First let's calculate how much money Philip saves each week.
In 4 weeks, he saved 520 - 300 = $220, so he saved 220/4 = $55 per week.
Then, we have that after 2 weeks of saving, he still needed $520, so before this saving, he needed:
[tex]\begin{gathered} 520+2\cdot55 \\ =520+110 \\ =630 \end{gathered}[/tex]So the computer costs $630.
George was painting a picture frame. The frame was 5inches wide & 3inches tall. What is the perimeter of the picture frame?
The perimeter can be calculated by adding the legnths off all 4 sides.
Since it is 5 inches wide and 3 inches tall, it has 2 sides of 5 inches and 2 sides of 3 inches. So, the perimeter is:
[tex]P=5+5+3+3=16[/tex]16 inches.
Explain why the two right triangles are not the same.
Step 1:
Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion. In other words, similar triangles are the same shape, but not necessarily the same size. The triangles are congruent if, in addition to this, their corresponding sides are of equal length.
Step 2:
Write the corresponding sides and angles
The angles are not corresponding to the sides
Step 3
[tex]\begin{gathered} \angle T\text{ }\ne\text{ }\angle E \\ \angle S\text{ }\ne\text{ }\angle D \\ \angle R\text{ }\ne\angle F \end{gathered}[/tex]Final answer
The two right angles are not the same because the sides and the angles are not corresponding.
Factorise 3x^2 + 5x + 2
After factorizing the expression we get the result as -1 and -2/3.
Given,
the expression is:
3x²+5x+2
Multiply the terms and get the factors.
6x²
Now split the numbers according to the term
3x² + 3x + 2x + 2
collect the like terms.
Arrange the like terms.
3x(x+1) + 2(x+1)
re arrange the terms.
(x+1)(3x+2)
now get the value of x:
x+1 = 0
x = -1
or
3x+2 = 0
3x=-2
x=-2/3
Hence the factors of x are -1 and -2/3
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Can I just have a very quick simple answer to this question?
We have a feasibility region and we have to find at which point of the region the function P can be maximized:
[tex]P=3x+2y[/tex]As this is a linear function, the maximum value will be in one of the vertices of the region. We can identify the vertices as:
We can calculate the value of P for each of the vertices and see which one has a maximum value. We can already guess that P(8,0) will be greater than P(0,8) as the coefficient for x is greater than the coefficient for y.
We can calculate the three values as:
[tex]\begin{gathered} P(0,8)=3\cdot0+2\cdot8=0+16=16 \\ P(6,5)=3\cdot6+2\cdot5=18+10=28\longrightarrow\text{Maximum} \\ P(8,0)=3\cdot8+2\cdot0=24+0=24 \end{gathered}[/tex]Answer: the maximum value of P is 28.
How should you solve the equation x + 10 = 80? What is the resulting equivalent equation?Choose the correct answer below.
Multiply each side by 10, then simplify
Here, we want to know how to proceed with solving the equation
As we can see, we have the division sign between the terms on the left hand side of the equation
To solve the equation, we have to find the value for x by isolating it
What this mean here is that we will have to multiply both sides by 10; so that we can isolate x
Thus, the correct answer here is to multiply each side by 10, then simplify
I need help to determine weather the slope on this graph is A. ZeroB. Negative C. Positive
The slope usually indicates the behavior of a line:
In the above picture there are 3 different lines with different slopes, let's describe them:
-L1. This red line has a positive slope, it means that as "x" increases, then "y" increases as well.
-L2. This blue line has a negative slope, which means that as "x" increases, then the value of "y" decreases.
-L3. This green line is horizontal and has zero slope . This means that it doesn't matter the value of "x", "y" always has the same value.
Using this description, we can now assure that the slope in your graph is NEGATIVE
At a parking garage in a large city, the charge for parking consists of a flat fee of $1.00 plus 1.60 /hr.(a) Write a linear function to model the cost for parking for hours.(Pt)(b) Evaluate P(1.4 )and interpret the meaning in the context of this problem.please make this right I keep making it wrong
Given:
The charge for parking consists of a flat fee of $1.00 and $1.60 per hour.
To find:
a) Write a linear function P(t).
b) Evaluate P(1.4)
Explanation:
a)
Since the flat fee is $1.00 and the varying fee is $1.60 per hour.
So, the linear function of the total cost for parking is,
[tex]P(t)=1.00+1.60t[/tex]Where t be the number of hours.
b)
Substituting t = 1.4 in the above function we get,
[tex]\begin{gathered} P(1.4)=1.00+1.60(1.4) \\ =1+2.24 \\ P(1.4)=\text{ \$}3.24 \end{gathered}[/tex]That means,
The total cost for parking for 1.4 hours is $3.24.
Final answer:
a) The linear function is,
[tex]P(t)=1.00+1.60t[/tex]b) The value is,
[tex]P(1.4)=3.24[/tex]6Question(15 Points)6. The volume of the cylinder below is 150 cubic centimeters. What is the area of its base?a. 20 cmb. 20 cmc. 10 cmd. 10 cm7.5 cm
The given cylinder has a height of 7.5 cm and volume of 150 cubic centimeters,
[tex]\begin{gathered} h=7.5\text{ cm} \\ V=150\text{ cm}^3 \end{gathered}[/tex]Consider that the volume and base area of a right circular cylinder are related as,
[tex]V=A\times h[/tex]Substitute the values and solve for A,
[tex]\begin{gathered} 150=A\times7.5 \\ A=\frac{150}{7.5} \\ A=20 \end{gathered}[/tex]Thus, the base area of the given cylinder is 20 sq. cm.
Therefore, option b is the correct choice.
finally surface area of the solid. use 3.14 for π. write your answer as a decimal.
To find the total surface area of this cone, we have that the total lateral area is given by the formula:
[tex]A_{\text{lateral}}=s\cdot\pi\cdot r[/tex]Where
s is the slant height of the cone, s = 12 inches.
r is the radius of the base of the cone, r = 7 inches.
To that area, we need to add the area of the base of the cone:
[tex]A_{\text{base}}=\pi\cdot r^2[/tex]That is, this is the area of a circle with this radius. Then, the total surface area is:
[tex]A_{\text{total}=}s\cdot\pi\cdot r+\pi\cdot r^2[/tex]Substituting the values in this formula, we have:
[tex]A_{\text{total}}=12in\cdot3.14\cdot7in+\pi\cdot(7in)^2=263.76in^2_{}+153.86in^2[/tex]Then
[tex]A_{\text{total}}=417.62in^2[/tex]Hence, the total area is equal to 417.62 square inches.
Valeria is ordering medals for her school's track meet. Company A charges $4.50 for each medal and a one-time engraving fee of$40. Company B charges $6.50 for each medal and a one-time engraving fee of $20. Which inequality can be used to find x, theleast number of medals that can be ordered so that the total charge for Company A is less than the total charge for Company B?esA)4.5+ 40x<6.5 + 20xB)4.5+ 40x > 6.5 + 20xo4.5x + 40 < 6.5x + 20D)4.5x + 40 > 6.5x + 20
We will determine the inequality as follows:
*First: We will determine the interception point of the two equations, that is:
[tex]y=4.50x+40[/tex][tex]y=6.50x+20[/tex]So:
[tex]4.50x+40=6.50x+20\Rightarrow4.50x-6.50x=20-40[/tex][tex]\Rightarrow-2x=-20\Rightarrow x=10[/tex]Now, we replace x = 10 on any of the two equations:
[tex]y=4.50x+40\Rightarrow y=4.50(10)+40[/tex][tex]\Rightarrow y=45+40\Rightarrow y=85[/tex]So, the interception point is located at (10, 85).
*Second: We determine the inequality that represents the problem, that is:
[tex]6.50x+20>4.50x+40[/tex][This is overall, the second equation represents greater cost].
*Third: The least number of medals that cab ve ordered so company's A cost is less than company's B cost is 10 medals.
Graph the line that passes through the points (-2,-7) and (5,0) anddetermine the equation of the lineKuationSubmit Answer
Given points:
(-2,-7) and (5,0)
To get the equation of the line, we will use the formula below:
[tex]y_{}-y_1=m(x_{}-x_1)[/tex]From the points given
[tex]\begin{gathered} x_1=-2,y_1=-7 \\ x_2=5,y_2=0 \end{gathered}[/tex]Where
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1}=\frac{0-(-7)}{5-(-2)}=\frac{7}{7}=1 \\ m=1 \end{gathered}[/tex]Substituting the values into the equation
[tex]\begin{gathered} y-(-7)=1(x-(-2)) \\ y+7=1(x+2) \\ y+7=x+2_{} \\ \end{gathered}[/tex]simplifying further
The equation of the line is:
[tex]y=x-5[/tex]The graph of the points (-2,-7) and (5,0) is given below:
Look at this diagram: GHIJKLMNIf HJ and KM are parallel lines and mJIG = 43°, what is mKLN?
We are given that lines HJ and KM are parallel. We notice that the angles:
[tex]\begin{gathered} \angle KLN \\ \angle HIL \end{gathered}[/tex]Are corresponding angles, and therefore they are congruent, that is:
[tex]\angle KLN\cong\angle HIL[/tex]Also, angles:
[tex]\begin{gathered} \angle HIL \\ \angle JIG \end{gathered}[/tex]Are vertical angles, therefore, they are equal:
[tex]\angle HIL\cong\angle JIG[/tex]Therefore, combining the two statements we get:
[tex]\angle KLN\cong\angle JIG[/tex]Therefore:
[tex]\angle KLN=43[/tex]Angle KLN equals 43 degrees.
Solve 8sin(pi/6 x) = 4 for the four smallest positive solutions
Simplify the given expression as shown below
[tex]\begin{gathered} 8sin(\frac{\pi}{6}x)=4 \\ \Rightarrow sin(\frac{\pi}{6}x)=\frac{4}{8}=\frac{1}{2} \\ \Rightarrow sin(\frac{\pi}{6}x)=\frac{1}{2} \end{gathered}[/tex]On the other hand,
[tex]\begin{gathered} sin(y)=\frac{1}{2} \\ \end{gathered}[/tex]Solving for y using the special triangle shown below
Thus,
[tex]\begin{gathered} \Rightarrow y=30\degree\pm360\degree n=\frac{\pi}{6}\pm2\pi n \\ and \\ y=150\degree+360\degree n=\frac{5\pi}{6}+2\pi n \end{gathered}[/tex]Then,
[tex]\begin{gathered} \Rightarrow\frac{\pi}{6}x=y \\ \Rightarrow\frac{\pi}{6}x=\frac{\pi}{6}+2\pi n \\ \Rightarrow x=1+12n \\ and \\ \frac{\pi}{6}x=\frac{5\pi}{6}+2\pi n \\ \Rightarrow x=5+12n \end{gathered}[/tex]The two sets of solutions are
[tex]x=1+12n,5+12n[/tex]Then, the four smallest positive solutions are[tex]\Rightarrow x=1,5,13,17[/tex]The answers are 1,5,13,174. Which is the best first step to write 2(x-4)^2-3=8 in standard form?A. Factor.B. Clear the parentheses.C. Set the function equal to 0.D. Combine like terms.
We will have that the best way to write it in standard form is B, we clear the parentheses and solve for x.
*That is because the function is already factored, and we will combine like terms and equal to 0 in the remaining steps.
Brian glues together 4 wooden cubes as shown. Each cube has an edge of 5 centimeters. He covers the surface area of this new figure with metallic paper that is cut to size for each face.A. 125 square cm B. 150 square cm C. 450 square cm D. 600 square cm
Explanation:
The new figure is a square prism, with the sides that measure 4x5 = 20 cm.
We have to find the surface area of this prism. To do this we have to find the area of the rectangular faces and the area of the base, which is the same as the area of the top. The total surface area is 4 times the area of the rectangular face plus 2 times the area of the base/top.
[tex]A_{\text{rectangular face}}=20\operatorname{cm}\times5\operatorname{cm}=100\operatorname{cm}^2[/tex][tex]A_{\text{base}}=5\operatorname{cm}\times5\operatorname{cm}=25\operatorname{cm}^2[/tex][tex]\begin{gathered} S=4\cdot A_{\text{rectangular face}}+2\cdot A_{base} \\ S=4\cdot100\operatorname{cm}+2\cdot25\operatorname{cm}^2 \\ S=400\operatorname{cm}+50\operatorname{cm}^2 \\ S=450\operatorname{cm}^2 \end{gathered}[/tex]Answer:
C. 450 cm²
step by step on how to solve -6.43 - 22.3
The given expression is
[tex]-6.43-22.3[/tex]Given that the numbers have the same sign, we have to sum.
The result must be negative because both numbers are negative.
Hence, the result is -28.73.Answer:
-28.73.
Step-by-step explanation:
State the rule of the perfect squares given the sequence shown below that starts with n = 1 1, 4, 9, 16, 26...
Given:
the sequence shown below that starts with n = 1
[tex]1,4,9,16,25,\ldots[/tex]The rule of the sequence will be as follows"
The first term = 1, when n = 1
The second term = 4 = 2², when n = 2
The third term = 9 = 3², when n = 3
..
..
So, the rule will be:
[tex]a_n=n^2[/tex]A plastic candy container and its dimensions are shown in the figure.What is the closest to the value of the volume?
The volume of this composite figure is the sum of the volume of the cylinder and the cone.
Volume of Cylinder
The formula is
[tex]V=\pi r^2h[/tex]Where
V is the volume
r is the radius
h is the height
Given,
r = 5
h = 17.8
Substituting, we find the volume:
[tex]\begin{gathered} V=\pi r^2h \\ V=\pi(5)^2(17.8) \\ V=1398.01 \end{gathered}[/tex]Volume of Cone
The formula is:
[tex]V=\frac{1}{3}\pi r^2h[/tex]Where
V is the volume
r is the radius
h is the height
Given,
r = 5
h = 6.2
Substituting, we find the volume:
[tex]\begin{gathered} V=\frac{1}{3}\pi r^2h \\ V=\frac{1}{3}\pi(5)^2(6.2) \\ V=162.32 \end{gathered}[/tex]The total volume of the figure is:
1398.01 + 162.32 = 1560.33
Point M is the midpoint of segment QR. If QM = 2x + 5 and MR = 5x – 1, find the length of QR. QR = 18 QR = 9 QR = -9QR = 8
Asnwer:
QR = 18
Explanation:
If Point M is the midpoint of segment QR, then the following expressions are true
QM = MR and;
QM + MR = QR
Given
QM = 2x + 5 and MR = 5x – 1,
Recall that QM = MR
2x + 5 = 5x - 1
2x - 5x = -1-5
-3x = -6
x = -6/-3
x = 2
Get the length of QR
QR = QM + MR
QR = 2x+5 + 5x -1
QR = 7x +4
QR = 7(2) + 4
QR = 14+4
QR = 18
Hence the length of QR is 18
HELP graph the solution of system of linear inequality's
y< - 5x - 3
y>x+5
The graph of solution of system of linear inequality can be obtained by plotting the given equations and and then shading the region according to the inequality sign.
How to graph two linear inequality?
To graph Linear equations with inequality consider the equations as linear equation in two variable.Obtain two points for each line which satisfies the equations and plot them on graph. For example (1,6) and (-1,4) satisfies the equation y=x+5.Now shade the region according to the inequality: < : below the line> : above the lineHence you obtain the graph for the solution of system of the given linear equation with inequality.Any point in this region will satisfy both the linear inequalities (check the graph attached below).To know more about linear inequality visit
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Which expression is equivalent to 64 -1/2
A. 8
B. 8^2
C. 1/4
D. 1/8
The expression is 64 - 1/2 is equivalent to 127/2.
Given,
In the question:
Which expression is equivalent to 64 -1/2
Now, According to the question:
The ex[pression is given as:
64 - 1/2
Find common denominator and write the numerator above common denominator
[tex]= \frac{64 . 2}{2} - \frac{1}{2}[/tex]
Calculate the product or quotient:
128/2 - 1/2
Write the numerator over common denominator:
(128 - 1)/2
= 127/2
Hence, The expression is 64 - 1/2 is equivalent to 127/2.
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what is the whole number equal to 1000 / 4
In this case, the answer is very simple.
We must perform the division and verify that the result is a whole number.
1000 / 4 = 250 ===> 250 is a whole number
The answer is:
The number is 250 .
Answer:
250, hope this helped my love have a good rest of your day ^^
Step-by-step explanation:
if you simply devide 1000 by 4 then you get 250 wich yes , is indeed a whole number ^^
10. There is a carnival at a local state park. It cost $5 to get in and $1.50 per ride. .Suppose Maya Mapleton has $25 to spend for the day. Which inequality wouldmodel this situation?5+ 1.50x 2 255x + 1.50 s 255 + 1.50x s 2525x + 1.50 s 5
Let:
B = Maya's budget = $25
c = cost of the entrance = $5
a = cost of each ride = $1.50
x = number of rides
T = total money spent
Therefore:
[tex]\begin{gathered} T\le B \\ where_{} \\ T=c+ax \\ so\colon \\ 5+1.5x\le25 \end{gathered}[/tex]What is the equation of this line? Responses y=−2x y equals negative 2 x y = 2x y, = 2, x y=−1/2x y equals fraction negative 1 half end fraction x y=1/2x y equals 1 half x
The equation of line which shown in graph will be;
⇒ y = 2x
Option 3 is true.
What is Equation of line?The equation of line passing through the points (x₁ , y₁) and (x₂, y₂) with slope 'm' is defined as;
y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The graph for the equation of line is shown in figure.
Now,
Take two points on the line of the graph.
Two points are ( 1, 2) and (2, 4)
Find the slope of the line with two points (1, 2) and (2, 4) as;
⇒ m = (4 - 2) / (2 - 1)
⇒ m = 2 / 1
⇒ m = 2
Thus, The equation of line passing through the points (1, 2) and (2, 4) with slope 2 is;
⇒ y - 2 = 2 ( x - 1 )
⇒ y - 2 = 2x - 2
⇒ y = 2x - 2 + 2
⇒ y = 2x
Therefore,
The equation of line will be;
⇒ y = 2x
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10 Which number line represents the solution to the inequality -7x - 13 2 8?A-10-5НЕН1005B-10-50510с-10-50510D-10-50510оооо
The correct option is option A
Explanation:
First we solve the inequality:
-7x -13 ≥ 8
collect like terms:
-7x ≥ 8 + 13
-7x ≥ 21
Divide through by -7:
x ≤ 21/-7
Note: when you divde an inequality by negative number, the iequality sign changes.
x ≤ -3
Since x is less than or equal to -3, the number line starts at -3 and moves towards the left of the number line.
The correct option is option A
NO LINKS!! Show that the triangle with vertices A, B, and C is a right triangle.
Answer:
[tex][d(A, B)]^2=\boxed{85}[/tex]
[tex][d(A,C)]^2+[d(B,C)]^2=\boxed{85}[/tex]
[tex]\sf Area=\boxed{17}\; units^2[/tex]
Step-by-step explanation:
From inspection of the given diagram, the vertices of the triangle are:
A = (-5, 5)B = (1, -2)C = (-1, 6)If ΔABC is a right triangle, the sum of the squares of the two shorter sides will equal the square of the longest side. This is the definition of Pythagoras Theorem.
Use the distance formula to find the side lengths of the triangle.
[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]
[tex]\begin{aligned}d[(A,B)]&=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\&=\sqrt{(1-(-5))^2+(-2-5)^2}\\&=\sqrt{(6)^2+(-7)^2}\\&=\sqrt{36+49}\\&=\sqrt{85}\end{aligned}[/tex]
[tex]\begin{aligned}d[(A, C)]&=\sqrt{(x_C-x_A)^2+(y_C-y_A)^2}\\&=\sqrt{(-1-(-5))^2+(6-5)^2}\\&=\sqrt{(-4)^2+(1)^2}\\&=\sqrt{16+1}\\&=\sqrt{17}\end{aligned}[/tex]
[tex]\begin{aligned}d[(B, C)]&=\sqrt{(x_C-x_B)^2+(y_C-y_B)^2}\\&=\sqrt{(-1-1)^2+(6-(-2))^2}\\&=\sqrt{(-2)^2+(8)^2}\\&=\sqrt{4+64}\\&=\sqrt{68}\end{aligned}[/tex]
Therefore:
The longest side of the triangle is line segment AB.The two shorter sides of the triangle are line segments AC and BC.[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]
The triangle is a right triangle if:
[tex][d(A,C)]^2+[d(B,C)]^2=[d(A,B)]^2[/tex]
Substitute the found side lengths into the formula:
[tex]\implies [\sqrt{17}]^2+[\sqrt{68}]^2=[\sqrt{85}]^2[/tex]
[tex]\implies 17+68=85[/tex]
[tex]\implies 85=85[/tex]
Therefore, this proves that ΔABC is a right triangle.
To find the area of a right triangle, half the product of the two shorter sides:
[tex]\begin{aligned}\implies \sf Area &= \dfrac{1}{2}bh\\&=\dfrac{1}{2} \cdot [d(A,C)] \cdot [d(B,C)]\\&=\dfrac{1}{2} \cdot \sqrt{17} \cdot \sqrt{68}\\&=\dfrac{1}{2} \cdot \sqrt{17 \cdot 68}\\&=\dfrac{1}{2} \cdot \sqrt{1156}\\&=\dfrac{1}{2} \cdot \sqrt{34^2}\\&=\dfrac{1}{2} \cdot 34\\&=17 \sf \; units^2\end{aligned}[/tex]
Therefore, the area of the given triangle is 17 units².
What is the volume of this cylinder in terms of Pi? radius=2height=5a.5πb.10πc.20πd.50πWhat is the volume of this cylinder? radius=7height=11a.77 cubic cmb.241.9 cubic cmc.539 cubic cmd.1,693.32 cubic cmWhat is the volume of this cylinder in terms of Pi? radius=10height=20a.2000πb.500πc.200πd.100πWhat is the volume of this cylinder? radius=34height=27a.98,055.39 cubic metersb.2,883.98 cubic metersc.24,513.85 cubic metersd.1,441.99 cubic meters
What is the volume of this cylinder in terms of Pi?
Volume
How many meters of binding are required to bind the edge of a rectangular quilt that measures 5 m by 7 m?
Answer: 24
Step-by-step explanation: To find the perimeter, add all of the sides. 5+5=10 and 7+7=14. 10+14=24.
Answer:
24 m of binding required===============
GivenDimensions of rectangle 5 m and 7 m.Find its perimeterP = 2(l + w)P = 2(5 + 7) = 2(12) = 24 m18 is 32% of what number w? what is w?
Given: 18 is 32% of a number
To Determine: The number
Let the number be w. Therefore:
[tex]\begin{gathered} 32\%ofw=18 \\ \frac{32}{100}\times w=18 \end{gathered}[/tex][tex]\frac{32w}{100}=18[/tex][tex]\begin{gathered} 0.32\times w=18 \\ 0.32w=18 \end{gathered}[/tex]Divide both sides by 0.32
[tex]\begin{gathered} \frac{0.32w}{0.32}=\frac{18}{0.32} \\ w=56.25 \end{gathered}[/tex]Hence,
an equation is 18 = 0.32 . w
The solution is w = 56.25
I A family of G holds a ceremony to determine each child's favorite Teenage Mutant Ninja Turtle. The ceremony involves each child's results of choosing 10 numbers out of a hat. If Raphael, Michelangelo, Donatello, and Leonardo are represented with the numbers 1, 2, 3, and 4, respectively, which Teenage Mutant Ninja Turtle would become the favorite of a Child having the following results? Construct a 90% confidence interval estimate of the mean to develop the reasoning for your answer 2 21 4 3 3 3 3 11
Solution
Step 1
Write an expression for the mean
[tex]\bar{x}=\text{ }\frac{\sum ^{\square}_{\text{ of terms}}}{\text{mumber of terms}}[/tex][tex]\begin{gathered} \bar{x}=\frac{2+2+1+\text{ 4 +3+3+3+3}+4+1}{10} \\ \bar{x}=\text{ }\frac{26}{10} \\ \bar{x}=2.6 \end{gathered}[/tex]Step 2
Find the standard deviation
[tex]SD=\sqrt[]{\frac{\sum |x-\bar{x}|^2}{n}}[/tex][tex]SD=\sqrt[]{\frac{|2-2.6|^2+|2-2.6|^2+|1-2.6|^2+|4-2.6|^2+|3-2.6|^2+|3-2.6|^2+|3-2.6|^2+|3-2.6|^2+|4-2.6|^2+|1-2.6|^2}{10}}[/tex][tex]\begin{gathered} SD=\sqrt[]{\frac{0.36+0.36+2.56+1.96+0.16+0.16+0.16+0.16+1.96+2.56}{10}} \\ =\sqrt[]{\frac{10.4}{10}}\text{ =}\sqrt[]{1.04} \\ =1.02 \end{gathered}[/tex]Find the Z (confidence interval level) value for 90%
[tex]Z_{90}=1.645[/tex]Find the confidence interval
[tex]\begin{gathered} CI=\bar{x}\pm_{}_{}z\times\frac{s}{\sqrt[]{n}} \\ \bar{x}\Rightarrow\operatorname{mean} \\ s\Rightarrow\text{standard deviation} \\ n\Rightarrow\text{sample size} \\ z\Rightarrow\text{confidence level} \end{gathered}[/tex][tex]\begin{gathered} CI=2.6\pm1.645\times\frac{1.02}{\sqrt[]{10}} \\ =2.6\pm1.645\times0.32 \\ =2.6\pm0.53 \\ \text{Thus,} \\ CI=2.6+0.53\text{ 0r 2.6-0.53} \\ CI=3.13\text{ or 2.07} \end{gathered}[/tex]Hence, a 90% confidence interval estimate of the mean lies between 2 and 3
Therefore, either Michelangelo or Donatello