Answers
The height is modelled by the equation:
[tex]h(t)=-0.2t^2+2t[/tex]Therefore
[tex]\begin{gathered} \text{ } \\ \frac{\text{ dh}}{\text{ dt}}=-0.4t+2 \end{gathered}[/tex]At the maximum height dh/dt = 0:
Hence,
[tex]\begin{gathered} -0.4t+2=0 \\ -0.4t=-2 \\ \text{ Dividing both sides by -0.4} \end{gathered}[/tex][tex]\begin{gathered} \frac{-0.4t}{-0.4}=\frac{-2}{-0.4} \\ t=5 \end{gathered}[/tex]Hence, the ball gets to the maximum height after 5s.
The maximum height is given by h(5):
[tex]h(5)=-0.2(5)^2+2(5)=5[/tex]Therefore, the maximum height is 5 ft.
When the ball reaches the ground h(t) = 0:
[tex]\begin{gathered} -0.2t^2+2t=0 \\ \text{ Dividing both sides by -0.2, we have:} \\ t^2-10t=0 \\ Factorising\text{ the left hand side, we have} \\ t(t-10)=0 \\ \text{ Therefore,} \\ t=0,\text{ t=10} \end{gathered}[/tex]The ball reaches the ground in 10s
.
Related Questions
[tex](6.648 \times {10}^{9}) - (2.9 \times {10}^{7} )[/tex]I am confused on what to do with this problem.
Answers
Explanation:
[tex](6.648\times{10}^9)-(2.9\times{10}^7)[/tex]We need to factor out like terms in order to solve the above:
[tex]{10}^9=10^7\times10^2[/tex]Inserting the above into the expression:
[tex]\begin{gathered} (6.648\times{10}^7\times10^2)-(2.9\times{10}^7) \\ 10^{7\text{ }}\text{is common to both expressions} \end{gathered}[/tex][tex]\begin{gathered} (6.648\times{10}^7\times10^2)-(2.9\times{10}^7) \\ 10^7\lbrack(6.648\times10^2)-(2.9)\rbrack \end{gathered}[/tex][tex]\begin{gathered} 6.648\times10^2\text{ = }6.648\times100\text{ = }664.8 \\ 10^7(664.8-2.9)\text{ = }10^7(661.9) \\ 661.9\text{ = 6.619}\times10^2 \\ \end{gathered}[/tex][tex]undefined[/tex]Can you please help me with 46Also can you please use all 3 formsOf expression: ups/downs, as _,_ and limits
Answers
46.
[tex]f(x)=-x^3[/tex][tex]\begin{gathered} \lim _{x\to\infty}f(x)=-(\infty)^3=-\infty \\ \lim _{x\to-\infty}f(x)=-(-\infty)^3=-(-\infty)=\infty \end{gathered}[/tex]We can conclude that as x approaches to infinity the function tends to minus infinity and as x approaches to minus infinity the function tends to infinity
Finally we can conclude that as x increases the function goes down, and as x decreases the function goes up
I only have 5 minutes help me please and thank you
Answers
Given:
Statements are given.
Every parallelogram ia a rectangle. False
Evey quadrilateral is a rhombus. False
Evey rhombus with four right angles is a square. True
Every rectangle is a quadrilateral. True
The purchasing of 1,000 grocery shoppers are noted. No association is found between the variables. Fill in the empty portion of the table with values that would support this claim. Explain your reasoning.
Answers
Answer: We need to fill in the table with the values that are reasonably true:
Left-bottom-value
[tex]\text{Milk = 422-228=}194[/tex]Therefore this is the value for left-bottom:
Right-bottom-value
[tex]0[/tex]Because there is nothing bought, and the two values add up to 422:
Shen will rent a car for the weekend. He can choose one of two plans. The first plan has an initial fee of $57.98 and costs an additional $0.14 per mile driven. The second plan has an initial fee of $49.98 and costs an additional $0.18 per mile driven. How many miles would Shen need to drive for the two plans to cost the same?
Answers
Shen would need to drive for the 200 miles for two plans to cost the same.
Describe cost.Given a specified quantity of goods produced, a cost function is a mathematical formula that may be used to determine the overall cost of production. Below, the cost function will be thoroughly examined. a representation of unit costs that depend on how many units of one or more were produced during construction.
Given,
Let x be the number of additional mile
Plan 1
cost = $57.98 + 0.14x
Plan 2
Cost = $49.98 + 0.18x
Equating,
57.98 + 0.14x = 49.98 + 0.18x
57.98 - 49.98 = 0.18x - 0.14x
8 = 0.04x
x = 200
Shen would need to drive for the 200 miles for two plans to cost the same.
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Solve10/7- x = 0.1/0.01
Answers
Answer:
x = - 60/7 = 8.57
Explanation:
The initial expression is:
[tex]\frac{10}{7}-x=\frac{0.1}{0.01}[/tex]Now, we can solve the expression of the right side of the equation:
[tex]\frac{10}{7}-x=10[/tex]Then, add x to both sides of the equation:
[tex]\begin{gathered} \frac{10}{7}-x+x=10+x \\ \frac{10}{7}=10+x \end{gathered}[/tex]Finally, subtract 10 from both sides:
[tex]\begin{gathered} \frac{10}{7}-10=10+x-10 \\ \frac{10}{7}-10=x \\ \frac{10}{7}-\frac{10}{1}=x \\ -\frac{60}{7}=x \\ -8.57=x \end{gathered}[/tex]Therefore, the answer is x = -8.57
I need help working out this question, and I need to show the work!
Answers
Recall that, to compute the product of two fractions, we use the following rule:
[tex]\frac{a}{b}\times\frac{c}{d}=\frac{a\times c}{b\times d}\text{.}[/tex]Therefore,
[tex]\frac{1}{6}\times\frac{2}{5}=\frac{1\times2}{6\times5}\text{.}[/tex]Simplifying the above result, we get:
[tex]\frac{1}{6}\times\frac{2}{5}=\frac{2}{30}=\frac{1}{15}\text{.}[/tex]Answer:
[tex]\frac{1}{15}\text{.}[/tex]I need help with this problemfind the slope of the line
Answers
We are required to find the line that has the following properties:
[tex]\begin{gathered} \perp\text{ to y = -}\frac{1}{3}x\text{ - 6} \\ \text{passes through (-2, 8)} \end{gathered}[/tex]By definition, when two lines are perpendicular, the multiplication of their slopes gives -1 :
[tex]\begin{gathered} m\text{ }\times m_1=-1^{} \\ \text{Where m and m}_1\text{ are the slopes of the two lines}\perp\text{ to each other} \end{gathered}[/tex]From here, we can find the slope of the line.
let the slope of the line be x
[tex]\begin{gathered} x\text{ }\times\text{ -}\frac{1}{3}\text{ = -1} \\ x\text{ = 3} \end{gathered}[/tex]The slope-intercept form of the equation of the line is:
[tex]\begin{gathered} y\text{ = mx + c} \\ \text{Where m is the slope} \\ \text{and c is the intercept} \end{gathered}[/tex]But the slope is 3:
[tex]y\text{ = 3x + c}[/tex]To find the intercept(c), we substitute the point (-2,8) and solve for c:
[tex]\begin{gathered} 8\text{ = 3}\times-2\text{ + c} \\ c\text{ = 8+ 6} \\ c\text{ = 14} \end{gathered}[/tex]Hence, the equation of the line is:
[tex]y\text{ = 3x + 14}[/tex]Match each equation with the property used to rewrite it (2 points) 80 1 III 23.25 28 (32) "3 :: same base product *: power to a power :: same base quotient :: zero power Type here to search е е
Answers
Answer
Explanation
1)
(5⁵/5²) = 5³
This rule of indices is the same base quotient rule. If the same number raised to different powers is to be used to divide each other, the answer will be that same number raised to the power of the difference of those powers.
2)
8⁰ = 1
This rule is the zero power rule. Any number raised to the power of 0 is equal to 1.
3)
2³.2⁵ = 2⁸
This rule is the same base product rule. If the same number raised to different powers is to be multiplied by each other,
Use the properties of logarithms to expand logyz2.Each logarithm should involve only one variable and should not have any exponents. Assume that all variables are positive.
Answers
Solution:
Given:
[tex]log(yz^2)[/tex]Applying the property of logarithm;
[tex]log(AB)=logA+logB[/tex]Hence,
[tex]log(yz^2)=log\text{ }y+log\text{ }z^2[/tex]Also, applying the property of logarithm:
[tex]log\text{ }a^x=xlog\text{ }a[/tex]Hence,
[tex]log\text{ }y+log\text{ }z^2=log\text{ }y+2logz[/tex]Therefore,
[tex]log(yz^2)=log\text{ }y+2log\text{ }z[/tex]
Solve the following system of inequalities graphically on the set of axes below. State the coordinates of a point in the solution set.y ≥ - x + 3y > 2x - 6LABEL ALL COORDINATES
Answers
Answer:
The inequalities are given below as
[tex]\begin{gathered} y\ge-x+3 \\ y>2x-6 \end{gathered}[/tex]Step 1:
Calculate the x-intercept by putting y=0
[tex]\begin{gathered} y=-x+3 \\ 0=-x+3 \\ x=3 \\ (3,0) \end{gathered}[/tex]Calculate the y-intercept by putting x=0
[tex]\begin{gathered} y=-x+3 \\ y=-0+3 \\ y=3 \\ (0,3) \end{gathered}[/tex]The graph is given below as
Step 2:
Calculate the x-intercept by putting y=0
[tex]\begin{gathered} y=2x-6 \\ 0=2x-6 \\ 2x=6 \\ \frac{2x}{2}=\frac{6}{2} \\ x=3 \\ (3,0) \end{gathered}[/tex]Calculate the y-intercept by putting x=0
[tex]\begin{gathered} y=2x-6 \\ y=2(0)-6 \\ y=0-6 \\ y=-6 \\ (0,-6) \end{gathered}[/tex]The graph is given below as
Combing the two graphs, we will have
Hence,
The coordinate of the point in the solution set will be (3,5)
Triangle ABC has coordinates A(-3, 4), B(3, 2), and C(1, -2). Find the area of triangle ABC.
Answers
Step 1: Write out the formula for finding the area of traingle given the three coordinates
[tex]\begin{gathered} \text{say:} \\ A(x_1,y_1);B(x_2,y_2);C(x_3,y_3) \\ \text{Area}=\frac{1}{2}(x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2) \end{gathered}[/tex]Step 2: Write out the given parameters
[tex]\begin{gathered} A(-3,4);B(3,2);C(1,-2) \\ x_1=-3;y_1=4 \\ x_2=3;y_2=2 \\ x_3=1;y_3=-2 \end{gathered}[/tex]Step 3: Substitute the parameters into the formula
[tex]\begin{gathered} \text{Area}=\frac{1}{2}(-3(2--2)+3(-2-4)+1(4-2)) \\ =\frac{1}{2}(-3(4)+3(-6)+1(2)) \\ =\frac{1}{2}(-12-18+2) \\ =\frac{1}{2}(-28) \\ \text{Area}=\lvert-14\rvert \\ A=14 \end{gathered}[/tex]Hence, the area is 14square unit
What is the slope of a line passing through (4,4) and (6,10)
Answers
Answer:
The slope of the line is;
[tex]3[/tex]Explanation:
We want to find the slope of the line passing through the points;
[tex](4,4)\text{ and (6,10)}[/tex]Recall that the slope m of a line can be calculated using the formula;
[tex]m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}[/tex]substituting the given coordinates;
[tex]\begin{gathered} m=\frac{10-4}{6-4} \\ m=\frac{6}{2} \\ m=3 \end{gathered}[/tex]Therefore, the slope of the line is;
[tex]3[/tex]
6. Which table shows a geometric sequence? Term 1 23 4 5 Term 12 3 4 5 C Value 15 30 45 | 60 | 75 Value 918 27 36 45 Term 1 1 2 mo 4 5 Term 1 2 3 4 5 D Value 2 16 128 1024 8192 Value 220 260 300 340 380 7. Which Statement is TRUE? a. 1,-5, 25, -125, ... is a geometric sequence because to get to the next term, you multiply -5 times the previous term. b. 1, 8, 15, 22, 29, ... is a geometric sequence because to get to the next term, you multiply 8 times the previous term.
Answers
In a geomeric sequence each term is related to its previous by the product of a ratio. To find the ratio we need to divide each term by its previous and if the ratio is the same throughout the sequence, then it is a geometric sequence.
We need to check the ratio n the sequences.
A)
[tex]\begin{gathered} \frac{a_2}{a_1}=\frac{a_3}{a_2} \\ \frac{30}{15}=\frac{45}{30} \\ 2=1.5 \end{gathered}[/tex]The equation isn't valid, therefore this is not a geometric sequence.
B)
[tex]\begin{gathered} \frac{a_2}{a_1}=\frac{a_3}{a_2} \\ \frac{16}{2}=\frac{128}{16} \\ 8=8 \end{gathered}[/tex]The equation is valid, so the sequence is a geometric sequence. This is the correct answer.
Luke started a weight-loss program. The first week, he lost X pounds. the second week he lost 3/2 pounds less then 3/2 times the punds he lost the first week. The third week, he lost 1 more pound than 3/4 of the pounds he lost the first week.Liam started the program when luke did. The first week, he lost 1 pound less than 3/2 times the pounds luke lost the first week. The second week, he lost 4 pounds less than 5/2 times the pounds luke lost the first week. The third week, he lost 1/2 more than 5/4 times the pounds luke lost the first week. Assuming they both lost the same number of pounds over the three weeks, complete the following sentences1. The expression for luke's weight loos over the three weeks is ______2. The expression for liam's weight loss over the three weeks is ______3. The number of pounds luke lost in the fist week is ____4. The number of pounds luke and liam each lost over the three weeks is ____And the answer bank has2 pounds13/4x-1/28/4x-9/221/4x-9/24 pounds 6 pounds
Answers
Luke started a weight-loss program.
The first week, he lost X pounds.
the second week he lost 3/2 pounds less then 3/2 times the pounds he lost the first week. so, he lost 3/2 x - 3/2
The third week, he lost 1 more pound than 3/4 of the pounds he lost the first week. so, he lost 3/4 x + 1
So, over 3 weeks he lost :
x + (3/2 x - 3/2) + (3/4 x + 1) = 13/4 x - 1/2
=========================================================
Liam started the program when Luke did.
The first week, he lost 1 pound less than 3/2 times the pounds luke lost the first week. so, he lost (3/2 x - 1)
The second week, he lost 4 pounds less than 5/2 times the pounds luke lost the first week. so ,he lost (5/2 x - 4)
The third week, he lost 1/2 more than 5/4 times the pounds luke lost the first week. so, he lost, ( 5/4 x + 1/2)
The expression for Liam's weight loss over the three weeks is =
= (3/2 x - 1) + (5/2 x - 4) + ( 5/4 x + 1/2) = 21/4 x - 9/2
=============================================================
Assuming they both lost the same number of pounds over the three weeks
So, equating the number of pounds lost by each one of them
so,
13/4 x - 1/2 = 21/4 x - 9/2
solve for x
13/4 x - 21/4 x = -9/2 + 1/2
-2x = -4
divide both sides by -2
so,
x = -4/-2 = 2
so,
The number of pounds luke lost in the fist week is 2 pounds
=============================================================
4. The number of pounds luke and liam each lost over the three weeks is
= 13/4 * 2 - 1/2 = 6 pounds
WebConnect 3270myGalaxyLogon2 ClassesCollege BoardinfoSolving for a side: exampleSolve to the nearest tenth7214с
Answers
Let's begin by identifying the information given to us:
BC = 14, AC = x
Angle B = 72°
We have one known side, one known angle & one unknown side. As such, we will use Trigonometric Ratio (SOHCAHTOA)
tan 72° = opposite/adjacent
tan 72° = x/14
x = 14 × tan 72°
x = -3.67 ≈ -3.7
diagrams are not drawn to scale. find y. all i care about is the answers & the steps you did to find the answer.
Answers
Answer:
The value of y is;
[tex]y=65^{\circ}[/tex]Explanation:
Let x represent the angle formed by the two secants supplementary to angle y.
Recall that the angle formed by two intercepting secants is equal to half the sum of the intercepted arcs.
[tex]\begin{gathered} x=\frac{1}{2}(170+60) \\ x=\frac{1}{2}(230) \\ x=115^{\circ} \end{gathered}[/tex]Since x is supplementary to y then;
[tex]\begin{gathered} x+y=180^{\circ} \\ y=180^{\circ}-x \\ y=180^{\circ}-115^{\circ} \\ y=65^{\circ} \end{gathered}[/tex]Therefore, the value of y is;
[tex]y=65^{\circ}[/tex]The Equations for the asymptotes for a hyperbola with a horizontal transverse axis are given by:y equals k plus or minus b over a times the quantity of x minus hTrueFalse
Answers
True, The given equation for the asymptotes for a hyperbola with horizontal transverse axis is y = k ± (b/a) (x - h).
Define Hyperbola
The collection of all points along a hyperbola such that the difference in distance between any point along the hyperbola and two fixed locations is constant is known as the hyperbola. The foci of the hyperbola are the two fixed points.
The standard equation for a hyperbola with a horizontal transverse axis is
(x - h)² / a² - (y - k)² / b² = 1
The distance between the vertices is 2a.
Every hyperbola has two asymptotes
A hyperbola with a horizontal transverse axis and center at (h, k) has one asymptote with equation
y = k + (b/a) (x - h)
and the other with equation
y = k - (b/a) (x - h)
Therefore, the answer is True.
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Find the product.-2xa(-4xb - 2x 3 + 5x)
Answers
-2x^a ( -4x^b -2x^3 + 5x)
We need to distribute the term on the left to each term inside the parentheses
-2x^a * -4x^b -2x^a ( -2x^3) -2x^a *5x
8x^a *x^b +4x^a*x^3 -10x^a *x
Since the bases are the same and we are multiplying, we can add the exponents
8x^(a+b) + 4 x^(a+3) -10 x^(a+1)
15. A ball shaped like a sphere has a radius of 2.8 centimeters. Which measurement is closest to the volume of the ball in cubic centimeters? A) 215.2 cm C) 92 cm B) 107.6 cm D) 253.9 cm
Answers
We know that the volume of a sphere is given by the following equation:
[tex]Volume=\frac{4}{3}\pi r^3[/tex]where π and r are numbers: π is pi and r is the radius.
Since
π = 3.14
and
r = 2.8 cm, then
[tex]\begin{gathered} Volume=\frac{4}{3}\pi r^3 \\ \downarrow \\ Volume=\frac{4}{3}\cdot3.14\cdot(2.8\operatorname{cm})^3 \end{gathered}[/tex]Since
(2.8 cm)³ = 21.952 cm³,
[tex]\begin{gathered} Volume=\frac{4}{3}\cdot3.14\cdot(2.8\operatorname{cm})^3 \\ \downarrow \\ Volume=\frac{4}{3}\cdot3.14\cdot21.952\operatorname{cm}^3 \\ \downarrow \\ Volume=91.9\operatorname{cm}^3 \end{gathered}[/tex]Since 91.9 is very near to 92, then
91.9 cm³ ≅ 92 cm³
Answer: C. 92 cm³amount as a single fraction and as a mixed number. One Fraction: Mixed Number:
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You take each circle as a unit and each part in the circle as 1/12:
One fraction: The shaded area is 20/12 (you can simplify the fraction):
[tex]\frac{20}{12}=\frac{10}{6}=\frac{5}{3}[/tex]Mixed number: The shaded are is 1 unit and 8/12 (you can simplify the fraction):
[tex]1\frac{8}{12}=1\frac{4}{6}=1\frac{2}{3}[/tex]Consider the following functions. Find five ordered pairs that satisfy the function, g(x)=x^2-5
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Evaluate for different values of x:
[tex]\begin{gathered} x=0 \\ g(0)=0^2-5=-5 \\ ------------- \\ x=1 \\ g(1)=1^2-5=-4 \\ ------------- \\ x=2 \\ g(2)=2^2-5=-1 \\ ------------- \\ x=3 \\ g(3)=3^2-5=4 \\ ------------- \\ x=4 \\ g(4)=4^2-5=11 \end{gathered}[/tex]Therefore:
[tex]\mleft\lbrace(0,-5\mright),(1,-4),(2,-1),(3,4),(4,11)\}[/tex]Please help me with this quickly, I have till 11:59 but still have one more hard question, please make it simple and easy
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Given:
Distance traveled for upstream = 60 km
Time taken for upstream = 5 hours
Distance traveled for downstream = 60 km
Time taken for downstream = 3 hours
Required:
The rate of the boat in the still water.
Explanation:
Let x be the speed of the water and y be the speed of the current.
For upstream , the speed is given as
[tex]x\text{ + y}[/tex]For downstream, the speed is given as,
[tex]x\text{ - y}[/tex]Now,
[tex]Distance\text{ = speed }\times\text{ time}[/tex]Therefore,
[tex][/tex]Answer:
30000
Step-by-step explanation:
60×1000=60000
60000×3=180000
Pam baked some cupcakes for her friends. Each cupcake is 2/15. If she packed 6 cupcakes in each box, what is the weight of each box?
Answers
Answer:
The weight of each box is 4/5.
Step-by-step explanation:
To determine the weight of each box, multiply the weight of each cupcake by the capacity of the box:
[tex]6\cdot\frac{2}{15}=\frac{4}{5}\text{ }[/tex]The weight of each box is 4/5.
The hardware store sells batteries individually. Five batteries cost $4.50, and sevenbatteries cost $6.30.Use the information above to write two ordered pairs
Answers
A ordered pair is given by (x, y)
So,
Let x be the number of batteries, and
Let y be the cost
The ordered pairs would be:
(5, 4.50)
(7, 6.30)
A family has two cars. The first car has a fuel efficiency of 20 miles per gallon of gas and the second has a fuel efficiency of 35 miles per gallon of gas. Duringone particular week, the two cars went a combined total of 925 miles, for a total gas consumption of 35 gallons. How many gallons were consumed by each ofthe two cars that week?Note that the ALEKS graphing calculator can be used to make computations easier.
Answers
Given:
Fuel efficiency of the first car = 20miles/gallon of gas
Fuel efficiency of the second car = 35 miles/gallon of gas
Total miles covered on a particular week = 925 miles
Total gas consumed = 35 gallons
Solution
Let the gallons of gas consumed by the first car is x, and the gallons of gas consumed by the second car be y.
From the last information, we have:
[tex]x\text{ + y = 35}[/tex]The distance covered by the first car in the said week is:
[tex]\begin{gathered} =\text{ 20 }\frac{miles}{gallon}\text{ }\times\text{ x gallons} \\ =\text{ 20x miles} \end{gathered}[/tex]The distance covered by the second car in the said week is:
[tex]\begin{gathered} =\text{ 35 }\frac{miles}{gallon}\text{ }\times\text{ y gallons} \\ =\text{ 35y miles} \end{gathered}[/tex]From the third statement, we have:
[tex]20x\text{ + 35y = 925 }[/tex]To obtain x and y, we can solve the equations simultaneously
[tex]\begin{gathered} x\text{ + y = 35} \\ 20x\text{ + 35y = 925} \end{gathered}[/tex]Solving simultaneously, we have:
[tex]x\text{ = 20 , y = 15}[/tex]Answer:
First car: 20 gallons
Second car: 15 gallons
Which graph shows the following inequality?To get a “B” in English class, you must have an 85% or higher, but less than a 93%.a.+ C.83 84 85 86 87 88 89 90 91 92 93 94+83 84 85 86 87 88 89 90 91 92 93 94b.4+83 84 85 86 87 88 89 90 91 92 93 94at d.+ +90 91+83 84 85 8687 88899293 94
Answers
Let x be the B result of the english test
So, the inequality would be represented as follows:
To get a “B” in English class=85%≤x<93%
Therefore, the graph that shows the following inequality above would be the graph b because it is highlighted there that To get a “B” in English class, you must have an 85% or higher, but less than a 93%.
What is the probability of drawing either a diamond or an ace from a deck of cars
Answers
In a regular deck, there are 52 cards from which 4 are aces (one of these aces belongs to the diamond type) and 13 are diamond cards.
Finally, the probability of drawing an ace or a diamond card is (13+3)/52.
Answer: 30.76% (or 0.3076)
The average life of an automobile tire of a certain manufacturer follows a Normal distribution, with a mean of 32,000 miles and a standard deviation of 1,250.
Use the z-table to answer the question.
What tire life span separates the upper 30% of the life spans from the lower 70% of the life spans?
31,344 miles
32,650 miles
32,875 miles
33,250 miles
Answers
The option that gives the tire life span that separates the upper 30% of the life spans from the lower 70%, obtained from the Z-table is 32,650 miles.
What is the Z-table?The Z-score table, gives the probability values of the likelihood that a z-value will be within a region of a normal distribution.
The given parameters are;
The given mean of the average life span of the automobile = 32,000 miles
The standard deviation = 1,250
The score at the upper 30% is given by the equation for the z-score; [tex]\displaystyle{z = \frac{x - \mu}{\sigma} }[/tex], which from the z-score table gives at point at a probability of 1 - 0.3 = 0.7, gives z ≈ 0.52;
The x-value is therefore, [tex]\displaystyle{0.52 = \frac{x - 32000}{1250} }[/tex], which gives, x = 32,650
Checking the value at 70%, from the Z-table gives, z ≈ 0.53, which gives, [tex]\displaystyle{0.52 = \frac{x - 32000}{1250} }[/tex], therefore;
0.52 × 1250 = x - 32000
x = 32000 + 0.52 × 1250 = 32,650
The tire life span that separates the upper 30% from the lower 70% is given by the z-score at 70% = 0.7, from which the tire life span is 32,000 miles
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Find the volume of the con to the nearest 10th period used three. 144 PI. In the last box, type the exponent for the label.
Answers
SOLUTION
From the question given,
The radius r is
[tex]r=\frac{diameter}{2}=\frac{8}{2}=4[/tex]Hence the radius of the cone is 4 in.
The height of the cone is the perpendicular height you see which is 10 in.
Hence the height of the cone is 10 in.
Volume of a cone V is given by the formula
[tex]\begin{gathered} V=\frac{1}{3}\pi\text{r}^2h \\ where\text{ r = radius = 4 in.} \\ h=\text{ height = 10 in } \\ \pi=3.14 \end{gathered}[/tex]Solving we have
[tex]\begin{gathered} V=\frac{1}{3}\times3.14\times4^2\times10 \\ V=\frac{1}{3}\times3.14\times16\times10 \\ V=167.4666 \\ V=167.5\text{ in}^3\text{ to the nearest tenth } \end{gathered}[/tex]Hence Volume of the cone is
[tex]V=167.5\text{ in}^3\text{ }[/tex]So write it as 167.5 in 3
