Answers
Given the data:
36, 14, 18, 18, 34
Let's find the standard deviation of the sample distances.
To find the standard deviation, apply the formula:
[tex]S=\sum_{i\mathop{=}1}^n\sqrt{\frac{(x_i-x_{avg})^2}{n-1}}[/tex]Where:
n = 5
Let's first find the average/,mean:
[tex]\begin{gathered} avg=\frac{36+14+18+18+34}{5} \\ \\ avg=\frac{120}{5} \\ \\ avg=24 \end{gathered}[/tex]The mean of the sample is 24.
Now, to find the standard deviation, we have:
[tex]\begin{gathered} S=\sqrt{\frac{(36-24)^2+(14-24)^2+(18-24)^2+(18-24)^2+(34-24)^2}{5-1}} \\ \\ S=\sqrt{\frac{(12)^2+(-10)^2+(-6)^2+(-6)^2+(10)^2}{4}} \\ \\ S=\sqrt{\frac{144+100+36+36+100}{4}} \\ \\ S=\sqrt{\frac{416}{4}} \\ \\ S=\sqrt{104} \\ \\ S=10.20 \end{gathered}[/tex]Therefore, the standard deviation of the given sample distances is 10.20
ANSWER:
10.20
Related Questions
Kyle is a secretory. She earns $12.38 per hout. She worked 2 hours last week. What is her straight fine pay
Answers
Answer:
Her pay is;
[tex]\text{ \$24.7}6[/tex]Explanation:
Given that;
She earns $12.38 per hour
and She worked 2 hours last week.
Her pay can be calculated as;
[tex]\text{Total pay}=Rate\times time[/tex]Substituting the given values;
[tex]\begin{gathered} \text{Pay}=\text{ \$12.38}\times2 \\ \text{Pay}=\text{ \$24.76} \end{gathered}[/tex]Her pay is;
[tex]\text{ \$24.7}6[/tex]Simplify Remove all perfectsquares from inside the square root. v52
Answers
The square root we need to simplify is:
[tex]\sqrt[]{52}[/tex]We need to find an expression equivalent to 54 which includes a perfect square number (4, 16, 25, etc,...)
In this case, we note that:
[tex]52=4\times13[/tex]We substitute this in the square root:
[tex]\sqrt[]{4\times13}[/tex]And we calculate the square root of 4 which is 2, and that goes outside the square root:
[tex]2\sqrt[]{13}[/tex]we left the number 13 inside the square root because the square root of 13 is not exact.
Answer:
[tex]2\sqrt[]{13}[/tex]Questions 12-14: The box below shows some of the steps of multiplying twopolynomials. Use this picture for the next THREE questions.+8x26x46x2-8x+3x18x3-24x2-64x16+22x2
Answers
In the red block will be the product of 6x^2 times +8 so:
[tex]6x^2\cdot8=48x^2[/tex]In the blue block will be the product of -8x and x^2
[tex]x^2\cdot(-8x)=-8x^3[/tex]and in the yellow block will be the product of 2 and 3x so:
[tex]3x\cdot2=6x[/tex]Please help me help help me please help help me out
Answers
1) We can find the inverse function, by following some steps. So let's start with swapping the variables this way:
[tex]\begin{gathered} f(x)=\sqrt[3]{x-1}+4 \\ y=\sqrt[3]{x-1}+4 \end{gathered}[/tex]2) Now let's isolate that x variable getting rid of that cubic root:
[tex]\begin{gathered} x=\sqrt[3]{y-1}+4 \\ x-4=\sqrt[3]{y-1} \\ (x-4)^3=(\sqrt[3]{y-1})^3 \\ (x-4)^3=y-1 \\ y=(x-4)^3+1 \end{gathered}[/tex]Note that when we isolate the y on the left we had to adjust the sign dividing it by -1, to get y, not -y.
A 1. Which of the following is equivalent to 37g - 11g? a. (37 - 11)g b. (37 - 11) +g c.(37 - 11) + g2 d. (37 - 11)9
Answers
From 37g - 11g we can factorize g. It yields
[tex]37g-11g=(37-11)g[/tex]Hence, the aswer is a.
how would I simplify 3x^3-12x÷3x^3+6x^2-24x?
Answers
To simplify:
[tex]3x^3-12x\div3x^3+6x^2-24x[/tex]On division we get,
[tex]\begin{gathered} \frac{3x^3-12x}{3x^3+6x^2-24x}=\frac{3x(x^2-4)}{3x(x^2+2x-8)} \\ =\frac{(x^2-4)}{(x^2+2x-8)} \\ =\frac{(x+2)(x-2)}{(x-2)(x+4)_{}} \\ =\frac{x+2}{x+4} \end{gathered}[/tex]Hence, the simplest form is,
[tex]\frac{x+2}{x+4}[/tex]Find area under standard normal curve between -1.69 and 0.84
Answers
Required:
We need to find the area under the standard normal curve between -1.69 and 0.84
Explanation:
We need to find P(-1.69
P-value form z-table is
[tex]P(x<-1.69)=0.045514[/tex][tex]P(x<0.84)=0.79955[/tex]We know that
[tex]P(-1.69Substitute know values.[tex]P(-1.69Final answer:0.7540 is the area under the standard normal curve between -1.69 and 0.84.
According to the complex conjugates theorem, if -3+i is a root of a function what else is a root?
Answers
To have an understanding of the question, we need to understand what the complex conjugates theorem is.
In a simpler form, what the complex conjugate theorem is saying is that perhaps, we have a Polynomial N with a complex root x + yi, then the complex conjugate of x + yi which in this case is x -yi is also a root of the polynomial N
Applying this to the question at hand;
x = -3 and y = 1
We find the conjugate of the above by negating y( turning it to a negative number)
So its conjugate will be -3 -i
Summarily; According to the complex conjugates theorem, if -3+i is a root of a function , -3 - i is also a root of the function
Can you please help me
Answers
The area for a trapezoid can be found through the fromula
[tex]A=\frac{1}{2}(B+b)\cdot h[/tex]in which B represents the major base, b the minor base and h the height of the trapezoid.
According to this the area of the trapezoid is going to be:
[tex]\begin{gathered} A=\frac{1}{2}(37+22)\cdot23 \\ A=\frac{1}{2}(59)23 \\ A=\frac{1357}{2}cm^2 \\ A=678.5cm^2 \end{gathered}[/tex]Solve the proportions 28/35=8/r
Answers
ANSWER
r = 10
EXPLANATION
To solve for r first we have to put r in the numerator. To do that, we have to multiply both sides of the proportion by r:
[tex]\begin{gathered} \frac{28}{35}\cdot r=\frac{8}{r}\cdot r \\ \frac{28}{35}r=8 \end{gathered}[/tex]Now, we have to multiply both sides by 35:
[tex]\begin{gathered} \frac{28}{35}r\cdot35=8\cdot35 \\ 28r=280 \end{gathered}[/tex]And finally divide both sides by 28:
[tex]\begin{gathered} \frac{28r}{28}=\frac{280}{28} \\ r=10 \end{gathered}[/tex]12. The PRODUCT of six and a number increased by 2, translates to ? *6 +x+26x + 2O 6-8-2
Answers
Call the unknown number x.
The product of six and a number, would be written as 6x.
The product of six and a number increased by 2, would be written as 6x+2.
base: 4 in. area: 22 in
Answers
Area of a triangle
The area of a triangle of base length b and height h is:
[tex]A=\frac{b\cdot h}{2}[/tex]We are given the area as A=22 square inches and the base length b=4 inches. We are required to find the height.
Solving for h:
[tex]h=\frac{2\cdot A}{b}[/tex]Substituting:
[tex]h=\frac{2\cdot22in^2}{4in}=\frac{44in^2}{4in}=11in[/tex]The height is 11 inches
Solve one-fourth + two-sixths = ___.
Answers
Answer:
7/12
Step-by-step explanation:
Explanation
Step 1. Find the common denominator, which would be 12
Step 2. Multiply the numerators.. 1 x 3 = 3 and 2 x 2 = 4
Step 3. Add the numerators; 3+4=7
Therefore 7/12 (can’t be simplified)
AISD estimates that it will need 280000 in 8 years to replace the computers in the computer labs at their high schools. if AISD establishes a sinking fund by making fixed monthly payments in to an account paying 6% compounded monthly how much should each payment be
Answers
The initial amount of money that must be spend to replace the computers is P = $280,000. The period of time expected to replace all the computers is t = 8 years = 96 months. The interest rate is r = 6%.
Then, the monthly payment A is given by the formula:
[tex]\begin{gathered} A=P\frac{r(1+r)^t}{(1+r)^t-1} \\ A=280,000\cdot\frac{0.06\cdot(1+0.06)^{96}}{(1+0.06)^{96}-1} \\ A=\text{ \$16,862.74} \end{gathered}[/tex]How many different ID cards can be made if there are four digits can be used more than once? What if digits can be repeated?
Answers
ANSWERS
1) 5,040
2) 10,000
EXPLANATION
1) If we have 10 numbers (from 0 to 9), the ID cards have 4 of them and the digits do not repeat, we have 10 numbers to choose from for the first digit, 9 numbers for the second digit, 8 numbers for the third digit, and 7 numbers for the fourth digit. So,
[tex]10\cdot9\cdot8\cdot7=5,040[/tex]Hence, there are 5,040 different ID cards that can be made if no digit can be used more than once.
2) In this case, the numbers can be repeated, so for each of the four digits we have 10 options to choose from,
[tex]10\cdot10\cdot10\cdot10=10^4=10,000[/tex]Hence, there are 10,000 different ID cards that can be made if digits can be repeated.
Estimate a 15% tip on a dinner bill of $89.14 by first rounding the bill amount to the nearest ten dollars. 1
Answers
Let:
C = Cost of the dinner
T = Tip
r = Percentage of the tip
[tex]\begin{gathered} C=89 \\ r=0.15 \\ T=C\cdot r \\ T=89\cdot0.15 \\ T=13.35 \end{gathered}[/tex]Answer:
$13.35
Solve theses equations by elimination y= 3/2x -10 and -2x -4y =-8
Answers
SOLUTION
We want to solve the question with elimination method
[tex]\begin{gathered} y=\frac{3}{2}x-10.\text{ . . . . . . equation 1} \\ -2x-4y=-8\text{ . . . . . . . equation 2} \\ multiply\text{ equation 1 by 2, so as to remove the fraction } \\ 2\times y=(2\times\frac{3}{2}x)-(2\times10) \\ 2y=3x-20 \\ re-arranging\text{ we have } \\ -3x+2y=-20 \end{gathered}[/tex]So our paired equation becomes
[tex]\begin{gathered} -3x+2y=-20 \\ -2x-4y=-8 \end{gathered}[/tex]To eliminate y, multiply the upper equation by 4 and the lower by 2, we have
[tex]\begin{gathered} 4(-3x+2y=-20) \\ 2(-2x-4y=-8) \\ -12x+8y=-80 \\ -4x-8y=-16 \\ we\text{ have } \\ (-12x-4x)+(8y-8y)+(-80-16) \\ -16x+0=-96 \\ -16x=-96 \\ x=\frac{-96}{-16} \\ x=6 \end{gathered}[/tex]So put x for 6 into the second equation, we have
[tex]\begin{gathered} -2x-4y=-8 \\ -2(6)-4y=-8 \\ -12-4y=-8 \\ -4y=-8+12 \\ -4y=4 \\ y=\frac{4}{-4} \\ y=-1 \end{gathered}[/tex]Hence x = 6 and y = -1
The graph is shown below
Hence the point of intersection is (6, -1)
a financial advisor estimates that a company's profits follow the equation.
Answers
The equation that represent the profit is given by:
[tex]y=1000\cdot2^x[/tex]So in 3 years there are 36 months so the equation will be:
[tex]\begin{gathered} y=1000\cdot2^{36} \\ y=68^{},719,476,736,000 \end{gathered}[/tex]So is option A) it don't have sence because the profits are to great.
A rectangular garden covers 690 square meters. The length of the garden is 1 meter more than three times its width. Find the dimensions of the gardenThe length isand the width is01(Type whole numbers.)
Answers
Ok, so
We got the situation here below:
We know that the area of the garden is 690 m².
So, we got that the height (1+3x) multiplied by the width (x), should be equal to 690.
[tex]\begin{gathered} (1+3x)(x)=690 \\ x+3x^2=690 \end{gathered}[/tex]We have to solve:
[tex]3x^2+x-690=0[/tex]If we solve this quadratic equation, we obtain two solutions.
One of both solutions is negative, so we will not use it.
The second one is positive and equals to 15. So, x=15.
Now that we know that x=15, we replace:
x, (Width) is equal to 15 meters.
1+3x (Length), is equal to 46 meters.
Therefore, these are the dimensions of the garden.
Width: 15 meters
Lenght: 46 meters.
I need help with my math. I am working on linear equations. I don’t understand what I am doing and I am struggling on my homework. C/-9 + 6 = 14
Answers
Given:
[tex]\frac{C}{-9}+6=14[/tex]Solve this equation to find the value of C,
[tex]\begin{gathered} \frac{C}{-9}+6=14 \\ \text{Subtract 6 from both sides} \\ \frac{C}{-9}+6-6=14-6 \\ \frac{C}{-9}=8 \\ Multiply\text{ both sides by -9} \\ \frac{C}{-9}(-9)=8(-9) \\ C=-72 \end{gathered}[/tex]Answer: C= -72
After being discounted 10%, a weather radio sells for $62.96. Find the original price. (Round your answer to the nearest cent.)&Enter a number.$
Answers
Let the original price be x.
The discount is 10% of original price. So discount is,
[tex]\frac{10}{100}\cdot x=0.1x[/tex]The selling price after 10% discout is,
[tex]x-0.1x=0.9x[/tex]The selling price price is $62.96. So equation is,
[tex]\begin{gathered} 0.9x=62.96 \\ x=\frac{62.96}{0.9} \\ =69.955 \\ \approx69.96 \end{gathered}[/tex]So original price is 69.96.
Answer: 69.96
Larry can spend at most $2800 to renovate his home. One roll of wallpaper costs $35, and one can of paint costs $40. He needs at least 20 rolls of wallpaper and at least 30 cans of paint. Identify the graph that shows all possible combinations of wallpaper and paint that he can buy. Also, identify two possible combinations.
Answers
Answer:
[tex]D[/tex]Explanation:
Here, we want to identify the correct graph and the possible combinations
Let the number of rolls of wallpaper be x and the number of cans of paints be y
The total amount needed is at most $2,800
That means:
[tex]35x\text{ + 40y}\leq\text{ 2,800}[/tex]He needs at least 20 rolls of wallpaper:
[tex]x\text{ }\ge\text{ 20}[/tex]He also needs at least 30 cans of paint:
[tex]y\text{ }\ge\text{ 30}[/tex]Now, we have to plot the graph of the given inequalities on the same axes
We have the image of the plot as follows:
Now, let us select the correct answer choice
The correct answer choice lies within the small triangle (where the three inequalities overlap)
All the points within the small triangle are right answers
The correct answer choice here is thus D
Given: triangle ABC is an equilateral triangle. L, M, and N are the midpoints of AC, CB, and AB respectively. Prove: LMNB is a rhombus
Answers
Given:
∆ABC is an equilateral triangle, hence, all the three sides have the same length.
L, M, N are the midpoints of AC, CB, and AB. Hence, for instance, the distance between segment CM and MB are equal, by definition of midpoint.
Prove: LMNB is a rhombus.
Statement → Proof
1. ∆ABC is an equilateral triangle. → Given
2. Segment AB ≅ Segment AC ≅ Segment BC → Definition of an Equilateral Triangle
3. 1/2AB ≅ 1/2AC ≅ 1/2BC → Division Property of Equality
4. M and L are midpoints of BC and AC respectively. → Given
5. 1/2AB = Segment ML. → Midpoint Theorem
6. 1/2BC = Segment MB → Definition of Midpoint
7. Segment ML = Segment MB → Transitive Property of Equality using Statement 5 and 6
8. L and N are midpoints of AC and AB respectively. → Given
9. 1/2BC = Segment LN → Midpoint Theorem
10. 1/2AB = Segment BN → Definition of Midpoint
11. Segment LN = Segment BN → Transitive Property of Equality using Statement 9 and 10
12. Segment ML = Segment BN → Transitive Property of Equality using Statement 5 and 10
11. Segment MB = Segment LN → Transitive Property of Equality using Statement 6 and 9
13. Segment LN = Segment BN = Segment ML = Segment MB → Substitution Property of Equality using Statement 11 and 12
14. LMNB is a rhombus. → Definition of a rhombus.
One of the properties of a rhombus is that all 4 sides are equal in length.
If lines l, m, and n are parallel,AE is perpendicular to l, AC = 10, CD = 14, andAF = 6, what is the length of DG ? Give your answer as a decimal.
Answers
Using the properties of parallel line and similar triangle we calculate the length of the side DG to be 19.4 units .
In triangle ACF by using the properties of Pythagoras Theorem we can say that
AC² = FA² + CF²
Given:
AC = 10 , FA = 6
∴10² = 6² + CF²
or, CF = 8 units.
Now in triangles ΔACF and triangle ΔADG
CF is parallel to DG , therefore the two triangles are similar.
therefore we can say that using the properties of similar triangle we will use the ratio of the sides to find the given side.
AC/AD=CF/DG
or, 10/24 = 8 / DG
or, DG = 192 /10
or, DG = 19.2 units
Triangles that share the same form but differ in size are said to be similar. All equilateral triangles and squares with equal sides serve as examples of related items.
In other words, two similar triangles have similar sides that are proportionately equal and similar angles that are congruent.
Hence the length of the side is 19.2 units.
To learn more about parallel lines visit:
https://brainly.com/question/29042593
#SPJ9
7. Which digital construction tool would help youdetermine whether point C or point D is the midpoint ofsegment AB?A. Angle bisectorB. Perpendicular bisectorC. Perpendicular lineD. Parallel line
Answers
The digital construction tool that would help determine wherer point C or point D is the midpoint of segment AB would be a Perpendicular Bisector. [Option B]
Since a bisector would divide the segment in two identical parts and the perpendicular line would mark the exact point in which the segment is being divided.
Find the area of this figure.Triangle: Rectangle: Half circle: Total area:
Answers
To determine the area of the figure given we need to divide the composite figure into figures in which we know how to find the area. We divide the figure into a triangle, a rectangle and a circle.
The area of a triangle is given by:
[tex]A=\frac{1}{2}bh[/tex]where b is the base and h is the height. For the triangle shown the base is 6 and its height is 6, therefore:
[tex]A=\frac{1}{2}(6)(6)=\frac{36}{2}=18[/tex]The area of the rectangle is given by:
[tex]A=lw[/tex]where l is the length and w is the width. For this triangle the length is 9 and the width is 6 then we have:
[tex]A=(9)(6)=54[/tex]The area of a circle is given by:
[tex]A=\pi r^2[/tex]where r is the radius of the circle. The circle shown has a diameter of 6; we know that the radius is half the diameter, then the radius is 3. Plugging the radius, we have:
[tex]A=(3.14)(3)^2=28.26[/tex]Now we add the areas of each figure, therefore we have:
[tex]18+54+28.26=100.26[/tex]Determine if the expression -w is a polynomial or not. If it is a polynomial, state thetype and degree of the polynomial.The given expression representsJa polynomial. The polynomial is aand has a degree of
Answers
SOLUTION
We want to show if the expression -w is a polynomial or not
-w can also be written as
[tex]-1(w^1)[/tex]Since it has one term, and the power or exponent is not negative number or fraction, it is a polynomial.
Since it has one term, it is a monomial
So it is a polynomial called a monomial.
Since it has an exponent or power of 1
It is a polynomial of degree 1
T x 3/4 for t = 8/9
Answers
repalce t=8/9
[tex]\begin{gathered} \frac{8}{9}\times\frac{3}{4} \\ \\ \frac{24}{36}=\frac{2}{3} \end{gathered}[/tex]the result is 2/3
Please help:What is the mean of the data set?108, 305, 252, 113, 191Enter your answer in the box. __
Answers
Solution
- The formula for finding the mean of a dataset is
[tex]\begin{gathered} \bar{x}=\sum_{i=1}^n\frac{x_i}{n}=\frac{x_1+x_2+x_3+x__4+...+x_n}{n} \\ where, \\ x_i=\text{ The individual data points} \\ n=\text{ The number of data points in the data set} \\ \bar{x}=\text{ The mean} \end{gathered}[/tex]- The dataset given is:
108, 305, 252, 113, 191
- Thus, we can infer that:
[tex]\begin{gathered} x_1=108,x_2=305,x_3=252,x_4=113,x_5=191 \\ \\ \text{ The number of datapoints is }n=5 \end{gathered}[/tex]- Now, we can proceed to find the mean of the dataset as follows:
[tex]\begin{gathered} \bar{x}=\frac{108+305+252+113+191}{5} \\ \\ \therefore\bar{x}=193.8 \end{gathered}[/tex]Final Answer
The mean of the dataset is 193.8
A car rental company charges a $85 initial fee and $45 dollars a day to rent a car. Write an equation representing the cost, y, of renting the car for x days. (y= mx + b)
Answers
The given equation, y = mx + b is the slope intercept form of a linear equation where
m represents slope
b represents y intercept
The slope represents the rate of change of the values of y with respect to x. The values of y in this case represents the cost of renting the car while x represents the number of days for which the car is rented. Therefore,
slope, m = $45
The y intercept is the value of y when x is zero. We can see that the initial fee is $85. This means that even if the car is rented for zero days, the initial fee of $85 must be charged, Thus, y intercept is 85
Therefore, the equation representing the cost, y, of renting the car for x days is
y = 45x + 85