The top-selling Red and Voss tire is rated 60000 miles, which means nothing. In fact, the distance the tires can run until wear-out is a normally distributed random variable with a mean of 72000 miles and a standard deviation of 7000 miles.A. What is the probability that the tire wears out before 60000 miles?Probability = What is the probability that a tire lasts more than 80000 miles? Probability=
Answers
a. 0.0436
b. 0.1271
We are given the following:
Distance (x) = 60,000
Mean (u) = 72,000
Standard Deviation(s) = 7,000
We are also told that it is a normal disribution relationship. The formula for ND is as follows:
z = (x - u) / s
Now we can continue with part a and b as follows:
a) P (x < 60,000)
= P (z < (60000 - 72000) / 7000)
= P (z < -1.714)
We can find the corresponding z score by looking at a z score table, and we find th probability to be 0.0436
b) P ( x > 80,000)
= P(z > (80000 - 72000) / 7000)
= P( z > 1.143)
We find the corresponding z score to be 0.8729, now we can substract this from 1 sinsce our probability is larger than the given distance (meaning we are trying to find the area to the right of the z score) to find our final answer:
1 - 0.8729 = 0.1271
Related Questions
Explain how you know 437,160 is greater than 43,716.4 grade student
Answers
437,160 is read as four hundred thirty-seven thousand one hundred sixty and 43,716 is read as fourty-three thousand seven hundred sixteen.
The first number has hundreds of thousand and the second one only has tens of thousand. It means that the first number is greater than the second one.
Another way to know this is because of the number of figures before the decimal point. The first number has 6 figures before the decimal point and the second one only has 5.
That way, we know that 437,160 is greater than 43,716.
Complete the table for y=-3x + 5 and graph the resulting line. -
Answers
We fill the table as follows:
*We assign values for x and solve for y, that is:
*x = 0:
[tex]y=-3(0)+5\Rightarrow y=5[/tex]So, the value of y when x = 0 is 5.
*x = 1:
[tex]y=-3(1)+5\Rightarrow y=2[/tex]So, the value of y when x = 1 is 2.
*x = 2:
[tex]y=-3(2)+5\Rightarrow y=-1[/tex]So, the value of y when x = 2 is -1.
*x = 3:
[tex]y=-3(3)+5\Rightarrow y=-4[/tex]So, the value of y when x = 3 is -4.
***The table should look like this:
x | y
0 | 5
1 | 2
2 | -1
3 | -4
***The graph is:
A 33-inch piece of steel is cut into three pieces so that the second piece is twiceas long as the first piece, and the third piece is one inch more than five times thelength of the first piece. What is the length of the first piece?
Answers
Let;
x = the length of the first piece
y=the length of the second piece
z=the length of the third piece
From the question;
"the second piece is twice as long as the first piece" can be written in equation as:
y = 2x
"the third piece is one inch more than five times the length of the first piece"
can be written as :
z= 5x+ 1
Total length of the 3 pieces = 33
This implies:
x + y + z =33
substitute y=2x and z=5x+1 into the above
x + 2x + 5x+1 = 33
8x + 1 = 33
subtract 1 from both-side of the equation
8x = 33 -1
8x = 32
divide both-side of the equation by 8
x= 32/8
x= 4
The length of the first piece is 4-inches
find the x value (6x+9)° (4x-19)°
Answers
In this problem m and n are parallel lines, and the first angle is an exteriar angle an the secon is a interior angle.
this two condition give us that the two angles are complementary anlges so the sum of them should be 180 so:
[tex]6x+9+4x-19=180[/tex]and we can solve for x so:
[tex]\begin{gathered} 10x-10=180 \\ 10x=180+10 \\ x=\frac{190}{10} \\ x=19 \end{gathered}[/tex]A train travels at 100 mph any equation can be written that compares the time with the distance to find the domain and range
Answers
ok
speed = distance / time
time = distance/speed
[tex]\text{ time = }\frac{dis\tan ce\text{ }}{speed}[/tex][tex]\text{ time = }\frac{dis\tan ce\text{ }}{100}[/tex]or
[tex]\text{ distance = 100 x time}[/tex]Hi, can you help me to solve this problem please!
Answers
We have the following function
[tex]f(x)=7+6x[/tex]Now, we must replace the variable x by the given value, that is,
[tex]f(10)=7+6(10)[/tex]which gives
[tex]\begin{gathered} f(10)=7+60 \\ f(10)=67 \end{gathered}[/tex]Therefore, the answer is f(10)=67
Is (6, –21) a solution to the equation y = –5x − –9?
Answers
Answer:
Explanation:
Given the equation:
[tex]y=-5x-(-9)[/tex]When x=6:
he multiplication table below can be used to find equivalent ratios.
A multiplication table.
Which ratio is equivalent to the ratio 18:24?
15:20
20:15
30:36
36:30
Answers
Answer:
15:20
Step-by-step explanation:
18:24 can be written [tex]\frac{18}{24}[/tex] if I simplify this by dividing the top and bottom by 6, I get [tex]\frac{3}{4}[/tex]
I am looking for what other ration will reduce to [tex]\frac{3}{4}[/tex]
[tex]\frac{15}{20}[/tex] Divide the top and bottom by 5 and you will get [tex]\frac{3}{4}[/tex]
A 14 m long ladder is placed against a tree. The top of the ladder reaches a point
13 m up the tree.
How far away is the base of the ladder from the base of the tree?
Give your answer in metres (m) to 1 d.p.
Answers
Answer:
Approximately 5.2 meters
Step-by-step explanation:
This formation will make a right triangle. The ground to the point in the tree is one of the legs. The base of the tree to the base of ladder is another leg and the length of the ladder is the hypotenuse. In this case, we already have the hypotenuse and one of the legs, so we need to find the value of another leg.
We can do so by using the Pythagorean Theorem which is [tex]a^2+b^2=c^2\\[/tex].
a and b represent the values of the two legs, and c is the hypotenuse. Since we already have the hypotenuse, we can change this equation a bit to find the other leg.
Let's assign the missing value, b in the theorem.
The new equation will be [tex]b^2=c^2-a^2[/tex].
We can insert the values for c and a and solve for b.
The new equation will be [tex]b^2 = 14^2-13^2[/tex].
[tex]b^2=196-169[/tex]
[tex]b^2=27[/tex]
[tex]\sqrt{b^2} =\sqrt{27}[/tex]
The square root of [tex]b^2[/tex] cancels out.
The approximate square root of 27 is 5.19 which we can round to 5.2.
use and show all conversion factors to convert 352 inches per second to miles per hour. 352 inches divided by 1 second
Answers
Okay, here we have this:
We need to convert 352 inches per second to miles per hour. So we obtain the following:
[tex]\begin{gathered} \frac{352in}{1sc}\cdot\frac{1mile}{63360in}\cdot\frac{3600sc}{1h} \\ =\frac{20\text{miles}}{h} \end{gathered}[/tex]Finally we obtain that 352 inches per second 20 are miles per hour.
omg i lost my tutor in the middle of math i need another one btw in fith grade not in middle school yet
Answers
by definition the division of fractions can be found by
[tex]\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{b\cdot c}{a\cdot d}[/tex]According to this
[tex]\frac{\frac{6}{10}}{\frac{1}{5}}=\frac{6\cdot5}{10\cdot1}=\frac{30}{10}=3[/tex]Which phrase represents this expression?
5 + 4 ÷ 2
Responses
the product of 5 and the quotient of 4 and 2
the product of 5 and the quotient of 4 and 2
the product of 5 and 4 is divided by 2
the product of 5 and 4 is divided by 2
the sum of 5 and 4 is divided by 2
the sum of 5 and 4 is divided by 2
the sum of 5 and the quotient of 4 and 2
Answers
Reason
According to the PEMDAS rule, we multiply and divide before add and subtract
So we find the “quotient” or divide 4 by 2 first. Then we add 5 to the quotient which is a “sum” of 5 and quotient
Figure RSTU has coordinates R = (3,4), S = (7.2), T = (5, 10), and U = (12,8). The figure is dilated from the origin by a scale factor r . Select the correct coordinates of R. A R' = (3,2) B R' = (1.5, 4) C R' = (3.5, 4.5) D R' = (1.5, 2) * Select the correct answer. 1 point Ο Α OB D
Answers
Answer
Option D is correct.
R' (1.5, 2)
Explanation
A dilation means the size is increased or decreased. If the scale factor is less than 1, then the size is decreased, but if the scale factor is more than 1, it means the figure is enlarged.
Dilating about the origin just multiplies the coordinates by the scale factor. So, dilating (x, y) about the origin by a scale factor k, gives new coordinates (kx, ky).
For this question, we need to dilate R (3, 4) by a scale factor, r = ½
R' = [½(3), ½(4)] = (1.5, 2)
Hope this Helps!!!
Marcy baked 132 cookies . She is packaging boxes of eight cookies to give as a gift to he friends how many boxes will she make .
Answers
She will make 16 boxes.
To answer this question we simply have to divide the number of cookies (132) by the number of cookies that each box can contain.
Mathematically speaking:
[tex]132/8\text{ }[/tex][tex]16.5[/tex]Since we can´t have half boxes, we have to round the number to 16.
16 boxes.
what does this mean i dont get it please help me thanks, :)
Answers
It means that you are supposed to group The like terms together and simplify them
you will find that 2t is the liketerm with -5t and -u is a like term with -6u
As a results we have
[tex] = 2t - 5t - u - 6u \\ = - 3t - 7u[/tex]
as indicated I have shown you the answer .
good luck
Jordan plotted the graph below to show the relationship between the temperature of his city and the number of cups of hot chocolate he sold daily:A scatter plot is shown with the title Jordans Hot Chocolate Sales. The x axis is labeled High Temperature and the y axis is labeled Cups of Hot Chocolate Sold. Data points are located at 20 and 20, 30 and 18, 40 and 20, 35 and 15, 50 and 20, 45 and 20, 60 and 14, 65 and 18, 80 and 10, 70 and 8, 40 and 2.Part A: In your own words, describe the relationship between the temperature of the city and the number of cups of hot chocolate sold. (2 points)Part B: Describe how you can make the line of best fit. Write the approximate slope and y-intercept of the line of best fit. Show your work, including the points that you use to calculate the slope and y-intercept. (3 points)
Answers
A.
Overall it has a relation that there are more sold cups when the temperature is lower. On the other hand, based on the 40 degrees part, that have to different values of two different days, we can say is not the only factor.
B.
The best lineal approach is the line created with the points at 20 and 80 degrees. First the slope:
[tex]m=\frac{y1-y2}{x1-x2}=\frac{20-10}{20-80}=\frac{10}{-60}=-\frac{1}{6}[/tex]Now the intercept with y axis, b:
[tex]\begin{gathered} y=mx+b \\ 20=20(-\frac{1}{6})+b \\ 20+\frac{20}{6}=b=23.33=\frac{70}{3} \end{gathered}[/tex]The final line formula is:
[tex]y=-\frac{x}{6}+\frac{70}{3}[/tex]how can you use the vertical line test and the horizontal line test to determine whether a graph represents a function and whether the graph is invertible?
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
vertical line test = ?
horizontal line test = ?
Step 02:
vertical line test ===> function
any vertical line intersect the graph at only one point
horizontal line test ===> invertible
any horizontal line intersect the graph at only one point
graph:
horizontal line test = red
vertical line test = brown
That is the full solution.
1. what is the area of the board shown on the scale drawing? explain how you found the area.2. how can Adam use the scale factor to find the area of the actual electronics board? remember, he uses a different method than Jason.3. what is the area of the actual electronics board?
Answers
Answer:
1. 1800 square cm.
2. See below
3. 45000 square cm.
Explanation:
Part 1
The dimensions of the drawing are 36cm by 50cm.
[tex]\begin{gathered} \text{The area of the board}=36\times50 \\ =1800\operatorname{cm}^2 \end{gathered}[/tex]Part 2
Given a scale factor, k
If the area of the scale drawing is A; then we can find the area of the actual board by multiplying the area of the scale drawing by the square of k.
Part 3
[tex]\begin{gathered} \text{Area of the scale drawing}=1800\operatorname{cm}^2 \\ \text{Scale Factor,k=5} \end{gathered}[/tex]Therefore, the area of the actual drawing will be:
[tex]\begin{gathered} 1800\times5^2 \\ =45,000\operatorname{cm}^2 \end{gathered}[/tex]The height of a pole is 15 feet. A line with banners is connected to the top of the poleto a point that is 8 feet from the base of the pole on the ground. How long would theline with banners need to be in order for the pole to be at a 90° angle with the ground?Explain your reasoning.
Answers
In order to have a 90º angle (right angle) the length of the line with banners needs to fullfit the Pythagorean theorem: In a right triangle the squared hypotenuse is equal to the sum of the legs squared:
[tex]h^2=l^2+l^2[/tex]In the given situation the hypotenusa is the line with banners, and the legs are the pole and the 8ft ground from the base of the pole to the end of the line with banners:
h= x
l= 15ft
l= 8ft
[tex]x^2=(15ft)^2+(8ft)^2[/tex]Solve the equation to find the value of x:
[tex]\begin{gathered} x^2=225ft^2+64ft^2 \\ x^2=289ft^2 \\ x=\sqrt[]{289ft^2} \\ x=17ft \end{gathered}[/tex]Then, to make a right triangle the length of the line witg banners need to be 17ftWhat is the measure of ?ХvO A. 46°42°42"38°NуvO B. 42°O C. 40°O D. 38°
Answers
The value Z is denoted as the center of the circle. Therefore, arc UV and arc XY should be the same .
[tex]undefined[/tex]Answer: A. 42°
Step-by-step explanation:
Hope this helps :)
9. If L 1 equals 120 then what is the measure of its supplement <2=
Answers
Supplementary angles are angles whose addition sums up to 180 degrees.
Therefore, if angle 1 measures 120, then its supplement which is angle 2, must mean both add up to 180.
Hence, you have
Angle 1 + Angle 2 = 180
120 + Angle 2 = 180
Subtract 120 from both sides of the equation
Angle 2 = 180 - 120
Angle 2 = 60 degrees
By definiton, two angles are complimentary angles if they both add up to 90 degrees. Hence if angle L5 equals 50 degrees, then its compliment would be derived as 90 - 50 which equals 40. The compliment of angle L5 which is 50 degrees, equals 40 degrees.
how many pennies are in a dollar
Answers
Answer: 100
Step-by-step explanation:
$1 =100 pennies
Function g is a transformation of the parent function exponential function. Which statements are true about function g?
Answers
For the given function, The following are true statements:
Four units separate function g from function f.There is a y-intercept for function g. (0,4)Function g has a range of (3,∞ ).Over the range (-, ∞), function g is positive.It may be seen from the graph below that
The g function's graph is 4 units higher than the parent exponential function's graph.
All of the input values for which the function is defined are referred to as the function's domain. The domain of the function is (-, ∞ ) according to the graph of function g.
The location where a function's graph crosses the y-axis is known as the y-intercept. G's graph crosses the y-axis at (0, 4). As a result, the Function g's y-intercept is (0,4).
growing function g across the range (- ∞, 0).
Function output values are referred to as the function's range. It can be seen from the graph that the range of function g is (3, ∞ ).
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On a 7 question multiple-choice test, where each question has 2 answers, what would be the probability of getting at least one question wrong?Give your answer as a fraction
Answers
Solution
- This is a Binomial probability question. The formula for Binomial probability is:
[tex]\begin{gathered} P(r)=\sum\text{ }^nC_rp^rq^{n-r} \\ where, \\ n=The\text{ total number of trials} \\ r=\text{ The number of successful trials\lparen where answer is correct\rparen} \\ p=\text{ The probability of success \lparen The probability of getting a question } \\ right) \end{gathered}[/tex]- We have been given:
[tex]\begin{gathered} n=7 \\ \text{ since there can only be two answers, it means that the} \\ \text{ probability of getting a question correct is:} \\ p=\frac{1}{2} \\ q=1-p=\frac{1}{2} \\ \\ \text{ The probability of getting at least 1 question wrong means the } \\ probability\text{ of getting 1, 2, 3, 4, 5, 6, or 7 question wrong.} \\ \\ \text{ Instead of calculating all these probabilities, we can simply say} \\ P(1)+P(2)+P(3)+P(4)+P(5)+P(6)+P(7)=1-P(0) \end{gathered}[/tex]- Thus, we have:
[tex]\begin{gathered} P(0)=^7C_0(\frac{1}{2})^0(\frac{1}{2})^7 \\ P(0)=\frac{1}{128} \\ \\ 1-P(0)=1-\frac{1}{128}=\frac{127}{128} \end{gathered}[/tex]Final Answer
The answer is
[tex]\frac{127}{128}[/tex]A toy car that is 0.5 ft long is used to model the actions of an actual car that is 15 ft long. Which ratio shows the relationship between the sizes of the model and the actual car? A. 2:5 B. 5:2 C. 30:1 D. 1:30
Answers
A toy car that is 0.5 ft long is used to model the actions of an actual car that is 15 ft long. Which ratio shows the relationship between the sizes of the model and the actual car?
A. 2:5
B. 5:2
C. 30:1
D. 1:30
_____________________
0.5 ft the toy car: 15 the actual car
0.5*2 =1
15 *2 = 30
1: 30
_____________________________________
The ratio1:30 shows the relationship between the sizes of the model and the actual car
____________
Do you have any questions regarding the solution?
b. Write
√x
as a single radical in simplest form.
5√x
Answers
Answer:
(tenth root of x to the third power)
see image
Step-by-step explanation:
To do this problem you need to know how to convert radicals to an expression with a fraction exponent(and back to radicals again), ALSO exponent rules for division ALSO subtracting fractions.
Square root x can be written as x^ 1/2
fifth root x can be written as x^ 1/5
When you are dividing expressions with the same base, exponent rules say to SUBTRACT the exponents.
1/2 - 1/5 change to common denominator
5/10 - 2/10
= 3/10
x^1/2 / x^1/5 =
x^ (1/2 - 1/5) =
x^ (5/10-2/10) =
x^ 3/10
Then change back to a radical. Remember "down and out" or "roots are down" and "up, up, up" or "exponents are up"
the number down below goes out (outside) the radical. And the number up top is up and exponents are up, up, up
see image.
x^3/10 =
tenth root (x^3)
see image.
Solve each equation for the variable. h/2 + 3.5 = 7.1
Answers
To answer this question, we can proceed as follows:
[tex]\frac{h}{2}+3.5=7.1[/tex]1. Subtract 3.5 to both sides of the equation:
[tex]\frac{h}{2}+3.5-3.5=7.1-3.5\Rightarrow\frac{h}{2}+0=3.6[/tex]2. Multiply by 2 to both sides of the equation:
[tex]2\cdot\frac{h}{2}=2\cdot3.6\Rightarrow h=7.2[/tex]We can check this result as follows:
[tex]\frac{7.2}{2}+3.5=3.6+3.5=7.1\Rightarrow7.1=7.1[/tex]This result is TRUE. Then, the value for h = 7.2.
helppppppppppppppppppppppppppp
Answers
Step-by-step explanation:
make the fractions decimals and put them on the plot
HELP PLEASEEEEE!!!!!!
Answers
The solutions of the indices are;
1) 2^7
2) 3^-4
3) 3^4
4) 2^4
What is the power?We know that in this case, we would have to apply the laws of indices and the particular law that we are to apply in each case is dependent on the nature of the problem that have been posed. Let us recall that we are asked to ensure that we express the answer or the solution to the problem as a single power.
1) 64 * 256/128
2^6 * 2^8/2^7
2^6 + 8 - 7 = 2^7
2) 3^4/3^3 * 3^5
3^4 - (3 + 5) = 3^-4
3) 3^9/ (3^4)^1/2 * 3^3
3^9/ 3^2 * 3^3
3^9 - (2 + 3)
3^4
4) (2^3)^4 * 2^4 ÷ 32/ 2 * 64
2^12 * 2^4 ÷ 2^5/2^1 * 2^6
2^12 + 4 -5/2^1 + 6
2^16 -5/2^7
2^11/2^7
2^11 - 7
2^4
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X+87°2x⁰ i have to solve for x it’s a 180 angle HELP ME!!!!!!!!!
Answers
Collect Like terms
X+2x°=180°-87°
3x=93°
Divide both sides by 3 to eliminate the coefficient of “x”
3x/3=93°/3
X=31°