Using the statistical formula, the median of the given data-set is 20.5.
It is given that
Number of touchdowns in 10 sessions are:
29, 5, 26, 20, 23, 18, 17, 21, 28, 20
What is a median?The median is the middle number in a sorted, ascending, or descending, list of numbers and can be more descriptive of that data set than the average.
For the median, let us arrange the given data in ascending order.
5, 17, 18, 20, 20, 21, 23, 26, 28, 29
Number of terms = 10
Median of n terms when n is even is given by:
(n/2^th term+ (n/2 +1)^th term)/2
n/2 th term = 5th term = 20
(n/2+1)th term = 6th term = 21
So median= (20+21)/2 = 20.5
Therefore, the median of the given data-set is 20.5
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Answer:
The range is 24 touchdowns.
The interquartile range is 8 touchdowns.
Step-by-step explanation:
4. If m 1 = (10x + 42)° and m 7 = (2x + 6)º,
what is the value of x, m 1?
Answer:
Value of x = 8
(3x - 7) = (5x - 23)
-2x = -16
x = 8
Value of m 8 = 17 degrees
5(8) - 23
40 - 23 = 17
Find the constant of proportionality if y varies directly with x for the values below.
x = 2
y = 11
Answer:
y=5.5x
Step-by-step explanation:
Lucien can buy 1 lb of Colombian coffee beans for $4.25 you can buy one pound of French roast coffee beans for $3.75 if he buys one pound mixture of the two kinds of beans for $4 how much of each kind of coffee bean does he buy
Answer:
Colombian coffee bought = 0.5 lbs
French roast coffee beans bought = 0.5 lbs
Step-by-step explanation:
Let Colombian coffee bought = [tex]x[/tex] lbs
Total weight of mixture bought = 1 lbs
Therefore, French roast coffee beans bought = (1 - [tex]x[/tex]) lbs
Price of 1 lb Colombian coffee = $4.25
Price of [tex]x[/tex] lbs of Colombian coffee = $[tex]4.25x[/tex]
Price of 1 lb French roast coffee beans = $3.75
Price of (1 - [tex]x[/tex]) lbs French roast coffee beans = $3.75(1 - [tex]x[/tex])
It is given that total money spent is $4.
As per given statement:
[tex]4.25x+3.75(1-x)=4\\\Rightarrow 0.50x=0.25\\\Rightarrow x=\bold{0.5\ lbs}[/tex]
Colombian coffee bought = 0.5 lbs
French roast coffee beans bought = 0.5 lbs
An object is thrown in the air with an initial velocity of 5 m/sec from a height of 9 m. The following equation models the height of the object in meters after t seconds. How many seconds does it take for the object to hit the ground?
Check the picture below.
[tex]~~~~~~\textit{initial velocity in meters} \\\\ h(t) = -4.9t^2+v_ot+h_o \quad \begin{cases} v_o=\textit{initial velocity}&5\\ \qquad \textit{of the object}\\ h_o=\textit{initial height}&9\\ \qquad \textit{of the object}\\ h=\textit{object's height}\\ \qquad \textit{at "t" seconds} \end{cases} \\\\\\ h(t)=-4.9t^2+5t+9\implies \stackrel{h(t)}{0}=-4.9t^2+5t+9 \implies 4.9t^2-5t-9=0[/tex]
since we don't get any neat integer values from it hmmm let's plug that in the quadratic formula to see what we get as h(t) = 0.
[tex]~~~~~~~~~~~~\textit{quadratic formula} \\\\ \stackrel{\stackrel{a}{\downarrow }}{4.9}t^2\stackrel{\stackrel{b}{\downarrow }}{-5}t\stackrel{\stackrel{c}{\downarrow }}{-9}=0 \qquad \qquad t= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a} \\\\\\ t= \cfrac{ - (-5) \pm \sqrt { (-5)^2 -4(4.9)(-9)}}{2(4.9)}\implies t=\cfrac{5\pm\sqrt{25+176.4}}{9.8} \\\\\\ t=\cfrac{5\pm \sqrt{201.4}}{9.8}\implies t\approx \begin{cases} 1.96~~\checkmark\\ -0.94 \end{cases}[/tex]
notice, we do not use the negative value for "t", since the seconds cannot be less than 0.
Solving a Two-Step Matrix Equation
Solve the equation:
Answer:
[tex]\boxed {x_{1} = 3}[/tex]
[tex]\boxed {x_{2} = -4}[/tex]
Step-by-step explanation:
Solve the following equation:
[tex]\left[\begin{array}{ccc}3&2\\5&5\\\end{array}\right] \left[\begin{array}{ccc}x_{1}\\x_{2}\\\end{array}\right] + \left[\begin{array}{ccc}1\\2\\\end{array}\right] = \left[\begin{array}{ccc}2\\-3\\\end{array}\right][/tex]
-In order to solve a pair of equations by using substitution, you first need to solve one of the equations for one of variables and then you would substitute the result for that variable in the other equation:
-First equation:
[tex]3x_{1} + 2x_{2} + 1 = 2[/tex]
-Second equation:
[tex]5x_{1} + 5x_{2} + 2 = -3[/tex]
-Choose one of the two following equations, which I choose the first one, then you solve for [tex]x_{1}[/tex] by isolating
[tex]3x_{1} + 2x_{2} + 1 = 2[/tex]
-Subtract [tex]1[/tex] to both sides:
[tex]3x_{1} + 2x_{2} + 1 - 1 = 2 - 1[/tex]
[tex]3x_{1} + 2x_{2} = 1[/tex]
-Subtract [tex]2x_{2}[/tex] to both sides:
[tex]3x_{1} + 2x_{2} - 2x_{2} = -2x_{2} + 1[/tex]
[tex]3x_{1} = -2x_{2} + 1[/tex]
-Divide both sides by [tex]3[/tex]:
[tex]3x_{1} = -2x_{2} + 1[/tex]
[tex]x_{1} = \frac{1}{3} (-2x_{2} + 1)[/tex]
-Multiply [tex]-2x_{2} + 1[/tex] by [tex]\frac{1}{3}[/tex]:
[tex]x_{1} = \frac{1}{3} (-2x_{2} + 1)[/tex]
[tex]x_{1} = -\frac{2}{3}x_{2} + \frac{1}{3}[/tex]
-Substitute [tex]-\frac{2x_{2} + 1}{3}[/tex] for [tex]x_{1}[/tex] in the second equation, which is [tex]5x_{1} + 5x_{2} + 2 = -3[/tex]:
[tex]5x_{1} + 5x_{2} + 2 = -3[/tex]
[tex]5(-\frac{2}{3}x_{2} + \frac{1}{3}) + 5x_{2} + 2 = -3[/tex]
Multiply [tex]-\frac{2x_{2} + 1}{3}[/tex] by [tex]5[/tex]:
[tex]5(-\frac{2}{3}x_{2} + \frac{1}{3}) + 5x_{2} + 2 = -3[/tex]
[tex]-\frac{10}{3}x_{2} + \frac{5}{3} + 5x_{2} + 2 = -3[/tex]
-Combine like terms:
[tex]-\frac{10}{3}x_{2} + \frac{5}{3} + 5x_{2} + 2 = -3[/tex]
[tex]\frac{5}{3}x_{2} + \frac{11}{3} = -3[/tex]
-Subtract [tex]\frac{11}{3}[/tex] to both sides:
[tex]\frac{5}{3}x_{2} + \frac{11}{3} - \frac{11}{3} = -3 - \frac{11}{3}[/tex]
[tex]\frac{5}{3}x_{2} = -\frac{20}{3}[/tex]
-Multiply both sides by [tex]\frac{5}{3}[/tex]:
[tex]\frac{\frac{5}{3}x_{2}}{\frac{5}{3}} = \frac{-\frac{20}{3}}{\frac{5}{3}}[/tex]
[tex]\boxed {x_{2} = -4}[/tex]
-After you have the value of [tex]x_2[/tex], substitute for [tex]x_{2}[/tex] onto this equation, which is [tex]x_{1} = -\frac{2}{3}x_{2} + \frac{1}{3}[/tex]:
[tex]x_{1} = -\frac{2}{3}x_{2} + \frac{1}{3}[/tex]
[tex]x_{1} = -\frac{2}{3}(-4) + \frac{1}{3}[/tex]
-Multiply [tex]-\frac{2}{3}[/tex] and [tex]-4[/tex]:
[tex]x_{1} = -\frac{2}{3}(-4) + \frac{1}{3}[/tex]
[tex]x_{1} = \frac{8 + 1}{3}[/tex]
-Since both [tex]\frac{1}{3}[/tex] and [tex]\frac{8}{3}[/tex] have the same denominator, then add the numerators together. Also, after you have added both numerators together, reduce the fraction to the lowest term:
[tex]x_{1} = \frac{8 + 1}{3}[/tex]
[tex]x_{1} = \frac{9}{3}[/tex]
[tex]\boxed {x_{1} = 3}[/tex]
5x+10y=20
graph it using y=mx+b
show your work please
Answer:
y=20-5x 10Step-by-step explanation:
5x+10y=20y=mx+b10y=20-5xdivide by 10 both side10y=20-5x 10 = 10y=20-5x 10answerQuestion is in the picture:
Answer:
here
Step-by-step explanation:
For the first one shade 38 squares
For the second one shade 65 of the squares
#1 is 38%
#2 is 65%
Answer:shade 19 out of 50 bloxks
Step-by-step explanation:
it shows on page
Which equation, when graphed, has x-intercepts at (−1, 0) and (−5, 0) and a y-intercept at (0, −30)? f(x) = −6(x 1)(x 5) f(x) = −6(x − 1)(x − 5) f(x) = −5(x 1)(x 5) f(x) = −5(x − 1)(x − 5).
Answer:
f(x) = −6(x+ 1)(x +5)
Step-by-step explanation:
x-intercepts at (−1, 0) and (−5, 0)
so the roots are -1 and -5 (where the graph intersects the x-axis)
this will give us that f(x) = (x- root1)(x-root2) = (x- -1)(x- -5) = (x+1)(x+5)
y-intercept at (0, −30) is telling us that when x= 0 the y = -30
y = a ( x+1)(x+5) , in general
y = a(0+1)(0+5), is the equation if x=0
-30 = a·1·5, we need y= -30 when x= 0
-30 = 5a , divide both sides of the equation by 5
-6 = a
The correct choice is :
f(x) = −6(x+ 1)(x +5)
f(x) = −6(x − 1)(x − 5)
f(x) = −5(x +1)(x +5)
f(x) = −5(x − 1)(x − 5).
Lola bought 6 bracelets for $7.50 and 10 rings for $13.00. At the same time, Bella bought 8 bracelets and 7 rings. What is the total price for the items Bella bought?
Answer:$51.5
Step-by-step explanation:
Ingnd mxes 3 6 pounds of almonds with some raisins to make a trail mix She divides the trail mix into 12 equal portions Each portion weighs 0.7 of a pound How many pounds of raisins did she use to make the trail mix? Express the answer to the nearest tenth 2.9 4.8 5.1 7.2
Answer:
The 12 portions weigh a total of 12*0.7 = 8.4 lbs
So, the almonds weigh 8.4 - 3.6 = 4.8 lbs
Answer:
4.8 poundsStep-by-step explanation:
Let raisins weight be x
Then we get equation
(3.6 + x)/12 = 0.7Solving for x
3.6 + x = 12*0.7x + 3.6 = 8.4x = 8.4 - 3.6x = 4.8 poundsOption B is correct one
what is the solution of the following equation? 2x-5+3x=35
2x - 5 + 3x = 35
simplify
5x - 5 = 35
add 5 to both sides
5x - 5 + 5 = 35 + 5
simplify
5x = 40
divide both sides by 5
5x/5 = 40/5
simplify
x = 8
At Gulfport Electronics, Randy earns a monthly salary of $1500 plus a 5% commission of x, his total monthly sales. If his March earnings total $2500, write and solve an equation that could be used to determine his total monthly sales for the month of March
Answer:
His March Earnings is $20000
Step-by-step explanation:
Given
[tex]Salary = \$1500[/tex]
[tex]Commission = 5\%\ of\ sales[/tex]
[tex]March\ Earnings = \$2500[/tex]
Required
Determine the monthly sales
Represent the monthly sales with x
The march earnings can be determined using:
[tex]March\ Earnings = Salary + Commission[/tex]
[tex]March\ Earnings = Salary + 5\%\ of\ x[/tex]
Substitute values of March Earnings and Salary
[tex]2500 = 1500 + 5\% * x[/tex]
[tex]2500 = 1500 + 0.05 * x[/tex]
[tex]2500 = 1500 + 0.05x[/tex]
Solve for 0.05x
[tex]0.05x = 2500 - 1500[/tex]
[tex]0.05x = 1000[/tex]
Solve for x
[tex]x = 1000/0.05[/tex]
[tex]x = 20000[/tex]
Hence:
His March Earnings is $20000
Distribute to create an equivalent expression with the fewest symbols possible.
1/2(10x+20y+10z) =
[tex]\\ \rm\longmapsto 1/2(10x+20y+10z)[/tex]
a(b+c)=ab+ac[tex]\\ \rm\longmapsto 10x/2+20y/2+10z/2[/tex]
[tex]\\ \rm\longmapsto 5x+10y+5z[/tex]
Answer:
5x+10y+5z
Step-by-step explanation: it was on khan academy and it was right
Besides 49 and 1, what is one factor of 49??????????????????????
Answer:
See below.
Step-by-step explanation:
The factors of 49 are 1, 7, and 49.
1 x 49 = 49
7 x 7 = 49
-hope it helps
what are the missing numbers?
Answer:
5, 30, and 70
Step-by-step explanation:
Multiply by number of quarters by 5 to get the number of nickels.
PLEASE HELP! I’ll mark you as brainliest or whatever it’s called❤️
Answer:
45% of 280 is 126
126
Hope This Helps!
35% of 280 is 98. 100% of 280 is 280, therefore 35 percent of 280 equals 98
80% of 280 = 224
45% of 280 = 126
Need help asap please
Answer:
A
Step-by-step explanation:
[tex] {16}^{2} = {14}^{2} + {x}^{2} [/tex]
[tex]256 - 196 = {x}^{2} [/tex]
[tex]x = \sqrt{60} = 2 \sqrt{15} [/tex]
Help me pleaseeee
I need to fund the point in the line using this equation
Answer:(1,2)
Step-by-step explanation: The signs may not be right(positive, negative) Sorry it’s been a long time since I did this
Simplify the following expression.
(8x + 4) - (2x2 + 4x - 7)
Answer:
-2x^2 + 4x + 11
Step-by-step explanation:
whats 2x2 ? do you mean 2x^2 ? if so then...
8x + 4 - 2x^2 - 4x + 7
4x + 11 - 2x^2
-2x^2 + 4x + 11
Answer:
this is the answers 2x^2+4x+11
There are 4 times as many dogs as cats if the total number of dogs and cats is 25 how many dogs are there
Answer:
6 times as many dogs as cats
Step-by-step explanation:
Answer:
20
Step-by-step explanation:
So we know that if we combine all of the dogs and cats, we get 25. We also know that there are 4 times more dogs than cats, so we can call cats x, and dogs 4x.
So 4x + x = 25
5x = 25
x=5
There are 5 cats. Now that we know the number of cats , we just need to multiply that by 4, which is 20 dogs.
Use the figure below to find angle PNO
Answer:
31 degrees
Step-by-step explanation:
A line has angle of 180 degrees.
So
[tex](2z+17)+(4z-23)=180\\6z-6=180\\6z=186\\z=31[/tex]
Calculate the surface are of each of the following. Show your work.
Hey there!
[tex]⇢ \: A = 2wl + 2lh + 2hw[/tex]
L = 17 inW = 8 inH = 12Substitute
[tex]⇢ \: = 2(8)(17) + 2(17)(12) + 2(12)(8)[/tex]
[tex]⇒872[/tex]
Surface area = 872 square inches
What critical value of t* should be used for a 98% confidence interval for the population mean based on a random sample of 25 observations?
A. t* = 2.485
B. t* = 2.492
C. t* = 2.787
D. t* = 2.797
Using a t-distribution calculator, it is found that the critical value of t* for a 98% confidence interval with 25 observations is given by:
B. t* = 2.492
How to find the critical value of the t-distribution?It is found using a calculator, with two inputs, which are given by:
The confidence level.The number of degrees of freedom, which is one less than the sample size.In this problem, we have a confidence level of 98% and 25 - 1 = 24 df, hence the critical value is of t* = 2.492, which means that option B is correct.
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1. Brother has 12 red blocks, 10 blue blocks, and 8 yellow blocks. What is the ratio of red blocks to yellow blocks?
[tex]ratio-of-red-blocks-to-yellow-blocks = \frac{number-of-red-blocks}{number-of-yellow-blocks} =\frac{12}{8} =\frac{3}{2}[/tex]
Answer: [tex]\frac{3}{2}[/tex] or 3 : 2
Hope it helps!
Answer:
3 : 2
Step-by-step explanation:
what is the complement of 37 degrees without using a protractor, sketch the two angles so that they are adjacent
Answer:
the complement of 37 degrees is 53 degrees.
Step-by-step explanation:
90-37=53
1.2y+4.5-3.4y-6.3 pls help me
Answer:
-2.2y-1.8
Step-byStep-byStep-byStep-byStep-byStep-byStep-byStep-byStep-by
1.2y-3.4y=-2.2y
4.5-6.3=-1.8
ssoso:-2.2y-1.8
PLEASE HELP PLEASE HELP!!!!
Write a problem that would result in the expression: -12 + 6(3/4). Solve your problem and show your work.
Answer:
-18 and 3/4
Step-by-step explanation:
I’m to lazy to do this right now anyone can give me an answer
Answer:
$75.50
Step-by-step explanation:
Please help!!!!!! Thank you so much!!!!!
Answer:
104 degrees
Step-by-step explanation:
RS is a line, so it is 180 degrees. PO is also a line and point O is touching line RS. The acute measure is 76 degrees, as shown. To find the other angle measure for SOP, subtract 76 from 180. That gives 104 degrees, which is the measure of SOP.
100 points pls right answers only it’s for apex
An outlier point is added to a set of bivariate data. In what way must your analysis change with the addition of the outlier?
A. The sign of the regression coefficient will change from positive to
negative, or vice versa.
B. The value of the correlation coefficient will move closer to 0.
C. The regression constant will change dramatically.
D. All of the above.
Answer:
I already said b in the comment area so I'm just putting it here now
Step-by-step explanation:
(B) The value of the correlation coefficient will move closer to 0.
Bivariate data:Bivariate data in statistics refers to data on two variables, each of which has a value coupled with a value of the other variable. Normally, it would be interesting to look into any potential relationships between the two variables. The association can be investigated using sample statistics that can be utilized for inference, a tabular or graphical display, or both. The approach taken to look into the association would depend on how the variable was measured. Bivariate correlation or bivariate association are terms used to describe the links, which only involve two variables.Therefore, the correct option is (B) The value of the correlation coefficient will move closer to 0.
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