Time 13.5 Time 16 Time 12.6 Time 15.2 Time 12.8 Time 11.8 Time 17.2 Time 12.1. what is the difference between Sarah's time and the mean time of the runners. I know that you divide eight by the sum when you add up all the numbers together from smallest to largest and could you answer this for me l really don't in a word problem when to multiply, add, divide,or, subtract could you ex plain or tell what the key words are that let a student know to add, multiply ,divide, subtract the key words please.
Answers
The mean of a data set is equal to the addition of the values of the data divided by the total number of values in the set.
In our problem:
[tex]\begin{gathered} \operatorname{mean}=\frac{13.5+16+12.6+15.2+12.8+11.8+17.2+12.1}{8}=\frac{111.2}{8} \\ \Rightarrow\operatorname{mean}=13.9 \end{gathered}[/tex]Although you already calculated that, as I understand from what you wrote in the question tab.
The median of a data set can be found by ordering the values in the data set from least to greatest and then taking the middle value. In our problem:
[tex]\begin{gathered} 11.8,12.1,12.6,12.8,13.5,15.2,16,17.2 \\ \Rightarrow\operatorname{median}=\frac{12.8+13.5}{2}=13.15 \\ \Rightarrow\operatorname{median}=13.15 \end{gathered}[/tex]How to divide 111.2 by 8:
The difference between Sarah's time and the mean time of the runners is:
[tex]\operatorname{mean}-\text{Sarah}=13.9-12.1=1.8[/tex]The answer we are looking for is 1.8
Related Questions
[4]How many solutions does the system of equations have?y = 7x-4y = 7x + 2 One Soluton Infinite Solutions No Solution
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Given system of equations:
[tex]\begin{gathered} y\text{ = 7x - 4} \\ y\text{ = 7x + 2} \end{gathered}[/tex]Let us attempt to solve the equations
From equation 1:
[tex]y\text{ = 7x -4}[/tex]Substituting the expression for y into equation 2:
[tex]\begin{gathered} y\text{ = 7x + 2} \\ 7x\text{ -4 = 7x + 2} \\ \text{Collect like terms} \\ 7x\text{ - 7x = 2 + 4} \\ 0\text{ = 6} \end{gathered}[/tex]This imples that there is no solution to the system of equations.
We can plot the graph of the equations to better visualize and see that the lines don't intersect
The lines are parallel and do not intersect. Hence, there is no solution to the system of equations
17. Write the equation of the line in slope-intercept form with the given information. 17. Passes through (-2, 6) with a slope of (-1/4)
Answers
Given:
Slope of line is m = -1/4 and passes through point (-2,6).
Explanation:
The general equation of line with slope m and passing through point (x_1,y_1) is,
[tex]y-y_1=m(x-x_1)[/tex]Determine the equation of line passing through point (-2,6) and have slope of -1/4.
[tex]\begin{gathered} y-6=-\frac{1}{4}(x-(-2)) \\ y-6=\frac{-1}{4}\cdot x-\frac{1}{4}\cdot2 \\ y=-\frac{x}{4}-\frac{1}{2}+6 \\ y=-\frac{x}{4}+\frac{11}{2} \end{gathered}[/tex]So equation of line is,
y = -x/4 + 11/2
Multiply 1.42 x 0.3
Answers
the given problem is 1.4*0.3
here the answer is 0.42
[tex]undefined[/tex]I need some help please Find the inverse function of the given function.1. F(x)= x^2-4/2x^2
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to solve this problem, we can follow some steps
step 1
replace f(x) with y
[tex]\begin{gathered} f(x)=\frac{x^2-4}{2x^2} \\ y=\frac{x^2-4}{2x^2} \end{gathered}[/tex]step 2
replace every x with a y and every y with an x
[tex]\begin{gathered} x=\frac{y^2-4}{2y^2} \\ \end{gathered}[/tex]step 3
solve for y
[tex]\begin{gathered} x=\frac{y^2-4}{2y^2} \\ \text{cross multiply both sides} \\ 2y^2\times x=y^2-4^{} \\ 2y^2x=y^2-4 \\ \text{collect like terms} \\ 2y^2x-y^2=-4 \\ \text{factorize y}^2 \\ y^2(2x-1)=-4 \\ \text{divide both sides by 2x - 1} \\ \frac{y^2(2x-1)}{(2x-1)}=-\frac{4}{(2x-1)} \\ y^2=-\frac{4}{2x-1} \\ \text{take the square root of both sides} \\ y=-\sqrt[]{\frac{4}{2x-1}} \end{gathered}[/tex]therefore the inverse of f(x) is
[tex]f^{-1}(x)=-\sqrt[]{\frac{4}{2x-1}}[/tex]A certain college has been raising tuition every year since the year it opened. The function T = 12,000 (1+.03)* represents the tuition, T, after x years. If the college opened in the year 1990, what was the tuition in 2020?
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The value y of a computer after its purchase is given by y(t)=3200-200t
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Problem Statement
The question gives us an equation that gives us the value of a computer after its initial value at purchase. The equation given is:
[tex]\begin{gathered} y(t)=3200-200t, \\ \text{where,} \\ t=years\text{ afer year of purchase} \\ y=\text{value of the computer} \end{gathered}[/tex]We are asked to find:
a. The y-intercept and its meaning.
b. The slope and its meaning
Solution
To solve this question, we simply need to compare the equation given to the general slope-intercept equation. The general slope-intercept equation is given by:
[tex]\begin{gathered} y(t)=mt+c \\ \text{where,} \\ c=y-\text{intercept} \\ m=\text{slope of the equation} \end{gathered}[/tex]With this equation, we can compare with the equation given in the question:
[tex]\begin{gathered} y=mt+c \\ y=3200-200t \\ \text{This implies that:} \\ \\ \text{slope(m)}=-200 \\ y-\text{intercept}=3200 \end{gathered}[/tex]Thus, let us answer the questions:
a. The y-intercept and its meaning:
The y-intercept is 3200.
When we vary the time variable in the equation given, we can get a sense of what this y-intercept means. This is done below:
[tex]undefined[/tex]What value is a discontinuity of x^2+5x+2/x^2+2x-35
Answers
Solution:
Given the expression:
[tex]\frac{x^2+5x+2}{2x^2+2x-35}[/tex]A function f(x) has disconituity at x=a if
[tex]\lim_{x\to a}f(x)[/tex]exists and is finite.
The function is thus undefined at x=a or when
[tex]\lim_{x\to a}(f(x))\ne f(a)[/tex]From the given function, we have
[tex]\begin{gathered} \frac{x^2+5x+2}{x^2+2x-35} \\ factorize\text{ the denominator,} \\ \frac{x^2+5x+2}{x^2-5x+7x-35}=\frac{x^2+5x+2}{x(x-5)+7(x-5)} \\ \Rightarrow\frac{x^2+5x+2}{(x-5)(x+7)} \end{gathered}[/tex]The function is undefined at
[tex]\begin{gathered} x-5=0 \\ \Rightarrow x=5 \\ x+7=0 \\ \Rightarrow x=-7 \end{gathered}[/tex]Hence, there is discontinuity at
[tex]x=5,\text{ x=-7}[/tex]What is the slope of a line that goes through (2,6) and (4,12)?
Answers
Answer:
Slope = 3
Explanation:
To determine the slope of the line that goes through the given points: (2,6) and (4,12), we use the slope formula.
[tex]\text{Slope}=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}}[/tex]Substituting the points, we have:
[tex]\begin{gathered} \text{Slope}=\frac{12-6}{4-2} \\ =\frac{6}{2} \\ =3 \end{gathered}[/tex]The slope of the line is 3.
given the function f defined by the formula f(x)=2x+1 find the following: Evaluate f(0)
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At a given function:
[tex]\text{ f(x) = 2x + 1}[/tex]At f(0), it means that we substitute x by 0.
We get,
[tex]\text{ f(x) = 2x + 1}[/tex][tex]\text{ f(0) = 2(0) + 1}[/tex][tex]\text{ f(0) = 1}[/tex]Therefore, f(0) = 1.
Solve for h.A=3h Can anyone help me?
Answers
You have the following expression:
[tex]A=3h[/tex]In order to solve for h, use the division property of equality. In this case divide by 3 both sides:
[tex]\begin{gathered} \frac{A}{3}=\frac{3h}{3} \\ \frac{A}{3}=h \end{gathered}[/tex]Hence, the solution for h = A/3
The volume of the oceans and their seas is nearly 1.5 . 109 cubic kilometers. Write this number in Standard Form A:0.00000000015km³ B: 1,500,000,000km³ C: 0.0000000015km³ D: 15,000,000,000km³
Answers
Given data:
[tex]\text{1}.5\cdot10^9[/tex]the above number in standard form is.
1,500,000,000km³.
The answer is option c. 1,500,000,000km³
Solve for x. 3 0 - 7 21 Answer: Submit Answer
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Cross multiply:
[tex]3\cdot21=x\cdot7[/tex]Isolate x:
[tex]63=7x[/tex][tex]\frac{63}{7}=x[/tex][tex]x=9[/tex]Scott borrowed $8000 at a rate of 19%, compounded annually. Assuming he makes no payments, how much will he owe after 8 years? Round your answer to the nearest cent
Answers
To answer this question we will use the following formula for compounded interest:
[tex]A=A_0(1+r)^t,[/tex]where A is the final amount, A₀ is the initial amount, r is the interest rate as a decimal number, and t is the number of times that the interest rate is applied.
Substituting A₀=8000, r=0.19, and t=8 we get:
[tex]A=8000(1+0.19)^8\text{.}[/tex]Simplifying the above result we get:
[tex]\begin{gathered} A=8000(1.19)^8, \\ A\approx32171.08 \end{gathered}[/tex]Answer: $32171.08.
To get rid of radicals in the denominator of a fraction, you should rationalize the denominator by multiplying the fraction by a helpful form of _____.A.the denominatorB.xC.1D.the numerator
Answers
Given:
To get rid of radicals in the denominator of a fraction
Required:
you should rationalize the denominator by multiplying the fraction by what
Explanation:
In fraction, a number is said to be a quotient, in which the numerator is divided by the denominator.
there are three types of fraction
1. Proper fraction
2. Improper fraction
3. Mixed
Final answer:
But to get rid of radival in the denominator of a fraction, you should rationalize the denimonator by multiplying the fraction with 1
7. On Friday, Stock 1 dropped 3/4 point and Stock 2 dropped 5/8 point. Based on this information, which statement is true? Stock 2 dropped more Stock 1 dropped more The stocks dropped the same amount O Both stocks sold at the same price Clear selection
Answers
Let's divide each fraction
[tex]\begin{gathered} \frac{3}{4}=0.75 \\ \frac{5}{8}=0.625 \end{gathered}[/tex]As you can observe, 3/4 is greater than 5/8.
Hence, Stock 1 dropped more.Question is in the picture.The options underneath are $100 per person $15 per person $10 per person and eight dollar per person I chose $100 but I need it to be explained
Answers
The graph provided plots the cost of a hall against the number of guests. The blue graph represents "Cosmic Hall".
The cost per person is the slope of the line that represents the hall in consideration.
The slope is calculated using the formula:
[tex]slope=\frac{y_2-y_1}{x_2-x_1}[/tex]From the graph, two points can be picked as shown below:
[tex]\begin{gathered} (x_1,y_1)=(0,6000) \\ (x_2,y_2)=(500,10000) \end{gathered}[/tex]Hence, the slope is calculated to be:
[tex]\begin{gathered} slope=\frac{10000-6000}{500-0}=\frac{4000}{500} \\ slope=8 \end{gathered}[/tex]*i will give you brainliest and 100 pts* Find the value of y. 3 cm 5 cm х 6 cm 2 cm 3cm. y = [?] cm Enter a decimal rounded to the nearest tenth. Enter
Answers
We have to use the secant theorem, which states
[tex](y+3)\cdot3=(9+2)\cdot2[/tex]Then, we solve for y
[tex]\begin{gathered} 3y+9=11\cdot2 \\ 3y=22-9 \\ y=\frac{13}{3}=4.3 \end{gathered}[/tex]Hence, y is equal to 4.3 cm.10,720MasteryLook at the image below.4Course suRatios, rateArithmetic10Course cheTest yourthe skillsWhat is the area of the triangle?
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The given triangle is not the regular drawing of a triangle. We need to identify the height and base.
From the diagram, the height = 10
base = 4
Substitute the values:
[tex]\begin{gathered} \text{Area of the triangle = }\frac{1}{2}\times\text{ 10}\times4 \\ \text{Area of the triangle = 20 units}^2 \end{gathered}[/tex]The distance d (in inches) that a beetle travels over time + (inseconds) is given by the function d (t) = 2t^3 . Find the averagespeed of the beetle from t1 = 0 second to t2 = 2 seconds.inches/second
Answers
Given distance,
[tex]d(t)=2t^3[/tex]Let v is the speed of the beetle.
It is given by
[tex]v=\frac{d(t)}{t}[/tex]Now,
[tex]\begin{gathered} v=\frac{2t^3}{t} \\ v=2t^2 \end{gathered}[/tex]At t = 0 sec.
[tex]\begin{gathered} v=2t^2 \\ v=2\times0 \\ v=0 \end{gathered}[/tex]At t = 2 sec.
[tex]\begin{gathered} v=2t^2 \\ v=2\times2^2 \\ v=8\text{ m/sec} \end{gathered}[/tex]So, the average speed of the beetle is 8 m/sec.
if ace of 21 = 856 find ace 20 and ace of 22 given a common ratio of 1/4.
Answers
Answer:
[tex]a_{20}=214,a_{22}=3424[/tex]Explanation:
We are told that the common ratio between the numbers is 1/4, meaning each consquetive number is
need help with the the association property etc
Answers
Line 1:
[tex](2+x)x[/tex]Line 2:
[tex]x(2+x)[/tex]Line 1 to Line 2 is:
Commutative property of Multiplication.
Line 3:
[tex]x(x+2)[/tex]Line 2 to Line 3 is:
Commutative property of Addition
Use synthetic division to find the result when 4x3 + 13x2 + 6x + 9 is divided byx + 3.
Answers
To solve this question, observe the figure and observe the steps below:
1) Organize the coefficient of the dividend according to the figure.
2) Write the zero of the divisor according to the figure.
3) Write down the first coefficient (4).
4) Multiply the coefficient by -3 and write it below 13 (second coefficient). Then, sum the result (-12) with 13. Write the answer (1).
5) Do the same with the other values, according to the figure.
6) The coefficients of the quotient are the values in green and the remainder is the value in red.
Answer: The quotient is:
[tex]4x^2+1x+3[/tex]Mrs. Thornton asked her students to draw a figure with a perimeter of 4x + 4. Shown below are 4 drawings madeby her students. (They are not drawn to scale.) Which one is NOT correct?А2x+11B2x2C.X + 4XDX+ 1X+ 1сdba
Answers
The perimeter is 4x+4
the formula of the perimeter of a rectangle is
[tex]P=2l+2w[/tex]for the first drawing
[tex]P=2(2x+1)+2(1)=4x+2+2=4x+4[/tex]It is correct
for the second drawing
[tex]P=2(2x)+2(2)=4x+4[/tex]It is correct
for the third drawing
[tex]P=2(x+4)+2x=2x+8+2x=4x+8[/tex]It is not correct
for the fourth drawing
[tex]P=2(x+1)+2(x+1)=2x+2+2x+2=4x+4[/tex]it is correct
As we can see the incorrect draw is C.
Let A = {0, 2, 4, 6, 8, 10}, B = {0, 1, 2, 3, 4, 5, 6}, and C = {4, 5, 6, 7, 8, 9, 10}. Find a) A ∩ B ∩ C. b) A ∪ B ∪ C. c) (A ∪ B) ∩ C. d) (A ∩ B) ∪ C.
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b) AuBuC = {0,1,2,3,4,5,6,7,8,9,10}
c) (AuB)nC ; (AuB) = {0,1,2,3,4,5,6,8,10}
:. (AuB)nC = {4,5,6,8,10}
d) (AnB)uC ; (AnB) = {0,2,4,6}
:. (AnB)uC = {0,2,4,5,6,7,8,9,10}
Solve the following equation for x by using the quadratic formula. If there is more than one solution, enter your solutions as a comma-separated list, like "1, 3".2x^2+9x+7=0
Answers
Answer:
Explanation:
Given the equation:
[tex]2x^2+9x+7=0[/tex]• The coefficient of x², a=2
,• The coefficient of x, b=9
,• The constant, c=7
Substitute these values into the quadratic formula:
[tex]\begin{gathered} x=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a} \\ \implies x=\dfrac{-9\pm\sqrt[]{9^2-4(2)(7)}}{2\times2}=\dfrac{-9\pm\sqrt[]{81-56}}{4}=\dfrac{-9\pm\sqrt[]{25}}{4} \\ \implies x=\dfrac{-9\pm5}{4} \end{gathered}[/tex]Thus, the values of x are:
[tex]undefined[/tex]
Using y= sin x OR y= cos x [Sinusoidal function] as the parent function, make your own transformations (5 units right, reflect on x axis, 2 units down, horizontal compression with factor 2). Then graph and state domain and range.
Answers
Using
[tex]y=\sin (x)[/tex]5 units right: Let's use the following rule:
[tex]\begin{gathered} y=f(x-5) \\ so\colon \\ y=\sin (x-5) \end{gathered}[/tex]Reflect on x-axis: Let's use the following rule:
[tex]\begin{gathered} y=-f(x) \\ so\colon \\ y=-\sin (x-5) \end{gathered}[/tex]2 units down: Let's use the following rule:
[tex]\begin{gathered} y=f(x)-2 \\ so\colon \\ y=-\sin (x-5)-2 \end{gathered}[/tex]Horizontal compression with factor 2: Let's use the following rule:
[tex]\begin{gathered} y=f(2x) \\ so\colon \\ y=-\sin (2x-5)-2 \end{gathered}[/tex]Let's graph the parent function, and the new function:
The blue graph is the parent function and the red graph is the new function after the transformations applied.
The domain and the range of the new function are:
[tex]\begin{gathered} D\colon\mleft\lbrace x\in\R\mright\rbrace_{\text{ }}or_{\text{ }}D\colon(-\infty,\infty) \\ R\colon\mleft\lbrace y\in\R\colon-3\le y\le-1\mright\rbrace_{\text{ }}or_{\text{ }}R\colon\lbrack-3,-1\rbrack \end{gathered}[/tex]write 77.56 as a scientific notation
Answers
The scientific notation/standard form of 77.56 can be represented below
[tex]7.756\times10^1[/tex]The logic behind it is we shift the dot backward until it get to the last number. The number of step we took represent the exponential of 10.
Give an example of a rational function that has a horizontal asymptote at y = 0 and a vertical asymptote atx = 2 and x = 1.
Answers
Solution
Step 1
Horizontal Asymptotes of Rational Functions
The horizontal asymptote of a rational function can be determined by looking at the degrees of the numerator and denominator.
If N is the degree of the numerator and D is the degree of the denominator, and…
N < D, then the horizontal asymptote is y = 0.
N = D, then the horizontal asymptote is y = ratio of leading coefficients.
N > D, then there is no horizontal asymptote.
Step 2
Identify Vertical Asymptotes of a Rational Function
Factor the numerator and denominator.
Simplify by canceling common factors in the numerator and the denominator.
Set the simplified denominator equal to zero and solve for x.
Step 3
x = 2 and x = 1
x - 2 and x - 1
The denominator expression will be (x-2)(x-1)
Step 4
[tex]\begin{gathered} The\text{ rational fraction is} \\ \\ y=\frac{1}{(x-2)(x-1)} \end{gathered}[/tex]Final answer
[tex]y\text{ = }\frac{1}{(x-2)(x-1)}[/tex]find the values for A and B. explain of show your reasoning
Answers
Answer:
The value of a is 5, and b is 6.
Explanation:
The points on the line are (6,10), (a,8), (4,b) and (2,2).
• The slope of a straight line is always constant.
First, determine the slope using the points (6,10) and (2,2).
[tex]\begin{gathered} \text{Slope}=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}} \\ =\frac{10-2}{6-2} \\ =\frac{8}{4} \\ =2 \end{gathered}[/tex]Next, using points (6,10) and (a,8):
[tex]\begin{gathered} m=\frac{10-8}{6-a} \\ 2=\frac{2}{6-a} \\ \text{Cross multiply} \\ 2(6-a)=2 \\ 12-2a=2 \\ -2a=2-12 \\ -2a=-10 \\ a=-\frac{10}{-2} \\ a=5 \end{gathered}[/tex]Next. using points (6,10) and (4,b):
[tex]\begin{gathered} m=\frac{10-b}{6-4} \\ 2=\frac{10-b}{2} \\ \text{Cross multiply} \\ 10-b=2\times2 \\ 10-b=4 \\ b=10-4 \\ b=6 \end{gathered}[/tex]The value of a is 5 and b is 6.
The Royal Fruit Company produces two types of fruit drinks. The first type is 65% pure fruit juice, and the second type is 90%pure fruit juice. The company is attempting to produce a fruit drink that contains 75% pure fruit juice. How many pints of each ofthe two existing types of drink must be used to make 170 pints of a mixture that is 75% pure fruit juice?First fruit drink:pintsХ5?Second fruit drink: pints
Answers
Let
x ----> number of pints of the First fruit drink
y ----> number of pints of the Second fruit drink
we have that
x+y=170 -------> x=170-y ----> equation A
65%=0.65
90%=0.90
75%=0.75
so
0.65x+0.90y=0.75(170) -----> equation B
Solve the system of equations
substitute equation A in equation B
0.65(170-y)+0.90y=0.75(170)
solve for y
110.5-0.65y+0.90y=