We are asked to find the mean of a set of data. Let's remember that the mean is the sum of all the terms in a set of data divided by the number of terms. The given set of data is:
[tex]1,2,2,2,3,4,4,5,6,7,7,8,9,9,10[/tex]We sum all the terms and divide them by 15, like this:
[tex]M=\frac{1+2+2+2+3+4+4+5+6+7+7+8+9+9+10}{15}[/tex]Solving the sum:
[tex]M=\frac{79}{15}[/tex]The mean is then:
[tex]M=5.3[/tex]find the slope of the line that passes through (2,3) and (10,10)
The slope of a line represents the change in y over the change in x.
[tex]m=\frac{y_1-y_2}{x_1-x_2}[/tex]We are given the points (2,3) and (10,10).
[tex]m=\frac{3-10}{2-10}=\frac{7}{8}=0.875[/tex]the function y=30+5x (represents the cost) in dollars of having your dog groomed where x represents buying extra services.graph the function using the 6 values of its domains.
Given function y = 30 +5x for the dog groomed
where x represent the value of the buying extra service
The equation is the linear equation so the graph will be staright line
For the coordinates of the graph, set any value for x and then solve for the y .
The x and y value are the coordinates:
Let for x = (-3)
y= 30+5(-3)
y=15
So coordinate 1. (-3,15)
Let for x = (-4)
y= 30+5(-4)
y=10
So coordinate 2. (-4,10)
Let for x = (-5)
y= 30+5(-5)
y=5
So coordinate 3. (-5,5)
Let for x = (-6)
y= 30+5(-6)
y=0
So coordinate 4. (-6,0)
Let for x = (-7)
y= 30+5(-7)
y=-5
So coordinate 5. (-7, -5)
Let for x = (-8)
y= 30+5(-8)
y=-10
So coordinate 6. (-8, -10)
Plot the resulting six coordinates on the graph :
find the reflection of (-1,-2) across the line y=2
Start by graphing the line y=2 and the point given
since the line y=2 is a straight line, then the reflection will stay on the same x coordinate and the y coordinate will be 4 units above the line.
The reflection will be at point (-1,6)
A scale drawing of a city plaza in which 1 inch (in.) = 1.5 feet (ft.) is shown below. 9 in. 9 in. To the nearest whole number, what is the area of the actual plaza? 0 81 square feet O 81 square inches 0 182 square feet 0 182 square inches
1 inch ---> 1.5 feet
9 inch ---> x feet
[tex]\begin{gathered} x\times1=1.5\times9 \\ x=13.5 \end{gathered}[/tex]therefore the area of the actual plaza
[tex]13.5\times13.5=182[/tex]answer: 182 square feet
tell whether each number is divisible by 2 3 4 5 6 9 or 10 then classify the number as even or odd
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
13. 24
Step 02:
classify the number and divisibility:
classify the number:
24 ===> even number
divisibility:
[tex]\begin{gathered} \frac{24}{2}=\text{ 12 } \\ \\ \frac{24}{3}=\text{ 8} \\ \\ \frac{24}{4}=6 \\ \\ \frac{24}{5}=4.8\text{ \lparen inexact division\rparen} \\ \\ \frac{24}{6}=4 \\ \\ \frac{24}{9}=2.66...\text{ \lparen inexact division\rparen} \\ \\ \frac{24}{10}=2.4\text{ \lparen inexact division\rparen } \\ \end{gathered}[/tex]That is the full solution.
I need a bit of help understanding this, please help
We know that
[tex]\begin{gathered} m\angle DAC=87^{\circ} \\ \text{ And} \\ m\angle ACD=43^{\circ} \end{gathered}[/tex]And we must find the measure of angle B
We can see the lines AB and DC are crossed by a transversal
We can see that blue angles are alternate interior angles, so
[tex]\begin{gathered} m\angle ACD=m\angle ACB \\ \text{ Then,} \\ m\angle CAB=43^{\circ} \end{gathered}[/tex]And knowing that lines AD and BC are parallels we can say that
[tex]\begin{gathered} m\angle DAC=m\angle ACB \\ \text{ Then,} \\ m\angle ACB=87^{\circ} \end{gathered}[/tex]Finally, using that the three interior angles of a triangle always add to 180° we can say that
[tex]\begin{gathered} m\angle ABC+m\angle ACB+m\angle CAB=180^{\circ} \\ \text{ Replacing the values of the angles} \\ m\angle ABC=180^{\circ}-(87^{\circ}+43^{\circ}) \\ m\angle ABC=50^{\circ} \end{gathered}[/tex]ANSWER:
The measure of angle B is 50°
point A is located at ( 3,4). find A'=T<3,5>(A)point A is located at(3,4).find after A has been reflected across the line y=x
Answer:
A(4,3)
Step-by-step explanation:
When we reflect a point over the line y = x, the values of x and y are exchanged in the point.
We have: Point A(3,4)
After reflection across the line y = x: A(4,3)
Hello I need help with this question pleaseFind the equation of the line containing the given points (3, -2) and (-4, -8)
Solution:
To find the equation of a line, the formula is
[tex]\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}[/tex]Where
[tex]\begin{gathered} (x_1,y_1)=(3,-2) \\ (x_2,y_2)=(-4,8) \end{gathered}[/tex]Substitute the values of the variable
[tex]\begin{gathered} \frac{y-(-2)}{x-3}=\frac{-8-(-2)}{-4-3} \\ \frac{y+2}{x-3}=\frac{-8+2}{-7} \\ \frac{y+2}{x-3}=\frac{-6}{-7} \end{gathered}[/tex][tex]\begin{gathered} Crossmultiply \\ -7(y+2)=-6(x-3) \\ -7y-14=-6x+18 \\ 6x-7y-18-14=0 \\ 6x-7y-32=0 \end{gathered}[/tex]Hence, the equation is
[tex]6x-7y-32=0[/tex]The midpoint of PQ is M=(1, -5) . One endpoint is P=(6, -8).Find the coordinates of the other endpoint, Q.
Given:
The midpoint of a line PQ is M = (1,-5).
THe coordinate of point P = (6,-8).
The objective is to find the coordinate of other point Q.
Explanation:
Since, M is the midpoint of PQ, the distance between PM and QM will be equal.
Consider the coordinate of P , M and Q as,
[tex]\begin{gathered} P(x_1,y_1)=P(6,-8) \\ M(x,y)=(1,-5) \\ Q\mleft(x_2,y_2\mright) \end{gathered}[/tex]The general midpoint formula is,
[tex]\begin{gathered} M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) \\ (x,y)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) \end{gathered}[/tex]To find the value of x value of point Q:
By equating only the variables of x,
[tex]\begin{gathered} x=\frac{x_1+x_2}{2} \\ 1=\frac{6+x_2}{2} \\ 1(2)=6+x_2_{} \\ x_2=2-6 \\ x_2=-4 \end{gathered}[/tex]To find the value of y value of point Q:
By equating only the variable of y,
[tex]\begin{gathered} y=\frac{y_1+y_2}{2} \\ -5=\frac{-8+y_2}{2} \\ -5(2)=-8+y_2 \\ y_2=-10+8 \\ y_2=-2 \end{gathered}[/tex]Hence, the coordinate of Q is (-4,-2).
What is the measure of n?515mnn = 5V[?]Give your answer in simplest form.Enter
We have the following relation
Therefore, we have
[tex]\begin{gathered} n^2=15\cdot5 \\ \\ n^2=3\cdot5\cdot5 \\ \\ n^2=3\cdot5^2 \\ \\ \sqrt[]{n^2}=\sqrt[]{3\cdot5^2} \\ \\ n=5\, \sqrt[]{3} \end{gathered}[/tex]The number in [?} is 3
PLEASE HELP!!What is the slope of a line of best fit if its equation is y = 5x - 4?0-40-1O1505
Step 1
Given;
[tex]y=5x-4[/tex]Required; To find the slope
Step 2
The equation of a line is given as;
[tex]\begin{gathered} y=mx+c \\ m=slope \\ c=y-intercept \end{gathered}[/tex][tex]\begin{gathered} differentiating\text{ the given equation gives} \\ \frac{dy}{dx}=5 \\ comparing\text{ both equations give m=5} \end{gathered}[/tex]Hence the slope of the line is;
[tex]5[/tex]1. Which of the following is not a radical expression that is equivalent to √1087A.√2-√54B.√3-√36C.√5-√21D. √6-√18
Solution:
Given the expression below
[tex]\sqrt{108}[/tex]To find the equivalence of the given expression, we will multiply the radicals to find the odd one out
[tex]\begin{gathered} \sqrt{2}\times\sqrt{54}=\sqrt{108} \\ \sqrt{3}\times\sqrt{36}=\sqrt{108} \\ \sqrt{5}\times\sqrt{2}=\sqrt{105} \\ \sqrt{6}\times\sqrt{18}=\sqrt{108} \end{gathered}[/tex]From the deductions above,
Hence, the radical expression that is not equivalent to the given expression is
[tex]\sqrt{5}\times\sqrt{21}[/tex]The answer is option C
Draw the graph of the circle (x + 1)2 + (y + 4)2 = 4
Given the equation of the circle:
[tex](x+1)^2+(y+4)^2=4[/tex]Let's draw a graph of the circle.
Apply the general equation of a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex]Where:
(h, k) is the center of the circle.
r is the radius of the circle.
Rewrite 4 = 2²
Now, we have the equation:
[tex](x+1)^2+(y+4)^2=2^2[/tex]Thus, we have the following:
Center of the circle: (h, k) ==> (-1, -4)
Radius of the circle = 2.
Since the radius is 2, let's find the four points around the circumference of the circle.
We have:
• Point by the right: (-1 +2, -4) ==> (1, -4)
,• Point by the left: (-1 -2, -4) ==> (-3, -4)
,• Point at the top: (-1, -4 + 2) ==> (-1, -2)
,• Point at the bottom: (-1, -4 - 2) ==> (-1, -6)
Therefore, the graph of the circle will be:
ANSWER:
Choose the best translation of the English phrase.The radius of a circle with a circumferenceof 10 feet.
12 / x equals 6 x equals what
First equation
[tex]\begin{gathered} \frac{12}{x}=6 \\ 12=\text{ 6x} \\ x=\text{ }\frac{12}{6} \\ x=\text{ 2} \end{gathered}[/tex]Which coupon should Mike use to save the most money on a dishwasher originally priced at $700? Save $200 one purchase of $625 or more or 30% off any item
Explanation
to solve this we need to find 30 % of the price and compare to $200
so
Step 1
find 30 % of 700
to find this we can use the formula
[tex]x\text{ \% of a number y = y*}\frac{x}{100}[/tex]hence
[tex]30\text{ \% of 700 = 700*}\frac{30}{100}=210[/tex]so, 30 % of 70o is 210
Step 2
finally, compare
[tex]\begin{gathered} coupon\text{ 1 = 200} \\ Coupon\text{ 2= 210} \\ 210>200 \\ so \\ Coupon\text{ 2}>copuon\text{ 1} \end{gathered}[/tex]therefore, Mike should use the 30% off any item coupon
Hi there. I think my eyes are playing tricks on me. Is this correct?
Solution:
Given the graphed system of equations:
The solution is the point (x, y) of the intersection of the line plots.
In the above graph, the lines intersect at the point shown below:
The corresponding x and y values of this point thus give the solution.
Hence, the solution of the system is
[tex](x,\text{ y\rparen=\lparen-1, -2\rparen}[/tex]The second option is the correct answer.
If s is directly proportional to v+3 and s = 8 when v=1, find s when v= -2
We are given that "s" is directly proportional to "v + 3". This means that the following relationship is given:
[tex]m=\frac{s}{v+3}[/tex]Where "m" is the proportionality constant. To determine the value of "m" we use the fact that when s = 8 then v = 1, therefore:
[tex]m=\frac{8}{1+3}[/tex]Solving the addition:
[tex]m=\frac{8}{4}[/tex]Now, we solve the quotient:
[tex]m=2[/tex]Therefore, the value of "m" is 2.
[tex]2=\frac{s}{v+3}[/tex]Now, we substitute the value v = -2:
[tex]2=\frac{s}{-1+3}[/tex]Solving the operation:
[tex]\begin{gathered} 2=\frac{s}{1} \\ \\ 2=s \end{gathered}[/tex]Therefore, the value of "s" is 2.
Consider the following equation: −10x+3y=11-10x+3y=11 A) Write the above equation in the form y=mx+b.y=mx+b. Enter the values of mm and bb in the appropriate boxes below as integers or reduced fractions (in the form A/B.)
Given the equation of the line:
[tex]-10x+3y=11[/tex]A) You need to remember the Slope-Intercept Form of the equation of a line:
[tex]y=mx+b[/tex]Where "m" is the slope of the line and "b" is the y-intercept.
Then, in order to write the equation, given in the exercise, in Slope-Intercept Form, you have to solve for the variable "y":
[tex]\begin{gathered} 3y=10x+11 \\ \\ y=\frac{10}{3}x+\frac{11}{3} \end{gathered}[/tex]Notice that in this case:
[tex]\begin{gathered} m=\frac{10}{3} \\ \\ b=\frac{11}{3} \end{gathered}[/tex]B) Given this value of "x":
[tex]x=6[/tex]You need to substitute it into the equation found in Part A, and then evaluate, in order to find the corresponding value of "y":
[tex]\begin{gathered} y=\frac{10}{3}(6)+\frac{11}{3} \\ \\ y=\frac{60}{3}+\frac{11}{3} \\ \\ y=\frac{60+11}{3} \\ \\ y=\frac{71}{3} \end{gathered}[/tex]Hence, the answers are:
A)
[tex]y=\frac{10}{3}x+\frac{11}{3}[/tex]
B)
[tex](6,\frac{71}{3})[/tex]
y ( 0.5 + 8) how can i expand these expressions with a variable
Given the initial expression
[tex]y(0.5+8)[/tex]
Therefore,
[tex]\begin{gathered} \Rightarrow y(0.5+8)=y\cdot0.5+y\cdot8=0.5y+8y \\ \Rightarrow y(0.5+8)=0.5y+8y \end{gathered}[/tex]The expanded form of y(0.5+8) is 0.5y+8y, without simplifying.
Hi, do you think u can solve this for me im kinda in a hurry cause I neednto answer the question soon please.
Step 1: Calculate the hours worked for the morning and afternoon
[tex]\begin{gathered} M\text{orning }\Rightarrow8\colon15-12\colon50=4\text{hours} \\ A\text{fternoon}\Rightarrow13\colon00-17\colon30=4.5\text{hours} \end{gathered}[/tex]Step 2: Calculate the entire hours worked for the day
[tex]\text{Morning+Afternoon=4+4.5=8.5hours }[/tex]Step 3: Given the wage to be $13.50 per hour, calculate the wage for the combined hours worked
A grocery store received two shipments of watermelon. each watermelon in a shipment was weighed, then a line plot was made of all of the weights in a shipment. what statement about the two plots' disributions is true? Choose EACH correct statement.
The correct statements are:
• The lightest watermelon in shipment 1 weighs the same amount as the lightest watermelon in shipment 2.
• The range of weighs in shipment 1 is greater than the range of weighs in shipment 2
Explanation:From the given line plots, the following are correct:
The lightest watermelon (16) in shipment 1 weighs the same amount as the lightest watermelon (16) in shipment 2.
The range (10) of weighs in shipment 1 is greater than the range (8) of weighs in shipment 2
Hi, can you help to find (all the roots/zeros), please!!!
Solution
Given the quadratic equation
[tex]x^2-2x-38=0[/tex]we need to find the zeros of the equation
To do that, we use the completing the square method
Step 1. Add 38 to both sides
[tex]\begin{gathered} \Rightarrow x^2-2x-38+38=38 \\ \\ \Rightarrow x^2-2x=38 \end{gathered}[/tex]Step 2: add the square of half of the coefficient of x to both sides
That is;
[tex]\begin{gathered} \Rightarrow x^2-2x+(\frac{1}{2}\cdot(-2))^2=38+(\frac{1}{2}\cdot(-2))^2 \\ \\ \Rightarrow x^2-2x+1=38+1 \\ \\ \Rightarrow x^2-2x+1=39 \\ \\ \Rightarrow(x-1)^2=39 \end{gathered}[/tex]Step 3: Simplify the above expression;
[tex]\begin{gathered} \Rightarrow x-1=\pm\sqrt[]{39} \\ \\ \Rightarrow x=1\pm\sqrt[]{39} \end{gathered}[/tex](x - 5)²Simplify the polynomial expression
x² - 10x + 25
Explanation:(x - 5)² = (x -5)(x -5)
Simplifying the expression:
x(x -5) -5(x - 5)
x(x) -x(5) -5(x) -5(-5)
Multiplication of same sign gives positive number. Multiplication of opposite signs give negative number.
x²- 5x - 5x + 25
collect like terms:
x² - 10x + 25
How do you put this in standard form with the y=mx+b method?
we have
point (3,5)
m=5/3
step 1
Put in slope intercept form
y=mx+b
substitute the given values
5=(5/3)(3)+b
solve for b
5=5+b
b=0
therefore
y=(5/3)x
step 2
Put in standard form
Ax+By=C
where
A is a postive integer
B and C are integers
so
y=(5/3)x
Multiply by 3 both sides
3y=5x
5x-3y=0 -------> standard formAnswer:
5x- 3y= 0
Step-by-step explanation:
y=mx+b---- (3,5) 5/3=m
x y
Y= 5; M= 5/3; X=3; B=B put it together
5 = 5/3(3) + b
solve for b
5 = 5+b
b = 0
now
y= (5/3)x
step 2
Put in standard form
Ax+By=C
y=(5/3)x
Multiply by 3 both sides
3y=5x
5x- 3y= 0 -------> standard form
What is the value of x in the solution to the system of equations -9x + y = 14 4x-8y=24
the given expression is
-9x + y = 14 ( 1 )
4x - 8y = 24 ( 2 )
to simplify the (2)
4x - 8y = 24
divide by 4
x -2y = 6 ( 3 )
the system of equation, appy substitution method :
Solve the equation ( 3 ) for x
x - 2y = 6
x = 6 + 2y
Substitute the value of x in the equation ( 1 )
-9x + y = 14
-9(6 + 2y) + y = 14
-54 -18y +y = 14
-17y = 14 + 54
-17y = 68
y = -68/17
y = -4
substitute the value of y = ( - 4) in the equation ( 3 )
x - 2y = 6
x -2( -4) = 6
x + 8 = 6
x = 6 - 8
x = ( - 2 )
Answer : x = ( - 2 ) and y = ( - 4 )
This question is confusing need help
The solution to the system of equations is the ordered pair where the graphs intersect. In this case, the point is at the coordinate (-3, 1).
Therefore:
x = -3
y = 1
Answer: D. x = -3, y = 1
Sam wants to visit every wax museum in the United States. Two that are left on his list are inSalem and Wildgrove, which are 7.8 miles apart. This distance is represented by 2 inches onSam's map. What scale does the map use?Write your answer as a decimal or whole number.ho1 inch : miles
Answer:
1inch : 3.9miles
Explanation:
Given that the distance between the museum which is 7.8miles apart is represented by 2inches, then;
7.8miles = 2inches
To get the scale used;
x = 1 inch
Divide both expressions
[tex]\begin{gathered} \frac{7.8}{x}=\frac{2}{1} \\ \end{gathered}[/tex]Cross multiply
[tex]\begin{gathered} 7.8\times1=2\times x \\ 7.8=2x \\ \text{Swap} \\ 2x=7.8 \end{gathered}[/tex]Divide both sides by 2
[tex]\begin{gathered} \frac{2x}{2}=\frac{7.8}{2} \\ x=3.9 \end{gathered}[/tex]Hence the scale used is 1inch : 3.9miles
I need help on 5 im stuck on where the mid point is
You have the following coordinates for the Theather and for Kaleb home:
Theater (8 , 20)
Kaleb home (18 , 4)
In order to determine what is the possible location midway between them, you proceed as follow:
you sum x-coordinates and y-coordinates of eaxh point, and you divide by 2 the result of such addition:
[tex](\frac{8+18}{2},\frac{20+4}{2})=(\frac{26}{2},\frac{24}{2})=(13,12)[/tex]Hence, the coordinates of a place miday between Theater and Kaleb home is (13 , 12).
You can notice tha the obtained point is near of Dave's Doorknobs
In a sketch of the graph you have:
15) *15. Last year Ms. Garcia ordered 24 pounds of apples from a local orchard. Thisyear, he plans to order 15 times as many pounds of apples as were ordered3lastyear.Mr. Garcia will use of this order to create fruit baskets. What isthe total amount, in pounds, of apples that Mr. Garcia will use in fruit baskets?Your answer16A) *
Last year order = 24
This year = 1 (1/2) = 3/2 more
Then we multiply
total amount of apples (in pounds)