the digit located in each of these positions for the number 7,890,432 would be the following:
a) 4
b) 7
c) 9
d) 3
e) 8
f) 0
Find the range, standard deviation and the variance of 7,9,14,16,18,22,23Round non-integer results to the nearest tenth.
To answer this question, we need to know that the asked statistics, namely, the standard deviation and the variance, in this question are for a sample, and the formula for this is given as follows:
1. Sample Variance
[tex](Sx)^2=\frac{1}{n-1}\sum ^n_{i\mathop=1}(x_i-\bar{x})^2[/tex]2. The standard deviation is the square root of the sample variance.
We have that:
• n = number of observations in the sample
,• x (bar) is the mean of the data
,• x_i are the values in the data
Now, we have that the data is: 7, 9, 14, 16, 18, 22, 23 (there are seven observations, n = 7).
Range3. The range of the values is the result of the subtraction, the difference, between the largest observation and the smallest observation in the data. Then, we have that the range is:
[tex]\text{Range}=23-7=16[/tex]Now, we can proceed to find the sample variance:
Sample VarianceWe need to find the mean of the data as follows:
[tex]\bar{x}=\frac{(7+9+14+16+18+22+23)_{}}{7}=\frac{109}{7}=15.5714285714[/tex]Now, we need to find the following sum:
[tex](7-\bar{x})^2+(9-\bar{x})^2+(14-\bar{x})^2+(16-\bar{x})^2+(18-\bar{x})^2+(22-\bar{x})^2+(23-\bar{x})[/tex]When calculating these statistics is good to round the value of the final result.
However, we were told to "round non-integer results to the nearest tenth". We will use the value of x (bar) (mean) as:
[tex]\bar{x}=15.5714285714[/tex]If we round this value to the nearest tenth, we will have a different result, but it is easier to work with:
[tex]\bar{x}=15.6[/tex]If we use mean = 109/7, the sum is:
[tex](7-\frac{109}{7})^2+(9-\frac{109}{7})^2+(14-\frac{109}{7})^2+(16-\frac{109}{7})^2+(18-\frac{109}{7})^2+(22-\frac{109}{7})^2+(23-\frac{109}{7})^2_{}[/tex]Then, the value is 221.714285714.
Now the value for the sample variance is:
[tex](Sx)^2=\frac{1}{n-1}\sum ^n_{i\mathop{=}1}(x_i-\bar{x})^2=\frac{1}{7-1}(221.714285714)=\frac{1}{6}(221.714285714)[/tex][tex]\frac{1}{6}(221.714285714)=36.9523809523[/tex]If we round the sample variance to the nearest tenth, we have that the value for the sample variance is 37.
Sample Standard DeviationWe know that the sample standard deviation is the square root of the sample variance. Then, we need to find the square root as follows:
[tex]SD_{\text{sample}}=\sqrt[]{36.9523809523}=6.07884700846[/tex]If we round the result to the nearest tenth, we have that the standard deviation is equal to 6.1.
In summary, we have that the range, the standard deviation, and the variance for given sample 7, 9, 14, 16, 18, 22, 23 are (rounded to the nearest tenth):
• Range = 16
,• Standard deviation = 6.1
,• Variance = 37
8. The temperature at 4pm was -8 degrees F. The temperature fell 5 degrees by 7pm. What was the temperature at 7pm? *
7 pm8. The temperature at 4 pm was -8 degrees F. The temperature fell 5 degrees by 7 pm. What was the temperature at 7 pm? *
___________________________
-8 º F - 5 = -13
_______________________________________
Answer
The temperature at 7pm is -13
___________
Unfortunately, I can help you with a question per session
he question is 13.5 x 12.1 using a regrouping strategy explain your answer and each step you take
Given expression ;
[tex]13.5\times12.1[/tex]First ignore the decimal place:
let 13.5 to 135
and 12.1 to 121
now multiply 135 by 121
Rewrite the product with 2 total decimal places.
thus, 16335 becomes 163.35
Answer: 163.35
What is the angle measure of the angle shown? Explainhow you know.
110º, because the arrow on the left is pointing to 110º. You have to see the angle that is shown the closest to the arrow, because the angle started on the right, on the 0º, so we use the first line.
If the arrow were to stat on the left, then we have to use the outermost value
on a bike trip Jeremy rode 60 miles in 4 hours. what was his average speed in miles per hour?
EXPLANATION
The average speed is obtained by dividing the miles that Jeremy did and the elapsed time.
Average Speed= 60miles / 4hours = 15 mph
The average speed was 15 mph
Megan Hughes deposits $3,500 in an account that pays simple interest. When she withdraws her money 6 months later, she receives $3,692.50. What rate of interest did the account pay? Round to the nearest whole percentOA 13% per yearOB 10% per yearOC 12% per yearOD 115 per year
We are given the following information
Deposited amount = $3,500
Final amount = $3,692.50
Number of years = 6/12 = 0.5
We are asked to find out what interest did the account pay?
Recall that the simple interest formula is given by
[tex]A=P(1+rt)[/tex]Let us substitute all the known values and solve for interest rate (r)
[tex]\begin{gathered} 3,692.50=3,500(1+0.5r) \\ \frac{3,692.50}{3,500}=1+0.5r \\ 1.055=1+0.5r \\ 0.5r=1.055-1 \\ 0.5r=0.055 \\ r=\frac{0.055}{0.5} \\ r=0.11\times100\% \\ r=11\% \end{gathered}[/tex]Therefore, the interest rate is 11% per year.
Chords WP and KZ intersect at point L in the circle shownWZx3.r - 22KL5PWhat is the length of KZ?7.591012
This is the intersecting chord theorem:
WL * PL = KL * ZL
x * 5 = 2 * (3x-2)
5x= 6x-4 .....(put like terms together)
6x-5x = 4
x=4
length KZ = KL +LZ = 2 +(3x-2)
KZ=2+ (3(4) -2)
KZ = 2+ (12-2)
KZ = 2 +10 =12
So option 4 is the correct choice.
select two fractions that are equivalent to 3/4
Let us simplify each answer to find the equivalent to 3/4
[tex]\frac{6}{12}=\frac{\frac{6}{6}}{\frac{12}{6}}=\frac{1}{2}[/tex][tex]\frac{9}{12}=\frac{\frac{9}{3}}{\frac{12}{3}}=\frac{3}{4}[/tex][tex]\frac{6}{16}=\frac{\frac{6}{2}}{\frac{16}{2}}=\frac{3}{8}[/tex][tex]\frac{6}{8}=\frac{\frac{6}{2}}{\frac{8}{2}}=\frac{3}{4}[/tex]The equivalents are B and D
$6.25$6.25$6.25$6.25+$6.25
We have to calculate 6.25 times 5:
[tex]1.25\cdot5=6.25[/tex]Answer: $6.25
Choose the correct response below and fill in the answer box to complete the choice
The function representing the percent of group H in the population is given to be:
[tex]H(x)=0.305x+9.5[/tex]The number of years after 1990 when the population percentage of group H will be 15.6% can be calculated as follows:
[tex]\begin{gathered} H(x)=15.6 \\ \therefore \\ 15.6=0.305x+9.5 \\ 0.305x=15.6-9.5=6.1 \\ x=\frac{6.1}{0.305} \\ x=20 \end{gathered}[/tex]Therefore, the year will be:
[tex]\Rightarrow1990+20=2010[/tex]What this means is that from 2010 and beyond, the population percentage will be 15.6% or more.
Hence, the population percentage will be at least 15.6% in the year 2010 and after.
help me to do this problem please. by factoring trinomials by Box method.
Here, we want to factorize the given trinomial using the box method
We follow the processes as highlighted below;
a) We multiply the leading coefficient and the term without a variable, i.e the constant term number
That will be 2 * (-12) = -24
b) Now, we find two numbers whose product will be equal to -24 and the sum will be the middle term which is +5
In this case, the numbers are -3 and 8
c) Now, we are going to place the following in the grids;
d) The next thing to do is to find the greatest common factor on each row and each columm and place these outside the box
We have this as follows;
e) The factors are the outside terms on the box and we have this as;
[tex]2z^2+5z-12\text{ = (}2z-3)(z+4)[/tex]Which tiles should be added to the model below to make zero?O6 negative tilesO6 positive tilesO3 negative tiles and 3 positive tilesO6 negative tiles and 6 positive tiles
If the tiles have the same value then to make 0 you need:
3 negative tiles and 3 positive tiles.
Explanation:
If one tile has the value of 1 and you pot:
- 1 -1 - 1 + 1+ 1 + 1
it will be zero.
10Determine whether each statement is true or false. If it is false, explain why.(a) Part AIf a quadrilateral is a kite, then it has two pairs of adjacent, congruent sides.в і
Step 1; Draw the diagram
Then the adjacent side of the kite are congruent side,
Hence part A is True
The diagonal of a Rhombus bisect each other at a right angle. hence the quadrilateral has its diagonals to be perpendicular to each other.
Hence Part B is True
Find the value of both variables. Answer must be in simplest radical form.
Statement Problem: Find the missing variables in the figure;
Solution:
Recall the trigonometry ratios;
[tex]\begin{gathered} \sin \theta=\frac{opposite}{hypotenuse} \\ \cos \theta=\frac{\text{adjacent}}{hypotenuse} \\ \tan \theta=\frac{opposite}{\text{adjacent}} \end{gathered}[/tex]In this case, the adjacent sides of the angle is given.
The hypotenuse side is y. Thus, we would apply the cosine, we have;
[tex]\begin{gathered} \cos 60^o=\frac{5\sqrt[]{7}}{y} \\ \frac{1}{2}=\frac{5\sqrt[]{7}}{y} \\ \text{cross}-m\text{ultiply, we have;} \\ y=2\times5\sqrt[]{7} \\ y=10\sqrt[]{7} \end{gathered}[/tex]Also, we would apply the pythagoras theorem to find the opposite side given as x.
The pythagoras theorem is;
[tex]\begin{gathered} h^2=o^2+a^2 \\ o^2=h^2-a^2 \\ a^2=h^2-o^2 \\ \text{Where h=hypotenuse, a=adjacent, o=opposite} \end{gathered}[/tex]Thus, the opposite side, x is;
[tex]\begin{gathered} x^2=(10\sqrt[]{7})^2-(5\sqrt[]{7})^2 \\ x^2=700-175 \\ x^2=525 \\ x=\sqrt[]{525} \\ x=5\sqrt[]{21} \end{gathered}[/tex]
Find the perimeter of the following figure.Parallelogram14 cmPerimeter =
Perimeter of the Parallelogram = a + b + a + b
a = 24 cm
b= 14 cm
Perimeter of the parallelogram = 24 + 14 + 24 + 14
= 76 cm
Select the correct answer.What is the factored formed of b^3 - 1,000?
Step 1: Concept/Formula
[tex]x^3-y^3=(x-y)(x^2+xy+y^2)[/tex]Step 2: Express each term as a cube of a number.
[tex]\begin{gathered} b^3\text{ - 1000} \\ =b^3-10^3 \\ \end{gathered}[/tex]Step 3: Factor in the result.
[tex]\begin{gathered} b^3-10^3=(b-10)(b^{2\text{ }}+10b+10^2) \\ =(b-10)(b^2\text{ + 10b + 100)} \end{gathered}[/tex]Final answer
[tex]\begin{gathered} (b-10)(b^2\text{ + 10b + 100)} \\ \text{Option B is the correct answer} \end{gathered}[/tex]What is the positive solution to 2x2 -4x -30.=0 ?
Answer:
[tex]x=1+\frac{\sqrt[]{40}}{4}[/tex]
Explanation: Given the folllowing equation, we need its positive solution or root:
[tex]2x^2-4x-30=0[/tex]Solution by Quadratic formula:
[tex]x=\frac{-B\pm\sqrt[]{B^6-4AC}}{2S}\rightarrow(1)[/tex]Where x can be positive and negative, but we are interested in the positive solution.
Constants A B C in (1) are as follows:
[tex]\begin{gathered} A=2 \\ B=-4 \\ C=-30 \end{gathered}[/tex]Plugging these values in (1) gives us:
[tex]x=\frac{-(-4)\pm\sqrt[]{(-4)^2-4(2)(-30)}}{2(2)}=\frac{4\pm\sqrt[]{16+(8)(30}}{4}[/tex]Firther simplification gives:
[tex]\begin{gathered} x=\frac{4\pm\sqrt[]{16+24}}{4}=\frac{4\pm\sqrt[]{40}}{4}\rightarrow positive\rightarrow x=\frac{4+\sqrt[]{40}}{4}=1+\frac{\sqrt[]{40}}{4} \\ \therefore\rightarrow \\ x=1+\frac{\sqrt[]{40}}{4} \end{gathered}[/tex]Necesito ayuda en mi trabajo de la escuela es bien importante y necesito ayuda pero no entiendo cómo puedo hacerlo
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the formula for calculating the area of a right triangle
[tex]\begin{gathered} Area=\frac{1}{2}ab\sin\theta \\ For\text{ a right angle,} \\ \theta=90 \\ \sin90=1 \\ \therefore Area\text{ of right triangle}=\frac{1}{2}ab \end{gathered}[/tex]STEP 2: Find the area of the bigger triangle
[tex]\frac{1}{2}\cdot7\cdot3=\frac{21}{2}=10.5cm^2[/tex]STEP 3: Find the area of the smaller triangle
[tex]\begin{gathered} a=6cm,b=2cm \\ Area=\frac{1}{2}\cdot6\cdot2=\frac{12}{2}=6cm^2 \end{gathered}[/tex]STEP 3: Find the difference in the areas
[tex]\begin{gathered} Area\text{ of big right triangle - Area of small triangle} \\ =10.5cm^2-6cm^2=4.5cm^2 \end{gathered}[/tex]Hence, the difference is 4.5cm²
find the area of a triangle if the base is 6 units and the height is 9 units.
can someone help me graph this equation and solve it?
3x + 8 <= 11 or 3x + 8 > 20
3x <= 3 or 3x > 12
x <= 1 or x > 4
The graph is a semi-line from negative infinity until 1 and another from 4 until positive infinity
Find the sum of 738 and659
2x+5 greater than or equal to -1
Solving an inequality
For inequalities separate variables and numerical terms
So then variables goes to left, and terms to right
2x + 5 ≥ -1
2x ≥ -1 -5
2x ≥ -6
and then
x≥ -6/2= -3
Is a plane formed by all numbers equal or bigger than -3
y=2/3×+8find the x and y intercept
x intercept is x-cutting point. Found by setting y equal to 0.
y intercept is y-cutting point. Found by setting x equal to 0.
X-intercept: (y = 0)
[tex]\begin{gathered} y=\frac{2}{3}x+8 \\ \frac{2}{3}x-8=0 \\ \frac{2}{3}x=8 \\ x=\frac{8}{\frac{2}{3}}=8\cdot\frac{3}{2}=12 \\ x=12 \end{gathered}[/tex]Y-intercept (x=0):
[tex]\begin{gathered} y=\frac{2}{3}x+8 \\ y=0-8 \\ y=-8 \end{gathered}[/tex]Write the following in interval notation: 2 > – 1 Interval notation solution: No solution
the interval notation is
[tex]\lbrack-1,+\infty)[/tex]Points B and C lie on line segment AD, with AB
Given:
Points B and C lie on the line segment AD, with AB
Required:
We need to find the value of BC.
Explanation:
Point B lies between A and C since AB < AC.
[tex]We\text{ know that AD=AB+BC+CD.}[/tex]Substitute AD=76, CD=24, and AB=BC in the equation.
[tex]76=BC+BC+24[/tex][tex]76=2BC+24[/tex]Subtract 24 from both sides of the equation.
[tex]76-24=2BC+24-24[/tex][tex]52=2BC[/tex]Divide both sides by 2.
[tex]\frac{52}{2}=\frac{2BC}{2}[/tex][tex]26=BC[/tex]Final answer:
[tex]BC=26[/tex]Translate the sentence into an inequality.Nine subtracted from the product of 6 and a number is at most - 19.Use the variable y for the unknown number.
Explanation:
9 subtracte from the product of 6 and x => 6x - 9
is at most -19 => the maximum the result can be is -19 => < or =
8 Find the value of x in this equation. 3/4(6x + 1) - 3x = 1/4(2x-1)Fractions btw
Find the value of x;
[tex]\begin{gathered} \frac{3}{4}(6x+1)-3x=\frac{1}{4}(2x-1) \\ \text{Expand the parenthesis and you now have;} \\ \frac{3(6x+1)}{4}-3x=\frac{(2x-1)}{4} \\ \frac{3(6x+1)}{4}-\frac{(2x-1)}{4}=3x \\ \frac{18x+3}{4}-\frac{2x-1}{4}=3x \\ \frac{18x-2x+3-1}{4}=3x \\ \frac{16x+2}{4}=3x \\ \text{Cross multiply and you have;} \\ 16x+2=3x\times4 \\ 16x+2=12x \\ \text{Collect like terms} \\ 16x-12x=-2 \\ 4x=-2 \\ \text{Divide both sides by 4} \\ x=\frac{-2}{4} \\ x=-\frac{1}{2} \end{gathered}[/tex]Hello! May I please have some guidance. I think I have it right but I'm not sure
STEP - BY - STEP EXPLANATION
What to find?
The number of faces a polyhedron with 5 vertices and 8 edges have.
Given:
[tex]V-E+F=2[/tex]Vertices (V) = 5
Edges (E)=8
Step 1
Substitute the values into the formula above.
[tex]\begin{gathered} 5-8+F=2 \\ \\ -3+F=2 \end{gathered}[/tex]Step 2
Add 3 to both-side of the equation.
[tex]\begin{gathered} F=2+3 \\ \\ =5 \end{gathered}[/tex]ANSWER
5
Solve: 9m + 12 = 15Solve: 9m + 12 = 15
Solution
Solve the equation
[tex]9m+12=15[/tex]Step 1: Subtract 12 from both side
[tex]\begin{gathered} 9m+12=15 \\ 9m+12-12=15-12 \\ 9m=3 \end{gathered}[/tex]Step 2: Divide both side by 9
[tex]\begin{gathered} 9m=3 \\ m=\frac{3}{9} \\ m=\frac{1}{3} \end{gathered}[/tex]Hence the solution for m = 1/3
Therefore the correct answer is Option B
Lena has scored 77 , 68 , 91 , 63 , and 68 on her previous five tests . What score does she need on her next test so that her average ( mean ) is 77 ?
Let us call x the score on Lena's next test, then we have
[tex]\frac{77+68+91+63+68+x}{6}=77[/tex]The above says that the average of six tests should be 77 and we just need to solve for x.
Simplifying the equation above gives
[tex]\frac{367+x}{6}=77[/tex]multiplying both sides by 6 gives
[tex]367+x=462[/tex]Finally, subtracting 367 from both sides gives
[tex]\begin{gathered} x=462-367 \\ \boxed{x=95.} \end{gathered}[/tex]Hence, Lena needs to score 95 in order that her average be 77.