Answer
Step-by-step explanation:
H*W*L
280=7*W*(6+W)
280=42W+7W^2
40=6w+w^2
W^2+6W-40=0
(W-4)(W+10)=0
W=4
We can only use positive results
L=6+W
L=4+6=10
Given that, the height of the cardboard box=10 inches and volume = 540 cubic inches.
Let the width of the cardboard box be x, then the length will be 3x.
What is the formula to find the volume of a rectangular prism?The formula to find the volume of a rectangular prism is Volume=Length×Width×Height.
Now, 540=10×x×3x
⇒x²=18
⇒x=3√2 inches.
Therefore, the width of a cardboard box is 3√2 inches.
To learn more about a rectangular prism visit:
https://brainly.com/question/21308574.
#SPJ2
Nadia is making a rectangular moisac out of 1/2 -inch by 1/2 -inch tiles. The rectangle is 12 inches long and 3 1/2 inches wide. How many tiles will nadia use to cover the rectangle completely
Answer:
168
Step-by-step explanation:
GIVEN: Nadia is making a rectangular moisac out of [tex]\frac{1}{2}[/tex] inch by [tex]\frac{1}{2}[/tex] inch tiles. The rectangle is [tex]12[/tex] inches long and [tex]3\frac{1}{2}[/tex] inches wide.
TO FIND: How many tiles will Nadia use to cover the rectangle completely.
SOLUTION:
Area of rectangular moisac[tex]=\text{length}\times\text{width}[/tex]
[tex]=12\times3\frac{1}{2}=\frac{12\times7}{2}[/tex]
[tex]=42 \text{ inch}^2[/tex]
Area of one tile [tex]=\text{side}^2[/tex]
[tex]=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}\text{ inch}^2[/tex]
According to question
Total tiles required [tex]=\frac{\text{Area of rectangular moisac}}{\text{Area of one tile}}[/tex]
[tex]=\frac{42}{\frac{1}{4}}=42\times4[/tex]
[tex]=168[/tex] tiles
Hence, 168 tiles are required to completely cover the rectangular moisac.
a whole number is squared. the result is between 200 and 260. the number is between?
Final answer:
The whole number squared resulting in a number between 200 and 260 must have the original whole number between 15 and 16.
Explanation:
If a whole number is squared and the result is between 200 and 260, we must determine which whole numbers will yield a square within that range. We find the square roots of both 200 and 260 to identify the range of whole number bases. The square root of 200 is approximately 14.14, and the square root of 260 is approximately 16.12. Therefore, the number must be greater than 14 but less than or equal to 16 because squaring whole numbers greater than 16 gives results exceeding 260. Hence, the number is between 15 and 16.
I've been trying this for days I can't get my head round it any help would be appreciated.
The one line of symmetry is vertical, so we could fold the hexagon in half in such a way that the vertices A and B would meet at the same point, and the same goes for the pairs C,F and D,E. Because of this symmetry, we know angle AFE is congruent to BCD, and angle FED is congruent ot CDE.
Let x be the measure of angle CDE.
In any convex polygon with n sides, the interior angles sum to (n - 2)*180º in measure. ABCDEF is a hexagon, so n = 6.
We have 2 angles of measure 123º, 2 of measure x, and 2 of measure 2x. So
2(123º + x + 2x ) = (6 - 2)*180º
246º + 2x + 4x = 720º
6x = 474º
x = 79º
Angle AFE is congruent to angle BCD, which is twice the measure of CDE, so angle AFE has measure 2*79º = 158º.
Auto pistons at Wemming Chung's plant in Shanghai are produced in a forging process, and the diameter is a critical factor that must be controlled. From sample sizes of 10 pistons produced each day, the mean and the range of this diameter have been as follows:
Day Mean Bold x overbar (mm) Range R (mm)
1 158.9 4.0
2 151.2 4.6
3 155.6 4.3
4 155.5 5.0
5 154.6 4.3
a) What is the value of x ?
Missing part of the question
b)What is the value of R?
Answer:
a. X = 155.2
b. R = 4.4
Step-by-step explanation:
a. Calculating the value of x.
The value of x is the mean of the mean observation; i.e. the mean column
Mean is calculated as: the summation of all observation divided by the number of observations.
Summation of Observation = 158.9 + 151.2 + 155.6 + 155.5 + 154.6
Summation of Observation = 775.8
Number of Observations = 5
X = Mean = 775.8/5
X = 155.16
X = 155.2 ----- Approximated to 1 decimal place
b. Calculating the value of R.
The value of R is the mean/average of the Range
Mean is calculated as: the summation of all observation divided by the number of observations.
Summation of Observation = 4.0 + 4.6 + 4.3 + 5.0 + 4.3
Summation of Observation = 22.2
Number of Observations = 5
R = Mean = 22.2/5
R = 4.44
R = 4.4 ----- Approximated to 1 decimal place
The average diameter [tex](\( \overline{x} \))[/tex] of the pistons from the provided data is 155.16 mm, calculated by summing the daily means and dividing by the number of days.
In the context provided, [tex]\( \overline{x} \)[/tex] refers to the average of the piston diameters measured across different days at Wemming Chung's plant.
To find this value, we need to calculate the mean of the daily means [tex](\( \overline{x} \))[/tex] which are 158.9, 151.2, 155.6, 155.5, and 154.6 mm. This is done by summing these values and dividing by the number of days (5 in this case).
[tex]\[ \overline{x} = \frac{158.9 + 151.2 + 155.6 + 155.5 + 154.6}{5} \][/tex]
[tex]\[ \overline{x} = \frac{775.8}{5} \][/tex]
[tex]\[ \overline{x} = 155.16 \text{ mm} \][/tex]
Hence, the value of [tex]\( \overline{x} \)[/tex] is 155.16 mm.
how do I find the answer to 3km 6hm 7dam 5m ÷ 15?
Final answer:
To solve 3km 6hm 7dam 5m ÷ 15, first convert the distance to meters (3675 m) and then divide by 15 to get 245 meters.
Explanation:
The question given by the student involves performing a division operation with a composite distance measurement in different units. First, we need to convert the entire distance into a single unit (meters) before we divide it by the given number (15).
To convert the given distance to meters, we use the metric system unit conversion:
1 kilometer (km) = 1000 meters (m), 1 hectometer (hm) = 100 meters (m), and 1 decameter (dam) = 10 meters (m). Therefore, 3 km is 3000 m, 6 hm is 600 m, 7 dam is 70 m, and adding the given 5 m to these conversions, we get a total distance of 3675 meters (3000 m + 600 m + 70 m + 5 m = 3675 m).
To find the final answer, divide 3675 meters by 15: which yields 245 meters. Thus, 3km 6hm 7dam 5m divided by 15 equals 245 meters.
A chef is going to use a mixture of two brands of Italian dressing. The first brand contains 7 vinegar, and the second brand contains 12 vinegar. The chef wants to make 390 milliliters of a dressing that is 11 vinegar. How much of each brand should she use
Answer:
78 ml of 7% vinegar and 312 ml of 12% vinegar.
Step-by-step explanation:
Let x represent ml of 7% vinegar brand and y represent ml of 12% vinegar brand.
We have been given that chef wants to make 390 milliliters of the dressing. We can represent this information in an equation as:
[tex]x+y=390...(1)[/tex]
[tex]y=390-x...(1)[/tex]
We are also told that 1st brand 7% vinegar, so amount of vinegar in x ml would be [tex]0.07x[/tex].
The second brand contains 12 vinegar, so amount of vinegar in y ml would be [tex]0.12y[/tex].
We are also told that the chef wants to make 390 milliliters of a dressing that is 11% vinegar. We can represent this information in an equation as:
[tex]0.07x+0.12y=390(0.11)...(2)[/tex]
Upon substituting equation (1) in equation (2), we will get:
[tex]0.07x+0.12(390-x)=390(0.11)[/tex]
[tex]0.07x+46.8-0.12x=42.9[/tex]
[tex]-0.05x+46.8=42.9[/tex]
[tex]-0.05x+46.8-46.8=42.9-46.8[/tex]
[tex]-0.05x=-3.9[/tex]
[tex]\frac{-0.05x}{-0.05}=\frac{-3.9}{-0.05}[/tex]
[tex]x=78[/tex]
Therefore, the chef should use 78 ml of the brand that contains 7% vinegar.
Upon substituting [tex]x=78[/tex] in equation (1), we will get:
[tex]y=390-78[/tex]
[tex]y=312[/tex]
Therefore, the chef should use 312 ml of the brand that contains 12% vinegar.
Chapin Manufacturing Company operates 24 hours a day, five days a week. The workers rotate shifts each week. Management is interested in whether there is a difference in the number of units produced when the employees work on various shifts. A sample of five workers is selected and their output recorded on each shift.
Units Produced
Employee Day Afternoon Night
Skaff 38 24 34
Lum 35 23 37
Clark 28 26 38
Treece 35 26 23
Morgan 22 23 24
1. At the 0.01 significance level, can we conclude there is a difference in the mean production rate by shift or by employee?
Answer:
The answer is there is a difference in the mean production rate by shift
Step-by-step explanation:
The level of significance is actually very low since the same production level is maintained for each of the 5 workers at the same time in the afternoon.
As for the other shifts, that is, the day shift and the night shift, the level of significance varies according to the production established by each worker.h
Angeline bought s yards of satin fabric priced at $8.09 per yard, and c yards of cotton fabric priced at $3.79 per yard. Use an expression to determine the amount that Angeline would spend in all if she bought 5 yards of satin fabric and 8 yards of cotton fabric. *
Answer:
$70.77
Step-by-step explanation:
A=8.09s+3.79c
A=8.09(5)+3.79(8)
A=40.45+30.32
A=70.77
Answer:
$70.77
Step-by-step explanation:
5s+8c=?
5(8.09) + 8(3.79) = ?
40.45 + 30.32 = ?
$70.77
Jonas earns $77 in 7 hours. At this rate, how many dollars will he earn in 20 hours?
Answer:
$220?
Step-by-step explanation:
Answer$220
Step-by-step explanation:
77/7=$11 so $11x20=220
He takes a random sample of 49 recent charterholders and computes a mean salary of $172,000 with a standard deviation of $35,000. Use this sample information to determine the 90% confidence interval for the average salary of a CFA charterholder.
Answer:
the 90% of confidence intervals for the average salary of a CFA charter holder
(1,63,775 , 1,80,000)
Step-by-step explanation:
Explanation:-
random sample of n = 49 recent charter holders
mean of sample (x⁻) = $172,000
standard deviation of sample( S) = $35,000
Level of significance α= 1.645
90% confidence interval
[tex](x^{-} - Z_{\alpha } \frac{s}{\sqrt{n} } , x^{-} + Z_{\alpha } \frac{s}{\sqrt{n} })[/tex]
[tex](172000 - 1.645 \frac{35000}{\sqrt{49} } , 172000 +1.645 \frac{35000}{\sqrt{49} })[/tex]
on calculation , we get
(1,63,775 , 1,80,000)
The mean value lies between the 90% of confidence intervals
(1,63,775 , 1,80,000)
PLEASE HURRY THE PICTURES IS ABOVE!!
Which inequality is represented by this graph?
A. x>-53
B. x_<- 53
C. X<-53
D. x_>-53
Answer:
x ≥ -53
Step-by-step explanation:
There is a closed circle at -53 which means equal to
The line goes to the right which means greater than
x ≥ -53
Answer:
D) x>=-53
Step-by-step explanation:
A closed dot means -53 is included in the inequality as a solution, and since it's going right, it's greater than or equal to -53.
PLLLLZZZ HELP ME. Given the function f(x)=3x^2-2x-5 : What are the zeros for this function? 5 extra credit points for an exact answer. 30 points if you get the exact answer and its 100% Correct.
Answer:
The zeros for this function are x = -1 and x = 1.67
Step-by-step explanation:
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = (x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]\bigtriangleup = b^{2} - 4ac[/tex]
In this question:
[tex]f(x) = 3x^{2} - 2x - 5[/tex]
The zeros of the function are the values of x for which
[tex]f(x) = 0[/tex]
Then
[tex]3x^{2} - 2x - 5 = 0[/tex]
This means that [tex]a = 3, b = -2, c = -5[/tex]
Then
[tex]\bigtriangleup = (-2)^{2} - 4*3*(-5) = 64[/tex]
[tex]x_{1} = \frac{-(-2) + \sqrt{64}}{2*3} = 1.67[/tex]
[tex]x_{2} = \frac{-(-2) - \sqrt{64}}{2*3} = -1[/tex]
The zeros for this function are x = -1 and x = 1.67
Layla and Sam are both dog sitters. Layla charges $2 per day plus a sign-up fee of $3. Sam charges a flat rate of $3 per day. The system of linear equations below represents y, the total amount earned in dollars for x days of dog sitting.
A. Write the equation to represent Layla’s fees.
B. Write the equation to represent Sam’s fees.
C. After how many days do Layla and Sam earn the same amount for dog sitting?
What is that amount?
Answer:
a) [tex]L(t) = 3 + 2\cdot t[/tex], b) [tex]S (t) = 3\cdot t[/tex], c) Third day.
Step-by-step explanation:
a) The equation to represent Layla's fees is:
[tex]L(t) = 3 + 2\cdot t[/tex]
b) The equation to represent Sam's fees is:
[tex]S (t) = 3\cdot t[/tex]
c) Both earn the same amount for dog sitting at the third day.
Students arrive randomly at the help desk of the computer lab. There is only one service agent, and the time required for inquiry varies from student to student. Arrival rates have been found to follow the Poisson distribution, and the service times follow the negative exponential distribution. The average arrival rate is 12 students per hour, and the average service rate is 20 students per hour. On average, how long does it take to service each student?
Considering Poissoniated student arrivals and exponential service times in a queueing situation, with an average service rate of 20 students per hour, it takes on average 3 minutes to service each student.
Explanation:
The student's question pertains to the field of queueing theory, more specifically dealing with Poisson arrivals and exponential service time. In this context, the given arrival rate (λ) is 12 students per hour and the service rate (μ) is 20 students per hour.
Since the service rate is provided in terms of how many students can be serviced per hour (20 students per hour), to find the average service time for each student, we take the reciprocal of the service rate.
Therefore, average service time = 1/μ = 1/20 = 0.05 hours per student.
Note that 0.05 hours is equivalent to 3 minutes, hence on average, it takes 3 minutes to service each student.
Learn more about Poisson Arrivals and Service Times here:https://brainly.com/question/37190818
#SPJ11
Miss Perkins want to rent a car for a day. It will cost a daily fee of $75 plus $.55 per mile driven. M equals the number of miles Miss Perkins drive for the day. Write an expression that shows the amount she will pay for the car. Evaluate the expression you wrote to find them out Miss Perkins will pay if she drive 300 miles.
Answer:
.55M + 75 = the total cost
.55(300) + 75 = $240
Step-by-step explanation:
Finish the following proof for Theorem 1.4.12. Assume B is a countable set. Thus, there exists f : N -+ B, which is 1-1 and onto. Let A ~ B be an infinite subset of B. We must show that A is countable. Let nI = min{n EN: f(n) E A}. As a start to a definition of g: N -+ A, set g(l) = f(nI). Show how to inductively continue this process to produce a 1-1 function 9 from N onto A.
Answer:
A is a countable set
Step-by-step explanation:
Assume B is a countable set, Go through the attached file for a detailed step by step explanation of the proof that A is a countable set.
Rearrange the equation so u is the independent variable.
4u+8w=−3u+2w
Answer:
w = [tex]-\frac{7}{6}u[/tex]
Step-by-step explanation:
If u will be the independent variable, then w will have to be made the subject of the equation so that w will depend on the changes in u
4u + 8w = −3u + 2w
First collect all like terms
8w − 2w = −3u − 4u
6w = −7u
divide both sides by 6
∴ w = [tex]-\frac{7}{6}u[/tex]
In the equation w = [tex]-\frac{7}{6}u[/tex] , U is independent variable.
Which expression is equivalent to 8-(6r+2)?
Answer:
6(1-r)
Step-by-step explanation:
8-6r+2
=6-6r
=6(1-r)
The volume of a cube is given by the expression s to the power of 3, and its surface area is given by the expression 6s to the power of 2, where s is the length of the cube’s side. What is the volume of a cube with a side length of 5 inches?
Answer:
The volume of the cube would be 125in³
Step-by-step explanation:
The volume of a cube is s³ (side). 5 x 5 x 5 = 125.
What is the formula for the expected number of successes in a binomial experiment with n trials and probability of success p? Choose the correct forumla below.
A. Upper E (Upper X )equalsStartRoot np (1 minus p )EndRoot
B. Upper E (Upper X )equalsp Superscript n
C. Upper E (Upper X )equals (1 minus p )Superscript n(1 minus p )Superscript n
D. Upper E (Upper X )equalsnp
Answer:
[tex](D)E[ X ] =np.[/tex]
Step-by-step explanation:
Given a binomial experiment with n trials and probability of success p,
[tex]f(x)=\left(\begin{array}{c}n\\k\end{array}\right)p^x(1-p)^{n-x}, 0\leq x\leq n[/tex]
[tex]E(X)=\sum_{x=0}^{n}xf(x)= \sum_{x=0}^{n}x\left(\begin{array}{c}n\\k\end{array}\right)p^x(1-p)^{n-x}[/tex]
Since each term of the summation is multiplied by x, the value of the term corresponding to x = 0 will be 0. Therefore the expected value becomes:
[tex]E(X)=\sum_{x=1}^{n}x\left(\begin{array}{c}n\\x\end{array}\right)p^x(1-p)^{n-x}[/tex]
Now,
[tex]x\left(\begin{array}{c}n\\x\end{array}\right)= \frac{xn!}{x!(n-x)!}=\frac{n!}{(x-)!(n-x)!}=\frac{n(n-1)!}{(x-1)!((n-1)-(x-1))!}=n\left(\begin{array}{c}n-1\\x-1\end{array}\right)[/tex]
Substituting,
[tex]E(X)=\sum_{x=1}^{n}n\left(\begin{array}{c}n-1\\x-1\end{array}\right)p^x(1-p)^{n-x}[/tex]
Factoring out the n and one p from the above expression:
[tex]E(X)=np\sum_{x=1}^{n}n\left(\begin{array}{c}n-1\\x-1\end{array}\right)p^{x-1}(1-p)^{(n-1)-(x-1)}[/tex]
Representing k=x-1 in the above gives us:
[tex]E(X)=np\sum_{k=0}^{n}n\left(\begin{array}{c}n-1\\k\end{array}\right)p^{k}(1-p)^{(n-1)-k}[/tex]
This can then be written by the Binomial Formula as:
[tex]E[ X ] = (np) (p +(1 - p))^{n -1 }= np.[/tex]
The correct formula for the expected number of successes in a binomial experiment with n trials and probability of success p is μ = np (Option D), which means that the expected number of successes is calculated by multiplying the total number of trials by the probability of success.
Explanation:The formula for the expected number of successes in a binomial experiment with n trials and probability of success p is given by μ = np. In this formula, 'n' represents the number of trials, and 'p' is the probability of success on each trial. Therefore, the correct option, in this case, is D. Upper E (Upper X ) equals np.
This essentially means that the expected number of successes is obtained by multiplying the total number of trials by the probability of success. For instance, if you were to flip a coin (where the probability of getting heads is 0.5) 10 times, the expected number of times you'd get heads would be 0.5 * 10 = 5.
Learn more about the Expected Number of Successes here:https://brainly.com/question/35646493
#SPJ3
Does the equation specify a function with independent variable x? If so, find the domain of the function. If not, find a value of x to which there corresponds more than one value of y. 6 x plus 19 yequals7
Yes, the equation specifies a function with independent variable x.
Equation: 6x + 19y = 7
This can be put in y = mx + b form,
6x + 19y = 7
19y = -6x + 7
y = -[tex]\frac{6}{19}[/tex]x + [tex]\frac{7}{19}[/tex]
Since the equation can be put in the form of a linear function, the domain is all read numbers (-∞,∞) or -∞ < x < ∞ .
The equation 6x + 19y = 7 does not specify a function in terms of x because for each value of x, there exist multiple possible values of y. A specific example is shown when x = 1.
Explanation:The equation "6x + 19y = 7" does not specify a function with the independent variable x. In a function, each input (x) corresponds to exactly one output (y). However, in this equation, each value of x corresponds to multiple values of y, thus it does not represent a function.
In order to find a value of x for which there are multiple corresponding values of y, we can set x to any arbitrary value. For example, if we set x = 1, we get "6(1) + 19y = 7", which simplifies to "19y = 1". This implies that there are infinite solutions for y when x = 1, confirming that the equation does not represent a function.
Learn more about Function & Domainhttps://brainly.com/question/1942755
#SPJ3
How do I find the area of a circle with the diameter of 4
Answer:
use [tex]a = 1/4\pi d^2\\[/tex]
all you have to do is plug 4 into d and then square it, and multiply everything together.
Step-by-step explanation:
The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the eighth grade level. Step 2 of 2 : Suppose a sample of 1291 tenth graders is drawn. Of the students sampled, 1098 read above the eighth grade level. Using the data, construct the 95% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level. Round your answers to three decimal places.
Answer:
The 95% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level is (0.13, 0.168).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
1291 tenth graders, 1098 read above the eighth grade level.
1291 - 1098 = 193 read at or below this level.
We want the 95% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level.
So [tex]n = 1291, \pi = \frac{193}{1291} = 0.149[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.149 - 1.96\sqrt{\frac{0.149*0.851}{1291}} = 0.13[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.149 - 1.96\sqrt{\frac{0.149*0.851}{1291}} = 0.168[/tex]
The 95% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level is (0.13, 0.168).
Michaela says that |3| is bigger than |-3|.
Is Michaela’s statement true or false?
Answer:
False
Step-by-step explanation:
Because with the lines on the outside automatically changes the number to a positive number so, therefor the numbers are equal hope this help.
Rate brainlest plz
Michaela's statement that |3| is bigger than |-3| is true.
Explanation:Michaela's assertion that |3| is greater than |-3| is accurate. The absolute value of a number represents its distance from zero on the number line. In this case, |3| signifies a 3-unit distance from zero, and |-3| also corresponds to a 3-unit distance from zero. Since both values are equidistant from zero, their magnitudes are equal. Consequently, |3| and |-3| both have a value of 3, emphasizing that the absolute value of a number signifies its distance from zero, regardless of its sign, and in this case, both distances are identical at 3 units.
Learn more about Absolute Value here:https://brainly.com/question/18731489
#SPJ11
What is 10x5??? Help
Answer:
The actual Answer is 10x5=50
Answer: 50
Step-by-step explanation: it’s like when you get 10 and add it up 5 times you get 50
whats the slope of the graph -4, 5 1,-7.5
Answer:
Slope (m)= -12.5/5= -2.5
-12.5/5 in fraction form
or
-2.5 in decimal form
Step-by-step explanation:
slope (m)= -12.5/5= -2.5
the points belong as a decreasing linear function
equation: y= -2.5x-5
ANSWER ONLY IF YK IT IM GIVING CORRECT BRAINLIEST
Factor the expression completely : -15x^3+5
Answer:
-5(3x^3-1)
Step-by-step explanation:
-15x^3+5
Factor out -5
-5(3x^3-1)
Help me! ? Its math and I I bad at it!!!!!!!
Answer:
C. 31
Step-by-step explanation:
(570.7 - n) ÷ 16
(570.7 - 74.7) ÷ 16
496 ÷ 16
31
The defect length of a corrosion defect in a pressurized steel pipe is normally distributed with mean value 32 mm and standard deviation 7.3 mm. (a) What is the probability that defect length is at most 20 mm? Less than 20 mm?
Answer:
The probability that defect length is at most 20 mm (or less than 20 mm) is 0.0505
Step-by-step explanation:
Mean defect length = u = 32
Standard deviation = [tex]\sigma[/tex] = 7.3
The distribution is normal and we have the value of population standard deviation so we will use the concept of z-score and probability from z-table to find the said probability.
We have to find the probability that the defect length is at most 20 mm. At most 20 mm means equal to or lesser than 20 mm. Since the normal distribution is a continuous distribution, the probability of at most is approximately equal to probability of lesser than.
If X represents the distribution of defect lengths, then we can write:
P(X ≤ 20) ≅ P(X < 20)
We can find the probability of defect length being lesser than 20 mm by converting it to z-score and find the corresponding probability from the z-table.
The formula to calculate the z-score is:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Substituting the values, we get:
[tex]z=\frac{20-32}{7.3}=-1.64[/tex]
Therefore, P(X < 20) is equivalent to P(z < -1.64)
From z-table we can find the probability of z being lesser than - 1.64, which comes out to be:
P(z < -1.64) = 0.0505
Therefore, we can conclude that:
The probability that defect length is at most 20 mm (or less than 20 mm) is 0.0505
The head of maintenance at XYZ Rent-A-Car believes that the mean number of miles between services is 2643 miles, with a standard deviation of 368 miles. If he is correct, what is the probability that the mean of a sample of 44 cars would differ from the population mean by less than 51 miles
Final answer:
To find the probability that the mean of a sample of 44 cars would differ from the population mean by less than 51 miles, use the Central Limit Theorem to approximate the distribution of sample means. Calculate the standard error using the formula: standard error = population standard deviation / sqrt(sample size). Then, standardize the sample mean using the z-score formula. Finally, find the probability using a standard normal distribution table or a calculator.Therefore, the probability that the mean of a sample of 44 cars would differ from the population mean by less than 51 miles is approximately 0.3595, or 35.95%.
Explanation:
To find the probability that the mean of a sample of 44 cars would differ from the population mean by less than 51 miles, we can use the Central Limit Theorem. According to the Central Limit Theorem, the distribution of sample means approximates a normal distribution, regardless of the shape of the population distribution, as long as the sample size is large enough (typically n ≥ 30).
First, we need to calculate the standard error, which is the standard deviation of the sampling distribution of the sample mean. The standard error is given by the formula: standard error = population standard deviation / sqrt(sample size). In this case, the population standard deviation is 368 miles, and the sample size is 44. Therefore, the standard error = 368 / sqrt(44) = 55.354 miles.
Next, we use the z-score formula to standardize the sample mean. The z-score = (sample mean - population mean) / standard error. Plugging in the given values, we get: z-score = (51 - 2643) / 55.354 = -0.3668.
Finally, we need to find the probability that the standardized sample mean (z-score) is less than -0.3668. We can use a standard normal distribution table or a calculator to find the corresponding probability. From the standard normal distribution table, we find that the probability corresponding to a z-score of -0.3668 is approximately 0.3595. Therefore, the probability that the mean of a sample of 44 cars would differ from the population mean by less than 51 miles is approximately 0.3595, or 35.95%.