The mean and median of the given data set are 5.55 and 4.
What are the mean and median?A data set's mean (average) is calculated by adding all of the numbers in the set, then dividing by the total number of values in the set. When a data set is ranked from least to greatest, the median is the midpoint. Identifying the median The data points should be arranged from smallest to largest. The median is the middle data point in the list if the number of data points is odd. The median is the average of the two middle data points in the list if the number of data points is even.So, the data is:
[0, 0, 0, 0, 0, 1, 1, 2, 3, 4, 4, 4, 4, 4, 4, 5, 6, 6, 8, 55](A) Mean of data:
Sum of all terms/number of terms111/205.55(B) Median of data:
The data set has even terms.Average of two middle terms:4 + 4 / 28/24Therefore, the mean and median of the given data set are 5.55 and 4.
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A rectangle's base is 2 in shorter than five times its height. The rectangle's area is 115 in². Find this rectangle's dimensions.
The rectangle's height is
The rectangle's base is
Answer:
The rectangle's height is 5 in,The rectangle's base is 23 in.Step-by-step explanation:
Let the dimensions are b and h.
The area of rectangle is the product of two dimensions.
We have:
b = 5h - 2,bh = 115 in².Solve the equation by substitution:
h(5h - 2) = 1155h² - 2h = 1155h² - 2h - 115 = 05h² - 25h + 23h - 115 = 05h(h - 5) + 23(h - 5) = 0(h - 5)(5h + 23) = 0h - 5 = 0 and 5h + 23 = 0h = 5 and h = - 23/5The second root is discarded as negative.
The height is 5 in,The base is: 5*5 - 2 = 23 inAnswer:
Height = 5 in
Base = 23 in
Step-by-step explanation:
[tex]\boxed{\textsf{Area of a rectangle} = \sf Base \times Height}[/tex]
Let x be the height of the rectangle.
Given values:
Height = x inBase = (5x - 2) inArea = 115 in²Substitute the values into the formula for area and solve for x:
[tex]\begin{aligned}\sf Area & = \sf Base \times Height\\\\115&=x(5x-2)\\115&=5x^2-2x\\5x^2-2x-115&=0\\5x^2-25x+23x-115&=0\\5x(x-5)+23(x-5)&=0\\(5x+23)(x-5)&=0\\\\\implies 5x+23&=0 \implies x=-\dfrac{23}{5}\\\implies x-5&=0 \implies x=5\end{aligned}[/tex]
As length is positive, x = 5.
To find the rectangle's dimensions, substitute the found value of x into the expressions for the height and base:
[tex]\implies \sf Height=5\;in[/tex]
[tex]\begin{aligned}\implies \sf Base&=\sf 5(5)-2\\&=\sf 25-2\\&=\sf 23\;in\end{aligned}[/tex]
please help this is for my study guide thanks! (simplify)
One way of simplifying the given expression is by using the following definition:
[tex]k^{-1}=\frac{1}{k}[/tex]So, for the given expression, we have:
[tex]-3k^{-1}=-3\cdot\frac{1}{k}=-\frac{3}{k}[/tex]Therefore, a possible answer is:
[tex]-\frac{3}{k}[/tex]Let x equals negative 16 times pi over 3 periodPart A: Determine the reference angle of x. (4 points)Part B: Find the exact values of sin x, tan x, and sec x in simplest form. (6 points)
The reference angle of x is -60 degree. The exact values of sin x, tan x, and sec x is [tex]$\sin \left(-60^{\circ}\right)=-\frac{\sqrt{3}}{2}$[/tex], [tex]$\tan \left(-60^{\circ}\right)=-\sqrt{3}$[/tex], [tex]$\sec \left(-60^{\circ}\right)=2$[/tex]
[tex]x=-\frac{16 \times 180}{3}$$[/tex]
Multiply the numbers: [tex]$16 \times 180=2880$[/tex]
[tex]$x=-\frac{2880}{3}$[/tex]
Divide the numbers: [tex]$\frac{2880}{3}=960$[/tex]
x=-960
Or, x = 2 [tex]\times[/tex] 360 - 960
Follow the PEMDAS order of operations
Multiply and divide (left to right) 2 [tex]\times[/tex]360 : 720 =720-960
Add and subtract (left to right) 720-960: -240
x= -240
Reference angle =180-240
Reference angle= -60
Sin (-60 degree)= [tex]$\sin \left(-60^{\circ}\right)=-\frac{\sqrt{3}}{2}$[/tex]
[tex]$\tan \left(-60^{\circ}\right)=-\sqrt{3}$[/tex]
[tex]$\sec \left(-60^{\circ}\right)=2$[/tex]
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Write a recursive formula for an, the nthterm of the sequence 8, -2, -12, ....
We have the sequence: 8, -2, -12...
We can prove that this is an arithmetic sequence as there is a common difference d=-10 between consecutive terms.
Then, the recursive formula (the expression where the value of a term depends on the value of the previous term) can be written as:
[tex]a_n=a_{n-1}-10[/tex]Answer: the recursive formula is a1 = 8, a(n) = a(n-1) - 10
The sum of a number and 4 times it’s reciprocal is 13/3. Find the number(s).
Let the unknown number be "x"
We will write an algebraic equation from the word problem given. Then we will solve for "x".
Given,
Sum of number (x) and 4 times the reciprocal is 13/3
We can convert it into an algebraic equation:
[tex]x+(4\times\frac{1}{x})=\frac{13}{3}[/tex]Now, let's solve for the unknow, x,
[tex]\begin{gathered} x+(4\times\frac{1}{x})=\frac{13}{3} \\ x+\frac{4}{x}=\frac{13}{3} \\ \frac{x^2+4}{x}=\frac{13}{3} \\ 3(x^2+4)=13\times x \\ 3x^2+12=13x \\ 3x^2-13x+12=0 \\ (x-3)(x-\frac{4}{3})=0 \\ x=3 \\ x=\frac{4}{3} \end{gathered}[/tex]The numbers are
[tex]\begin{gathered} 3 \\ \text{and} \\ \frac{4}{3} \end{gathered}[/tex]Write the limit as a definite integral on the interval [a, b], where ci is any point in the ith subinterval.
We have the following integral in the discrete sum form:
[tex]\lim_{||\Delta||\to0}\sum_{i\mathop{=}1}^{\infty}(6c_i+3)\Delta x_i.[/tex]In the interval [-9, 6].
To convert to the integral form, we convert each element of the discrete sum form:
[tex]\begin{gathered} \lim_{||\Delta||\to0}\sum_{i\mathop{=}1}^{\infty}\rightarrow\int_{-9}^6 \\ 6c_i+3\rightarrow6x+3 \\ \Delta x_i\rightarrow dx \end{gathered}[/tex]Replacing these in the formula above, we get the integral form:
[tex]\int_{-9}^6(6x+3)\cdot dx.[/tex]AnswerThe probability that an individual is left-handed is 12%, In a randomly selected class of 30students, what is the probability of finding exactly 4 left-handed students?
Given that:
- The probability that an individual is left-handed is 12%.
- There are 30 students in the class.
You need to use this Binomial Distribution Formula, in order to find the probability of finding exactly 4 left-handed students :
[tex]P(x)=\frac{n!}{(n-x)!x!}p^x(1-p)^{n-x}[/tex]Where "n" is the number being sampled, "x" is the number of successes desired, and "p" is the probability of getting a success in one trial.
In this case:
[tex]\begin{gathered} n=30 \\ x=4 \\ p=\frac{12}{100}=0.12 \end{gathered}[/tex]Therefore, by substituting values into the formula and evaluating, you get:
[tex]P(x=4)=\frac{30!}{(30-4)!4!}(0.12)^4(1-0.12)^{30-4}[/tex][tex]P(x=4)\approx0.2047[/tex]Hence, the answer is:
[tex]P(x=4)\approx0.2047[/tex]use this figure for questions 1 through 4 1. are angles 1 and 2 a linear pair?2. are angles 4 and 5 a linear pair ?3.are angles 1 and 4 vertical angles?4. are angles 3 and 5 vertical angles ?
Linear pair angles form a straight line, so, both angles add up to 180°.
1 and 2 are not a linear pair.
4 and 5 are a linear pair.
Vertical angles are opposite angles, that are equal.
1 and 4 are vertical angles
3 and 5 are NOT vertical angles-
help me please
thank you
Answer:
Domain: A, [tex](-\infty, \infty)[/tex]
Range: A, [tex][4, \infty)[/tex]
Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
Solve the triangle: a = 12,c = 2-2, B = 33". If it is not possible, say so.A= 25.1",b = 1.8, C = 121.9"This triangle is not solvable.A = 45*,b= V2.C = 102VEA= 30', b = -, C = 117"
ANSWER:
A=25.1 degrees
b = 1.8
C = 121.9 degrees
SOLUTION:
We can solve this problem using the cosine law, since we are given the length of 2 sides of triangle and the angle they formed.
[tex]b\text{ =}\sqrt[]{c^2+a^2-2ac\cos B}[/tex]We substitute the given
[tex]\begin{gathered} b\text{ =}\sqrt[]{(2\sqrt[]{2})^2+(\sqrt[]{2})^2-2(\sqrt[]{2})(2\sqrt[]{2})\cos 33} \\ b\text{ = 1.8} \end{gathered}[/tex]Using Sine Law, we can get the angles
[tex]\begin{gathered} \frac{1.8}{\sin 33}=\frac{\sqrt[]{2}}{\sin A} \\ A=25.1 \end{gathered}[/tex]Since the total angle inside a triangle is 180, the angle at C is
[tex]C-33-25.1=121.9[/tex]6. Takao scores a 90, an 84, and an 89 on three out of four math tests. Whatmust Takao score on the fourth test to have an 87 average (mean)?a. 87b. 88c. 85d. 84e. 86
Consider x as Takao's fourth score.
Then, to achieve an 87 average, we have:
[tex]\begin{gathered} 87=\frac{90+84+89+x}{4} \\ x+263=4\cdot87 \\ x=348-263 \\ x=85 \end{gathered}[/tex]Answer:
c. 85
In the answer section, give the question letter and the word TRUE or FALSE for each of the following:
a) We rewrite the right side of the expression as:
[tex](-2)^4=((-1)\cdot2)^4=(-1)^4\cdot2^4=1\cdot2^4=2^4\ne-2^4.[/tex]So we see that the expression of point a is FALSE.
b) We consider the expression:
[tex]b^x.[/tex]We take the logarithm in base b, we get:
[tex]\log_b(b^x)=x\cdot\log_b(b)=x\cdot1=x.[/tex]We see that the logarithm of a number x to a base b is just the exponent you put onto b to make the result equal x. We conclude that this expression is TRUE.
c) We know that in any base a, we have:
[tex]\log_a(0)\rightarrow-\infty.[/tex]We conclude that the expression of this item is FALSE.
d) Logarithms are defined only for numbers greater than 0. So we conclude that this expression is FALSE.
e) We consider the expression:
[tex]\log_b(b^{10})-\log_b(1)=10.[/tex]Applying the properties of logarithms, we get:
[tex]\begin{gathered} 10\cdot\log_bb-0=10, \\ 10\cdot1=10, \\ 10=10\text{ \checkmark} \end{gathered}[/tex]We see that this expression is TRUE.
Answera) FALSE
b) TRUE
c) FALSE
d) FALSE
e) TRUE
thanks for the help!!!!!
The required values of given the trigonometric functions are sin(A + B) = -100/2501 and sin(A - B) = -980/2501.
What are Trigonometric functions?Trigonometric functions are defined as the functions which show the relationship between the angle and sides of a right-angled triangle.
We have been given that the trigonometric function
sin (A) = -60/61 and cos(B) = 9/41
So cos (A) = √1 - (-60/61)² = 11/61, and sin(B) = √1 - (9/41)² = 40/41
To compute the trigonometric functions sin(A + B) and sin(A - B)
⇒ sin(A + B) = sinA cosB + cos A sinB
⇒ sin(A + B) = (-60/61)(9/41) + (11/61)(40/41)
⇒ sin(A + B) = -540/2501 + 440/2501
⇒ sin(A + B) = -100/2501
⇒ sin(A - B) = sinA cosB - cos A sinB
⇒ sin(A - B) = (-60/61)(9/41) - (11/61)(40/41)
⇒ sin(A - B) = -540/2501 - 440/2501
⇒ sin(A - B) = -980/2501
Thus, the required values of given the trigonometric functions are sin(A + B) = -100/2501 and sin(A - B) = -980/2501.
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Allied Health - A wound was measured to be 0.8 cm in length. Whaat is the greatest possible error of this weight in grams?
Ok, so
First of all, we got that the wound was measured to be 0.8cm.
This measurement equals to:
[tex]0.8\operatorname{cm}\cdot\frac{10\operatorname{mm}}{1\operatorname{cm}}[/tex]0.8cm is equal to 8 millimeters.
Now, the greatest possible error in a measurement is one half of the precision (smallest measured unit).
8 mm was measured to the nearest 1 mm, so the measuring unit is 1 mm.
So, one half of the precision (1mm) is 0.5
Therefore, the greatest possible error is 0.5 mm
Solve for x. (x-8a)/ 6 = 3a-2x
Given the equation:
[tex]\frac{x-8a}{6}=3a-2x[/tex]To solve for x, first we move the 6 to the other side of the equation:
[tex]\begin{gathered} \frac{x-8a}{6}=3a-2x \\ \Rightarrow x-8a=(3a-2x)\cdot6 \end{gathered}[/tex]Since the 6 was dividing, we pass it to the other side multiplying. Now we apply the distributive property and move the term -8a to the other side:
[tex]\begin{gathered} x-8a=(3a-2x)\cdot6 \\ \Rightarrow x-8a=18a-12x \\ \Rightarrow x=18a-12x+8a \\ \end{gathered}[/tex]Finally, we move the -12 to the other side with its sign changed:
[tex]\begin{gathered} x+12x=18a+8a=26a \\ \Rightarrow13x=26a \\ \Rightarrow x=\frac{26}{13}a=2a \\ x=2a \end{gathered}[/tex]therefore, x=2a
A money market account offers 1.25% interest compounded monthly. If you want to save $500 in two years, how much money would you need to save per month?
If you want to save $500 in two years, you need to save $20.58 per month with a 1.25% interest compounded monthly.
How is the periodic saving determined?The monthly savings can be determined using an online finance calculator as follows:
N (# of periods) = 24 months (2 x 12)
I/Y (Interest per year) = 1.25%
PV (Present Value) = $0
FV (Future Value) = $500
Results:
Monthly Savings = $20.58
Sum of all periodic savings = $494.04
Total Interest = $5.96
Thus, the investor needs to save $500 in two years to save $20.58 monthly.
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How can I solve this equation if x = -2 and y = -3? 3y (x + x² - y) I've also included a picture of the equation.
In order to calculate the value of the equation, let's first use the values of x = -2 and y = -3 in the equation and then calculate every operation:
[tex]\begin{gathered} 3y(x+x^2-y) \\ =3\cdot(-3)\cdot(-2+(-2)^2-(-3)) \\ =-9(-2+4+3) \\ =-9\cdot5 \\ =-45 \end{gathered}[/tex]Therefore the final result is -45.
graph the line with slope 1/3 passing through the point (4,2)
To graph a line we need two points, to find a second one we need the equation of the line. The equation of a line is given by:
[tex]y-y_1=m(x-x_1)[/tex]Plugging the values given we have:
[tex]\begin{gathered} y-2=\frac{1}{3}(x-4) \\ y-2=\frac{1}{3}x-\frac{4}{3} \\ y=\frac{1}{3}x-\frac{4}{3}+2 \\ y=\frac{1}{3}x+\frac{2}{3} \end{gathered}[/tex]Once we know the equation of a line we find a second point on the line, to do this we give a value to x and use the equation to find y. If x=1, then:
[tex]\begin{gathered} y=\frac{1}{3}\cdot1+\frac{2}{3} \\ y=\frac{1}{3}+\frac{2}{3} \\ y=\frac{3}{3} \\ y=1 \end{gathered}[/tex]Then we have the point (1,1).
Now that we have two points of the line we plot them on the plane and join them with a straight line. Therefore the graph of the line is:
What is the product in simplest form? State any restrictions on the variable9X^2+9X+18)/(X+2) TIMES (x^2-3x-10)/(x^2+2x-24)
So, here we have the following expression:
[tex]\frac{9x^2+9x+18}{x+2}\cdot\frac{x^2-3x-10}{x^2+2x-24}[/tex]The first thing we need to notice before simplifying, is that the denominator can't be zero.
As you can see,
[tex]\begin{gathered} x+2\ne0\to x\ne-2 \\ x^2+2x-24\ne0\to(x+6)(x-4)\ne0\to\begin{cases}x\ne-6 \\ x\ne4\end{cases} \end{gathered}[/tex]These are the restrictions on the given variable.
Now, we could start simplyfing factoring each term:
[tex]\begin{gathered} \frac{9x^2+9x+18}{x+2}\cdot\frac{x^2-3x-10}{x^2+2x-24},x\ne\mleft\lbrace2,4,-6\mright\rbrace \\ \\ \frac{9(x^2+x+2)}{x+2}\cdot\frac{(x-5)(x+2)}{(x+6)(x-4)},x\ne\lbrace2,4,-6\rbrace \end{gathered}[/tex]This is,
[tex]9(x^2+x+2)\cdot\frac{(x-5)}{(x+6)(x-4)},x\ne\lbrace4,-6\rbrace[/tex]So, the answer is:
[tex]\frac{9(x^2+x+2)(x-5)}{(x+6)(x-4)},x\ne\lbrace4,-6\rbrace[/tex]It could be also written as:
[tex]\frac{(9x^2+9x+18)(x-5)}{(x+6)(x-4)},x\ne\lbrace4,-6\rbrace[/tex]Find the Discriminant and describe the number and type of solutions of the equations. 1) 4x^2 + 8x + 4 =0
Given:
[tex]4x^2+8x+4=0[/tex]To find the discriminant, use the formula:
[tex]\Delta=b^2-4ac[/tex]Where a = 4, b = 8, c = 4
Thus, we have:
[tex]\begin{gathered} \Delta=8^2-4(4)(4) \\ \\ \Delta=64-64\text{ =0} \end{gathered}[/tex]The discriminant is = 0
To find the number of solutions, since the disriminant is zero, we have two real and identical roots.
ANSWER:
Discriminant = 0
Number of roots = 2 real and identical roots
Circle O shown below has an are of length 47 inches subtended by an angle of 102°.Find the length of the radius, x, to the nearest tenth of an inch.
We will have the following:
[tex]\begin{gathered} 47=\frac{102}{360}\ast2\pi(x)\Rightarrow\pi(x)=\frac{1410}{17} \\ \\ \Rightarrow x=\frac{1410}{17\pi}\Rightarrow x\approx26.4 \end{gathered}[/tex]So, the radius is approximately 26.4 inches.
Determine the smallest possible co-terminal
angle for a) 410. b)-45
The smallest possible co-terminal are:
a)50
b) -495
Define co terminal angles.Angles that share the terminal side with an angle occupying the standard position are said to be co terminal angles. In the conventional position, the vertex is at the origin and one side of the angle is fixed along the positive x-axis.
In other words, two angles are co terminal when their vertices and sides are the same but their angles themselves differ.
Additionally, you can recall the concept of co terminal angles as angles that differ by an exact number of full circles.
Given Data
The smallest co terminal angle for:
a) 410
Divide the first number by the second, rounding down (towards the floor).
[tex]\frac{360}{410}[/tex]
= 1
after that, multiply the divisor by the result (called the quotient),
360(1)
= 360
Take this amount out of your starting amount.
410-360
= 50
b) -45
- 45 [tex]\frac{pie}{4}[/tex]
= -495
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A rectangle has vertices at (-2, 11), (-2,4), (6, 11), and (6, 4). Pablo says the area of the rectangle is 49 square units and his work is shown below. Steps Step 1 Pablo's Work Base: 1- 21+61= 8 Step 2 Step 3 Height: 11-4-7 Area: 8x7=49 square units Where, if at all, did Pablo first make a mistake finding the area of the rectangle? Step 1 Step 2 Step 3
The result of the calculation of the base is good because the distance between -2 and 6 is 8. The result of the calculation of the height is good because the distance between 4 and 11 is 7. The mistake is seen in the part of the multiplication, because 8x7 is equal to 56 , not 49.
So, the mistake was made when doing the Step 3.
What is the graph of the equation y = 2x + 4?
The y-intercept is which means the line crosses the y-axis at the
). Plot this point.
point
The slope of the line is positive, so it goes
Start at the y-intercept. Move up
0
0 and then move right
). Plot this point.
You are now at the point (
0
Draw a line to connect the two points.
from left to right.
Answer: 8
Step-by-step explanation: x2 + 4 is 4 x 2
:D
Work out the following sums and write the answers correctly.
a) £1.76 + £2.04
b) £5.62 + £2.38
Answer of a is €3.8
Answer of b is €8
Solution :
To get the answer add two decimal number
ie. the sum of first question is €1.76 + €2.04 = €3.8
the sum of second question is €5.62 + €2.38 = €8
Addition is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division.The addition of two whole numbers results in the total amount or sum of those values combined.Addends are the numbers added, and the result or the final answer we get after the process is called the sum.To learn more about Addition refer :
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5. Four hamsters have a combined weight of 5.112 grams. If all the hamsters weigh the same, how many kilograms does one hamster weigh? kilograms
We were told that Four hamsters have a combined weight of 5.112 grams. We know that
1000 grams = 1 kilogram
Thus,
5.112 grams = 5.112/1000
= 0.005112 kilograms
Since all the hamsters weigh the same, then the weight of one hamster is
0.005112 /4
= 0.001278 kilogram
The weight of one hamster is 0.001278 kilogram
Simplify 2f+ 6f help me pls
Answer:
[tex]{ \tt{ = 2f + 6f}}[/tex]
- Factorise out f as the common factor;
[tex]{ \tt{ = f(2 + 6)}} \\ = 8f[/tex]
Two people start walking at the same time in the same direction. One person walks at 2 mph and the other person walks at 6 mph. In how many hours will they be 2 mile(s) apart?
Let's define the following variable:
t = number of hours for them to be 2 miles apart
Distance covered by Person A after "t"hours would be 2t or 2 miles times "t" hours.
Distance covered by Person B after "t" hours would be 6t or 6 miles times "t" hours.
If the distance of Person A and B is 2 miles apart after "t" hours, we can say that:
[tex]\begin{gathered} \text{Person B}-PersonA=2miles \\ 6t-2t=2miles\text{ } \end{gathered}[/tex]From that equation, we can solve for t.
[tex]\begin{gathered} 6t-2t=2miles\text{ } \\ 4t=2miles\text{ } \\ \text{Divide both sides by 4.} \\ t=0.5hrs \end{gathered}[/tex]Therefore, at t = 0.5 hours or 30 minutes, the two persons 2 miles apart.
At 0.5 hours, Person A will
find slope -1,4 3,15
Answer:11/4
Step-by-step explanation: First you put the points in m=x1-x2/y1-y2
m=15-4/3+1=15
Tow "N" Go Towing Company charges a flat fee of $75 plus an additional $5 for every mile the car is towed. Which function models the cost, T(), of towing a car for miles?
Answer:
5N + 75 I believe
