this right I'll make you the brainiest
39+19*989/2*3+55
Answer:28280.5?
Step-by-step explanation: was this right
Answer:
using order of operations you will want to simplify your equation using PEMDAS
39 + 19 * 989/2 * 3 + 55
39 + 9395.5 * 3 + 55
39 + 28186.5 + 55
28225.5 + 55 = 28280.5
Step-by-step explanation:
Hope this is right! Have a nice day
edit: you said its wrong so is this right ? if so u did not use order of operations correctly 57968.5
Mateo has 31/2 pounds of apples he uses 3/4 of a pound of apples for each batch of applesauce how many batches of applesauce can he make
Answer:
20 2/3
Step-by-step explanation:
Solve the equation and enter its solution set below. Enter the solutions in solution set notation separated by a comma and in order from smallest to largest. Enter fractional answers using / as in 2/3 for
\frac23
.
6x(x+2)=-25x+35
Answer:
5/6, 7
Step-by-step explanation:
Can anyone help me plz
Answer:
11
Step-by-step explanation:
BRAINLIEST PLZ
f(2) = (3x2) + 5
= 6+5 = 11
Add the two expressions.
32 – 4 and 2z + 5
Pls help quick!
Answer:
2z + 33
Step-by-step explanation:
Add like terms like below:
(32 - 4) + (2z + 5) = 28 + 2z + 5
Combine like terms again:
(28 + 5) + 2z = 33 + 2z or 2z + 33
11. Twyla and Tony have a 30/5 balloon mortgage for $389,900 with a rate of 4.85%. How much will they pay in interest over the life of the loan? (3 points)
O $81,373.41
$92,263.82
O $107,536.50
O $121,390.73
Answer:
Explanation:
Twyla and Tony with a balloon mortgage of 30/5 will make constant payments over the space of 5 years and then complete the bulk balloon payment for 25 years remaining.
Given mortgage loan value of $389900
Interest rate of 4.85%
We are asked to calculate the interest over the life of the loan.
We will calculate interest by calculating constant payments over the period of 5 years before balloon payment is due and adding them together then subtracting the mortgage loan given $389900
Formula for constant payments :
A= P×r×r(1+r)^n/(1+r)^n-1
Where A= constant/monthly payments
r= interest rate on the mortgage loan
n= number of payments = 30×12= 360
P= mortgage loan given
A= $389900×0.0485×0.0485(1+0.0485)^360/(1+0.0485)^360-1
=$389900×0.0485×1231340.79/25388468.94
=$389900×0.0485×0.04850
A= $917.142
Payment for five years(with interest)= $917.142×60= $55028.52
Calculate balloon payment:
FV= PV(1+r)^n - P((1+r)^n-1/r)
Where FV= future value of balloon payment
PV= initial loan given
r= interest rate on loan
n= number of payments
P= monthly payments
Substitute:
FV= $389900(1+0.0485/12)^60-917.142((1+0.0485/12)^60-1/0.0485/12)
=$389900×1.2738-917.142(0.2738/0.004041)
=$389900×1.2738-917.142×67.756
= 496654.62-62141.87
FV = $434512.75
Therefore total payment made with interest over the life of the loan= balloon payment+ constant payments for five years= $434512.75+$55028.52
=
Solve this simultaneous equations: picture below
Answer:
x = p/11, y = 13p/11
Step-by-step explanation:
The value of x is p/11
The value of y is 13p/11
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 - 9 is an equation.
We have,
5x + 3y = 4p _____(1)
y = 2x + p ____(2)
Substituting (2) in (1) we get,
5x + 3(2x + p) = 4p
5x + 6x + 3p = 4p
11x = p
x = p/11
Now,
y = 2x + p
y = 2(p/11) + p
y = 2p/11 + p
y = 13p/11
Thus,
x is p/11
y is 13p/11
Learn more about equations here:
https://brainly.com/question/17194269
#SPJ2
A water pipe is 4t beneath the surface of the road. What is the elevation of the pipe, in feet, expressed as a decimal?
0 -4.583 ft
0 -4.583 ft
0 -4.583 ft
O -4.583 ft
what are Latitude lines
Answer:
The latitude of a place is its distance north or south of the equator.
Researchers interviewed street prostitutes in Canada and the United States. The mean age of the 100 Canadian prostitutes upon entering prostitution was 19 with a standard deviation of seven. The mean age of the 130 United States prostitutes upon entering prostitution was 21 with a standard deviation of eight. Is the mean age of entering prostitution in Canada lower than the mean age in the United States
Answer:
Step-by-step explanation:
The null and the alternative hypothesis can be computed as:
[tex]H_o: \mu_{c} \ge \mu_{us}[/tex]
[tex]H_a: \mu_{c} < \mu_{us}[/tex]
The t- student test statistics can be computed as:
[tex]t = \dfrac{ x_c - x_{us} }{\sqrt { \dfrac{\sigma_c^2}{n_c} + \dfrac{\sigma_{us} ^2}{n_{us}} } }[/tex]
[tex]t = \dfrac{ 19 - 21 }{\sqrt { \dfrac{7^2}{100} + \dfrac{8^2}{130} } }[/tex]
t = -2.017
degree of freedom = (n₁-1)+(n₂-1)
= (100-1) + (130-1)
= 228
At t = -2.017 and 228 df
P-value = -0.224
Decision rule: Not to reject the null hypothesis if the p-value is greater than ∝(0.01)
Conclusion: We reject the null hypothesis since the p-value is less than ∝.
Thus, there is sufficient evidence to conclude that the mean age of entering prostitution in Canada is lower than that of the United states.
What’s the surface area (Blank) square units
Answer:
570
Step-by-step explanation:
The car vacuum cleaner at a gas station near Gina’s house costs $0.25 a minute to operate. Gina has $3.25 to spend on vacuuming her car. What is the maximum number of minutes Gina can use the vacuum cleaner?
Answer:
13 min
Step-by-step explanation:
3.25/0.25=13
Answer:
Gina has 13 minutes to use the vacuum cleaner.
Step-by-step explanation:
3.25/.25= 13 minutes
HELPPPPPPPPPPPPPPPPPPPPPP
Answer:
A. x= 3, y= -2
Step-by-step explanation:
[2] 2x= 4y+14
[1] 3y+5x=9
Solve equation [2] for the variable x
[2] 2x = 4y + 14
[2] x = 2y + 7
// Plug this in for variable x in equation [1]
[1] 5•(2y+7) + 3y = 9
[1] 13y = -26
// Solve equation [1] for the variable y
[1] 13y = - 26
[1] y = - 2
// By now we know this much :
x = 2y+7
y = -2
// Use the y value to solve for x
x = 2(-2)+7 = 3
good luck, I hope this helps!!!
Select all the equations that represent this situation. Diego has run 2/3 of a race's
distance. He has run 8 & 1/2 kilometers. How long is the whole race?
8 & 1/2 divided by 2/3 = ?
2/3 divided by 8 & 1/2 = ?
2/3 x ? = 8 & 1/2
8 & 1/2 x ? = 2/3
8 & 1/2 times 3/2 = ?
8 & 1/2 x 2/3 = ?
Step-by-step explanation:
Diego has run 2/3 of a race's
Let total distance of the race = y
He has run 8 & 1/2 kilometers.
This means 2/3 of y = 8 & 1/2 km
How long is the whole race?
2 / 3 x y = 8 & 1/2
The following equations can be used to calculate the distance of the whole race;
8 & 1/2 divided by 2/3 = ?
2/3 x ? = 8 & 1/2
8 & 1/2 times 3/2 = ?
which values are solutions to the inequality below? check all that apply √x < 5
A.) 1296
B.) 17
C.) 22
D.) 36
E.) -2
F.) 77
Answer:
B); C).
Step-by-step explanation:
1) if sqrt(x)<5, then x∈(0:25);
2) if x∈(0;25), then the values 17; 22 are correct
A bag contains 10 red marbles .15 yellow marbles, 5 Green marbles and 20 blue marbles. Five marbles are drawn from the bag. what is the approximate probability that exactly 2 of the five are blue?
Answer:
c
Step-by-step explanation: