Answer:
77/17 = 4.52941Nearest tenth = 4.5Step-by-step explanation:
[tex]\frac{x}{11}=\frac{7}{17}\\\\\mathrm{Multiply\:both\:sides\:by\:}11\\\\\frac{11x}{11}=\frac{7\cdot \:11}{17}\\\\\mathrm{Simplify\:}\frac{11x}{11}:\quad x\\\\\mathrm{Simplify\:}\frac{7\cdot \:11}{17}:\quad \frac{77}{17}\\\\x=\frac{77}{17}[/tex]
Julio ran 1 1/2 miles In 15 minutes. What is his unit rate in miles per minute?
Answer:
= 0.1 miles per minute
Step-by-step explanation:
= 1.5 miles / 15 min.
= 0.1 miles per minute
The valve was tested on 210 engines and the mean pressure was 5.0 pounds/square inch (psi). Assume the population standard deviation is 0.9. The engineer designed the valve such that it would produce a mean pressure of 4.9 psi. It is believed that the valve does not perform to the specifications. A level of significance of 0.02 will be used. Find the value of the test statistic. Round your answer to two decimal places.
Answer:
1.6101529
Step-by-step explanation:
Given the following :
Number of samples (n) = 210
Sample mean (x) = 5
Population standard deviation = 0.9
Population mean (m) = 4.9
Since the standard deviation of the population is known, we can use the z statistic
Z = (x - m) / standard error
Standard error = sd / √n
Standard error = 0.9 / √210
Standard error = 0.9 / 14.491376
Standard error= 0.0621059
Z statistic = (5 - 4.9) / 0.0621059
Z statistic = 0.1 / 0.0621059
Z statistic = 1.6101529
You decide to take three part-time jobs: Work at a convenience store 60% of your time, and earn $11.00 an hour. Referee games at your city park 25% of your time, and earn $19.00 an hour. Do your elderly neighbor’s housework 15% of your time, and earn $16.00 an hour. What will your average hourly wage be? Enter your answer up to two decimal places. its on edmentum
Answer:
13.75
Step-by-step explanation:
The expected value of the hourly wage is the sum of the probabilities (percentage of time spent on each job) multiplied by the payoff (money earned) from each possible occurrence (job): 0.6 × 11 + 0.25 × 19 + 0.15 × 16 = $13.75.
The average hourly wage will be equal to 13.75 hours.
What is an average?An average is a single number chosen to represent a group of numbers; it is often the sum of the numbers divided by the number of numbers in the group.
Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Given that work at a convenience store 60% of your time, and earn $11.00 an hour. Referee games at your city park 25% of your time, and earn $19.00 an hour. Do your elderly neighbor’s housework 15% of your time, and earn $16.00 an hour.
The expected value of the hourly wage will be calculated as below:-
The expected value of the hourly wage is the sum of the probabilities (percentage of time spent on each job) multiplied by the payoff (money earned) from each possible occurrence (job):
0.6 × 11 + 0.25 × 19 + 0.15 × 16 = $13.75.
Therefore, the average hourly wage will be equal to 13.75 hours.
To know more about an average follow
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Which of these can all be found on the figure?
Answer:
third answer
point Y, ray YZ, angle XYZ
Step-by-step explanation:
These can all be found on the figure are; point Y, ray YZ, angle XYZ. Hence, option C is correct.
How does an angle form?An angle requires two straight line/ line segments/rays, such that they're connected on one of their endpoints.
The point of their joint is called vertex of that angle.
Those two line segments forming it are called arms of that angle.
The angle is the degree of rotation that it will take for the moving side to go from initial side to the position it is currently on...
These can all be found on the figure are; point Y, ray YZ, angle XYZ.
Hence, option C is correct.
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Find the area of a TV screen with a width = 40 inches and height = 32 inches
1280 sq inches
1500 sq inches
1800 sq inches
2000 sq inches
Answer:
1280 sq inches
Step-by-step explanation:
A = LW
A = 40 in. * 32 in.
A = 1280 sq inches
Answer:
The answer is option AStep-by-step explanation:
Since the TV screen is a rectangle
Area of a rectangle = l × w
where
l is the length / height
w is the width
From the question
height = 32 inches
width = 40 inches
Substitute the values into the above formula
That's
Area of TV screen = 32 × 40
We have the answer as
1280 square inchesHope this helps you
In what direction is the line containing the point (5, 4) and (-2, 4) going?
O A. vertical
O B. up and to the right
O c. horizontal
D. down and to the right
How many more pumpkins have a mass between 9 and 12 kg than between 0 and 3 kg?
Answer:
According to the graph, there are 6 pumpkins with the mass of 9kg to 12kg and 4 pumpkins with the mass of 0kg to 3kg.
In order to find how many pumpkins more, you have to subtract it so it will be 6 pumpkins - 4 pumpkins = 2 pumpkins.
Therefore, there are 2 more pumpkins with the mass of 9 to 12kg compared to the pumpkins with the mass of 0 to 3kg.
Answer:
2
Step-by-step explanation:
1) You are attending the first Lil Baby concert after quarantine. There are two levels, one level
that is standing room only. The dimensions of the room are 62 feet by 31 feet. 15 people fit in a 3
feet by 6 feet space. Upstairs there can be 80 people. How many people can attend? (Note: It
helps if you make a sketch of the problem).
Answer:
Total number of people in the concert
= 186
Step-by-step explanation:
There are 80 people in level 2
Then in level one
The dimensions of the room are 62 feet by 31 feet.
15 people fit in a 3 feet by 6 feet space.
Area of the room= 62*31= 1922 feet²
area of 15 people space= 3*6= 18 feet²
To know how many 15 people we get in the 2nd level
=Area of room/area of 15 people space
= 1922/18
= 106.77
= 106 (we round down because this is human being.)
Total number of people in the concert
= 106+80
= 186
A rectangular box has a length of 9 inches, width of 5 inches, and hight of 1 foot. Find the volume of the box in cubic inches.
Answer:
[tex]45^{3}[/tex] inches
Step-by-step explanation:
To calculate the volume of a rectangular prism(or in this case, the rectangular box), you need to multiply the length, width and height together.
length x width x height
9 x 5 x 1
= [tex]45^{3}[/tex] inches
Can somebody please help me find the surface area of this shape
Answer:
The surface area is 7600
I would really appreciate brainliest!
Step-by-step explanation:
L=Ph
L=(40x2 50x2) 20
L=3600
S= L+2B
S=3600 +2(40x50)
S= 3600+4000
S= 7600
Answer: Hi!
There are three different rectangles that make up this closed box. We need to calculate the area of them to find the surface area of this shape. Here are the measurements:
Rectangle 1: 40 * 20
Rectangle 2: 50 * 20
Rectangle 3: 50 * 40
Note that there are two of each type of rectangle, so when we are done calculating the area of each rectangle we will multiply each by 2.
Rectangle 1: 40 * 20 = 800(2) = 1600
Rectangle 2: 50 * 20 = 1000(2) = 2000
Rectangle 3: 50 * 40 = 2000(2) - 4000
Now, we add the areas together: 1600 + 2000 + 4000 = 7600
The surface area of this closed box is 7600cm squared.
Hope this helps!
Hayley is 5feet 5 inches tall. What is tis i metres to the nearest centimetre
Answer:
It might be 168 centimetres
Step-by-step explanation:
Let f(x) = 1/x+2 and g (x) = 1/x-3. Find (f/g) (x). Assume all appropriate restrictions to the domain. help!!!!
Answer:
x ≠ -2 or 3
Step-by-step explanation:
No denominator can be zero, so ...
x +2 ≠ 0
x ≠ -2
__
x -3 ≠ 0
x ≠ 3
__
g(x) ≠ 0 . . . . . true for all x; no restriction needed for this
__
The appropriate restrictions are x ∉ { -2, 3 }.
A researcher found a study relating the distance a driver can see, y, to the age of the driver, x. When researchers looked at the association of x and y, they found that the coefficient of determination was r = 0.542 Select two conclusions that the researcher can make from this data.
a.) About 54% of the variation in distance that the driver can see is explained by a linear relationship with the driver's age.
b.) The correlation coefficient, r, is -0.736.
c.) About 74% of the variation in the driver's age is explained by a linear relationship with the distance that the driver can see.
d.) About 46% of the variation in distance that the driver can see is explained by a linear relationship with the driver's age.
e.) The correlation coefficient, r, is -0.458.
f.) The correlation coefficient, r, is -0.271.
Answer: a.) About 54% of the variation in distance that the driver can see is explained by a linear relationship with the driver's age.
b.) The correlation coefficient, r, is -0.736.
Step-by-step explanation:
The coefficient of determination is denoted [tex]R^2 \ or \ r^2[/tex] which gives the percent of the variance in the dependent variable that is predictable from the independent variable.
Given, [tex]r^2= 0.542[/tex]
That means 54% of the variation in distance that the driver can see is explained by a linear relationship with the driver's age.
Also, [tex]r=\sqrt{0.542}\approx\pm0.736[/tex] , where r determines the correlation coefficient.
As driver;s age increases the distance he can see decreases, so there is a negative correlation between them.
So r= -736.
Hence, The correlation coefficient, r, is -0.736.
So, the correct options are a.) and b.)
The following data shows marks obtained by students in a mathematics test; 6,9,5,0,5,3,7,5,2,7,10,2,9,8,0,6,2,6,6,3,6,9,7,7,4,1,6,68 a. construct a frequency distribution table data using a discrete values 0, 1, 2,............. 10 b. State the modal score of the distribution c. if a student is chosen at random, what is the probability that a student scored more than 5 means d. Using assumed mean of 6, calculate the arithmetic mean score of the distribution
Data
6,9,5,0,5,3,7,5,2,7,10,2,9,8,0,6,2,6,6,3,6,9,7,7,4,1,6,8
Answer:
(a) shown in the attachment
(b) 0.54
(c) 5.32
Step-by-step explanation:(a) The frequency distribution table has been added to this response.
The table contains four columns:
First column (x): The discrete values of the marks
Second column (f): The corresponding frequency of the marks
Third column (d) : The difference between each mark(x) and the assumed mean(A). i.e d = x - A (Where A = 6 from the question)
Fourth column (fd): The product of the first column and the third column. i.e f * d
(b) From the table, it can be deduced that the modal score is 6
This is because the score 6 has the highest number of frequency which is 6
(c) If a student is selected at random, the probability P(>5), that the student scored more than 5 is given as follows;
P( >5 ) = [The sum of frequencies of marks greater than 5] / [Total frequency]
P( >5 ) = [6 + 4 + 2 + 3 + 1] / [28]
P( >5 ) = 15 / 28 = 0.54
Therefore, the probability that the student scored more than 5 is 0.54
(d) To get the arithmetic mean, M, from the assumed mean A = 6, we use the following relation;
M = A + [∑fd / N] -----------(*)
Where
N = total frequency = 28
A = 6
∑fd = sum of the items on the fourth column = -19
Substitute these values into equation (*)
M = 6 + [-19 / 28]
M = 149 / 28
M = 5.32
Therefore, the arithmetic mean is 5.32
Your forecasted income statement shows sales of $1,362,000, cost of goods sold at $830,000, depreciation expense of $310,000, and a forecasted free cash flow of $470,200. What are your forecasted earnings? What is your tax rate?
Answer:
Forecasted earning = $160,200
Tax rate = 27.84%
Step-by-step explanation:
The calculation of forecasted earning and tax rate is shown below:-
Earnings before income and taxes = Sales - Cost of goods sold - Depreciation Expense
= $1,362,000 - $830,000 - $310,000
= $222,000
So,
Forecasted Free cash flow = Net Income + Depreciation
$470,200 = Net Income + $310,000
Net Income = $470,200 - $310,000
= $160,200
Now, the Tax rate is
Net Income = EBIT × (1 - Tax Rate)
$160,200 = $222,000 × (1 - Tax rate)
(1 - Tax rate) = $160,200 ÷ $222,000
(1 - Tax rate) = 0.721622
Tax rate = 27.84%
what is the degree of the term 96?
–3(x + n) = x aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
First thing to do is distribute the [tex]-3[/tex]:
[tex]-3(x+n)=x\\-3x+-3n=x[/tex]
Now we're gonna solve for [tex]x[/tex]:
[tex]-3x-3n=x\\-4x=3n\\x=-\frac{3n}{4}[/tex]
To solve for [tex]n[/tex]:
[tex]-3x-3n=x\\-3n=4x\\n=-\frac{4x}{3}[/tex]
Write the number shown in standard notation. 1.02 x 10 First Correct answer gets Brainliest
Answer:
1.02×10¹ = 10.2
Step-by-step explanation:
We have given a number in scientific notation as follows 1.02×10¹
We need to convert it into standard notation.
1 is in ones place, 0 is in tenths place and 2 is in hundredths place.
[tex]1.02\times 10^1=\dfrac{102}{100}\times 10\\\\=\dfrac{102}{10}\\\\=10.2[/tex]
So, the standard notation of 1.02×10¹ is 10.2
Write an equation in point slope form for the line through the given point with the given slope. (4,-6);m=3/5
Answer:
y+6 = 3/5(x-4)
Step-by-step explanation:
Point slope form is
y-y1 = m(x-x1)
where m is the slope and (x1,y1) is a point on the line
y --6 = 3/5( x-4)
y+6 = 3/5(x-4)
geometric mean between 8 and 1/4
Answer:
√2
1.414
Step-by-step explanation:
ⁿ√x₁*x₂*x₃*...*xₙ
√8*1/4
√2
1.414
The geometric mean between 8 and 1/4 is; 1.414.
According to the question:
We are required to determine the geometric mean between 8 and 1/4.In essence, the geometric mean can be evaluated as follows;
Geometric mean = √(8×1/4)G.M = √2G.M = 1.414Read more on geometric mean:
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The formula below represents Celsius temperature C as a function of Fahrenheit temperature F.
C (F) = 5/9 (F - 32), where F greaterthanorequalto -459.6
(a) Find the inverse function of C.
(b) What does the inverse function of C represent?
A. The inverse represents the temperature F corresponding to a temperature C.
B. The inverse represents the temperature 1/C corresponding to a temperature C.
C. The inverse represents the temperature 1/F corresponding to a temperature C.
D. The inverse represents the temperature C corresponding to a temperature F.
(c) Determine the domain of the inverse function.
a. all real numbers
b. C greaterthanorequalto 0
c. C lessthanorequalto -273.1
d. C greaterthanorequalto -273.1
(d) If the temperature is 90 degree C, what is the corresponding temperature in degrees Fahrenheit?
Answer:
The inverse represents the temperature F corresponding to a temperature C.
The domain of the inverse function is all real numbers.
194°F
Step-by-step explanation:
Let C= y
y= 5/9 (F - 32),
F= 9/5y + 32
But y= C, hence;
F= 9/5 C +32
The inverse represents the temperature F corresponding to a temperature C.
Given;
F= 9/5 C +32
The domain of the inverse function is all real numbers.
Given C= 90°
F= 9/5 C +32
F= 9/5 (90°) +32
F= 194°F
A basketball court is 94 feet by 50 feet. Eight fans ca
fit next to each other in a 3 ft. by 3 ft. area. How
many kids would you estimate can fit side by side
over the entire floor?
Answer:
The entire floor can contain approximately 4178 fans
Step-by-step explanation:
The first step is to calculate the area of the basketball floor.
we can do this by multiplying the length by the breadth as such 94 X 50 = 4700 square feet.
The second step is to calculate the area occupied by 8 of the fans. We can do this by multiplying 3 ft by 3ft = 9 square feet.
From this, it will be easier to estimate the area occupied by only one fan. This can be got by dividing 9 square feet by 8.
This is = 1.125 square feet.
To get the number of students it can occupy, we divide the total area of the court by the area occupied by one student.
4700/ 1.125 =4177.8 [tex]\approx[/tex] 4178 fans
Assignment
Modeling Real-World Problems with Composite Functions
A retailer is having a promotional sale for 35% off all items. There is a 7% sales tax added to the price. Which
represents the situation, where x is the original cost of the item(s)?
Of(x) = 0.35x represents the discount price and g(x) = 0.07x represents the price after taxes. The total price would
be (fog)(x) = 0.35(0.07x) = 0.0245x.
Of(x) = 0.65x represents the discount price and g(x) = 0.07x represents the price after taxes. The total price would
be (fºg)(x) = 0.65(0.07x) = 0.0455x
f(x) = 1.07x represents the price after taxes and g(x) = 0.65x represents the discount price. The total price would
be (fºg)(x) = 1.07(0.65x)= 0.6955x.
Of(x) = 1.07x represents the price after taxes and g(x) = 0.35x represents the discount price. The total price would
be (fºg)(x) = 0.35(1.07x)=0.3745x.
Answer:
Total Price = 1.07(0.65x)= 0.6955x.
Step-by-step explanation:
The discount percentage is, d% = 35%.
The sales tax percentage is, s% = 7%.
The variable x represent the original cost of the item(s).
The discount is subtracted from the original amount.
So, the discounted amount will be, 0.65x.
And the sales tax is added to the original amount.
So, the value of tax plus price will be, 1.07x.
Then the final price of the item(s) will be:
Total Price = 1.07(0.65x)= 0.6955x.
Answer:
It's C for those on edgenuity
Step-by-step explanation:
If the computed minimum sample size n needed for a particular margin of error is not a whole number, round the value of n (up or down) to the next (smaller or larger) whole number.
a) down; smaller
b) down; larger
c) up; larger
d) up; smaller
Answer:
The correct option is c.
Step-by-step explanation:
The margin of error is the range of values lower than and more than the sample statistic in a confidence interval. It is the number of percentage point by which the sample result will differ from the population result.
The general formula to margin of error is:
[tex]MOE=CV\times\frac{SD}{\sqrt{n}}[/tex]
Here,
CV = critical value
SD = standard deviation
n = sample size
Now, if the computed minimum sample size needed for a particular margin of error is not a whole number, then round the value of n up to the next larger whole number.
Thus, the correct option is c.
to find the distance between a point x and an inaccessible point z, a line segment xy is constructed. measurements show that xy=966 m, angle xyz=38°24', and angle yzx=94°6'. find the distance between x and z to the nearest meter.
Answer:
[tex]\approx \bold{602\ m}[/tex]
Step-by-step explanation:
Given the following dimensions:
XY=966 m
[tex]\angle XYZ[/tex] = 38°24', and
[tex]\angle YZX[/tex] = 94°6'
To find:
Distance between points X and Z.
Solution:
Let us plot the given values.
We can clearly see that it forms a triangle when we join the points X to Y, Y to Z and Z to X.
The [tex]\triangle XYZ[/tex] has following dimensions:
XY=966 m
[tex]\angle XYZ[/tex] = 38°24', and
[tex]\angle YZX[/tex] = 94°6'
in which we have to find the side XZ.
Kindly refer to the image attached.
Let us use the Sine rule here:
As per Sine Rule:
[tex]\dfrac{a}{sinA} = \dfrac{b}{sinB} = \dfrac{c}{sinC}[/tex]
Where
a is the side opposite to [tex]\angle A[/tex]
b is the side opposite to [tex]\angle B[/tex]
c is the side opposite to [tex]\angle C[/tex]
[tex]\dfrac{XZ}{sin\angle Y} = \dfrac{XY}{sin\angle Z}\\\Rightarrow \dfrac{966}{sin94^\circ6'} = \dfrac{XZ}{sin38^\circ24'}\\\Rightarrow XZ=\dfrac{966}{sin94^\circ6'} \times sin38^\circ24'\\\Rightarrow XZ=\dfrac{966}{0.997} \times 0.621\\\Rightarrow XZ=601.69 \m \approx \bold{602\ m}[/tex]
Find the equation of the line with slope −5 and that contains the point (−9,−5). Write the equation in the form y=mx+b and identify m and b. Find the equation of the line that contains the points (2,4) and (10,2). Write the equation in the form y=mx+b and identify m and b.
Answer & Step-by-step explanation:
Slope-intercept form:
[tex]y=mx+b[/tex]
m is the slope and b is the y-intercept. Insert the given slope:
[tex]y=-5x+b[/tex]
To find the y-intercept, take the given coordinate point and insert:
[tex](-9_{x},-5_{y})\\\\-5=-5(-9)+b[/tex]
Solve for b:
Simplify multiplication:
[tex]-5=45+b[/tex]
Subtract 45 from both sides:
[tex]-50=b\\\\b=-50[/tex]
The y-intercept is -50. Insert:
[tex]y=-5x-50[/tex]
[tex]m=-5\\b=-50[/tex]
Use the slope formula for when you have two points:
[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{rise}{run}[/tex]
The slope is the change in the y-axis over the change in the x-axis, or rise over run. Insert the points:
[tex](2_{x1},4_{y1})\\(10_{x2},2_{y2})[/tex]
[tex]\frac{2-4}{10-2}=\frac{-2}{8}=-\frac{2}{8}=-\frac{1}{4}[/tex]
The slope is [tex]-\frac{1}{4}[/tex] . Insert:
[tex]y=-\frac{1}{4}x+b[/tex]
Now follow the steps from the last problem to find the y-intercept. Choose a point and insert into the equation:
[tex](2_{x},4_{y})\\\\4=-\frac{1}{4}(2)+b[/tex]
Solve for b:
Simplify multiplication:
[tex]-\frac{1}{4}*\frac{2}{1}=-\frac{2}{4}=-\frac{1}{2}[/tex]
Re-insert:
[tex]4=-\frac{1}{2} +b[/tex]
Subtract b from both sides:
[tex]4-b=-\frac{1}{2} +b-b\\\\4-b=-\frac{1}{2}[/tex]
Subtract 4 from both sides:
[tex]4-4-b=-\frac{1}{2}-4\\\\-b=-\frac{1}{2}-4[/tex]
Simplify subtraction:
[tex]-\frac{1}{2}-4=-\frac{1}{2} -\frac{4}{1} =-\frac{1}{2} -\frac{8}{2} \\\\-\frac{1}{2} -\frac{8}{2}=-\frac{9}{2}[/tex]
Re-insert:
[tex]-b=-\frac{9}{2}[/tex]
Divide both sides by -1 to make the variable positive (can be seen as -1b):
[tex]b=\frac{9}{2}[/tex]
The y-intercept is [tex]\frac{9}{2}[/tex] .
Write the equation:
[tex]y=-\frac{1}{4}x+\frac{9}{2}[/tex]
:Done
sara quiere guardar 48 manzanas y 36 duraznos en cajas con el mismo numero de frutas de cada tipo en cada caja cuantas cuantas frutas pude guardar teniendio en cuenta que nesecita el mayor numero de cajas posibles
Answer:
Se requiere 12 cajas con 4 manzanas y 3 duraznos cada una.
Step-by-step explanation:
Se requiere el menor número posible de manzanas y duraznos para obtener el mayor número de cajas. Puesto que no se considera cortar fruta alguna en porciones y sabiendo que hay más manzanas que duraznos, se determina la razón mínima de manzanas por duraznos:
[tex]x = \frac{48\,manzanas}{36\,duraznos}[/tex]
[tex]x = \frac{4 manzanas}{3\,duraznos}[/tex]
Se requiere 4 manzanas por cada 3 duraznos. Entonces, cada caja debe contener 3 duraznos y 4 manzanas. El número máximo de cajas es:
[tex]n = \frac{48\,manzanas}{4\,\frac{manzanas}{caja} } = \frac{36\,duraznos}{3\,\frac{duraznos}{caja} }[/tex]
[tex]n = 12\,cajas[/tex]
Se requiere 12 cajas con 4 manzanas y 3 duraznos cada una.
write the desimale 3.17 in word form
Answer:
There are multiple ways this can be said :
Three and seventeen hundredthsThree-point seventeenThree-point one sevenTire pressure monitoring systems (TPMS) warn the driver when the tire pressure of the vehicle is 26% below the target pressure. Suppose the target tire pressure of a certain car is 29 psi (pounds per square inch.) (a) At what psi will the TPMS trigger a warning for this car? (Round your answer to 2 decimal place.) (b) Suppose tire pressure is a normally distributed random variable with a standard deviation equal to 2 psi. If the car’s average tire pressure is on target, what is the probability that the TPMS will trigger a warning? (Round your answer to 4 decimal places.) (c) The manufacturer’s recommended correct inflation range is 27 psi to 31 psi. Assume the tires’ average psi is on target. If a tire on the car is inspected at random, what is the probability that the tire’s inflation is within the recommended range? (Round your intermediate calculations and final answer to 4 decimal places.)
Answer:
(a) At 21.46 psi, the TPMS trigger a warning for this car.
(b) The probability that the TPMS will trigger a warning is 0.0001.
(c) The probability that the tire’s inflation is within the recommended range is 0.6826.
Step-by-step explanation:
We are given that tire pressure monitoring systems (TPMS) warn the driver when the tire pressure of the vehicle is 26% below the target pressure. Suppose the target tire pressure of a certain car is 29 psi (pounds per square inch).
(a) It is stated that TPMS warns the driver when the tire pressure of the vehicle is 26% below the target pressure.
So, the TPMS trigger a warning for this car when;
Pressure = 29 psi - 26% of 29 psi
= [tex]29-(0.26 \times 29)[/tex] = 21.46 psi
At 21.46 psi, the TPMS trigger a warning for this car.
(b) Suppose tire pressure is a normally distributed random variable with a standard deviation equal to 2 psi.
Let X = The pressure at which TPMS will trigger a warning
So, X ~ Normal([tex]\mu=29, \sigma^{2} =2^{2}[/tex])
Now, the probability that the TPMS will trigger a warning is given by = P(X [tex]\leq[/tex] 21.46)
P(X [tex]\leq[/tex] 21.46) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{21.46-29}{2}[/tex] ) = P(Z [tex]\leq[/tex] -3.77) = 1 - P(Z < 3.77)
= 1 - 0.9999 = 0.0001
The above probability is calculated by looking at the value of x = 3.77 in the z table which has an area of 0.9999.
(c) The manufacturer’s recommended correct inflation range is 27 psi to 31 psi.
So, the probability that the tire’s inflation is within the recommended range is given by = P(27 psi < X < 31 psi)
P(27 psi < X < 31 psi) = P(X < 31 psi) - P(X [tex]\leq[/tex]27 psi)
P(X < 31 psi) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{31-29}{2}[/tex] ) = P(Z < 1) = 0.8413
P(X [tex]\leq[/tex] 27 psi) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{27-29}{2}[/tex] ) = P(Z [tex]\leq[/tex] -1) = 1 - P(Z < 1)
= 1 - 0.8413 = 0.1587
Therefore, P(27 psi < X < 31 psi) = 0.8413 - 0.1587 = 0.6826.
At 21.46 psi, the TPMS trigger a warning for this car.
The probability that the TPMS will trigger a warning is 0.0001.
The probability that the tire’s inflation is within the recommended range is 0.6826.
Given that,
Tire pressure monitoring systems (TPMS) warn the driver when the tire pressure of the vehicle is 26% below the target pressure.
Suppose the target tire pressure of a certain car is 29 psi (pounds per square inch).
We have to determine,
At what psi will the TPMS trigger a warning for this car.
What is the probability that the TPMS will trigger a warning.
What is the probability that the tire’s inflation is within the recommended range.
According to the question,
It is stated that TPMS warns the driver when the tire pressure of the vehicle is 26% below the target pressure.So, the TPMS trigger a warning for this car when;
Pressure = 29 psi - 26% of 29 psi
[tex]Pressure = 29- (0.26 \times 29) = 21.46psi[/tex]
At 21.46 psi, the TPMS trigger a warning for this car.
Suppose tire pressure is a normally distributed random variable with a standard deviation equal to 2 psi.
Let X = The pressure at which TPMS will trigger a warning
So, X ~ Normal [tex]\mu = 29, \sigma^2 = 2^2\\[/tex]
Now, the probability that the TPMS will trigger a warning is given by = P(X≤ 21.46).
[tex]P(X\leq 21.46) = P (\dfrac{X-\mu}{\sigma}\leq \dfrac{21.46-29}{2}) = P(Z\leq -3.77) = 1-P(Z<3.77) \\\\= 1-0.9999 = 0.0001[/tex]
The above probability is calculated by looking at the value of x = 3.77 in the z table which has an area of 0.9999.
The manufacturer’s recommended correct inflation range is 27 psi to 31 psi.
So, the probability that the tire’s inflation is within the recommended range is given by = P(27 psi < X < 31 psi)
[tex]P(27psi<X<31psi) = P(X<31psi)-P(X\leq psi)\\\\P(X<31psi) = P(\dfrac{x-\mu}{\sigma}\leq \dfrac{31-29}{2}) = P(Z<1) = 0.8413\\\\P(X<27psi) = P(\dfrac{x-\mu}{\sigma}\leq \dfrac{27-29}{2}) = P(Z\leq -1) = 1-P(Z<1) = 0.8413\\[/tex]
Therefore, , P(27 psi < X < 31 psi) = 0.8413 - 0.1587 = 0.6826.
To know more about Probability click the link given below.
https://brainly.com/question/18227798
Solve this quadratic equation using the quadratic formula. 5 - 10x - 3x2 = 0
Answer:
x = (-5 ± 2√10) / 3
Step-by-step explanation:
5 − 10x − 3x² = 0
Write in standard form:
-3x² − 10x + 5 = 0
Solve with quadratic formula:
x = [ -b ± √(b² − 4ac) ] / 2a
x = [ -(-10) ± √((-10)² − 4(-3)(5)) ] / 2(-3)
x = [ 10 ± √(100 + 60) ] / -6
x = (10 ± 4√10) / -6
x = (-5 ± 2√10) / 3
Step-by-step explanation:
[tex]5 - 10x - 3 \times 2 = 0[/tex]
[tex]multiply \: the \: numbers \\ \\ 5 - 10 x- 6 = 0[/tex]
[tex]collect \: like \: terms \\ \\ 5 - 6 - 10x[/tex]
[tex] - 1 - 10x = 0[/tex]
[tex] - 10x = 1[/tex]
[tex]divide \: both \: sides \: of \: the \: equation \: by \: - 10[/tex]
[tex]x = - \ \frac{1}{10} [/tex]
[tex]alt \: form \: = \\ \\ = 0.1 \\ x = - 10 {}^{ - 1} [/tex]
Hope this helps. :)