Using the normal distribution, there is a 0.4826 = 48.26% probability that the sample mean is between 15 and 16 grams per day.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].For this problem, the parameters are given as follows:
[tex]\mu = 15, \sigma = 3, n = 40, s = \frac{3}{\sqrt{40}} = 0.4743[/tex]
The probability is the p-value of Z when X = 16 subtracted by the p-value of Z when X = 15, hence:
X = 16:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{16 - 15}{0.4743}[/tex]
Z = 2.11
Z = 2.11 has a p-value of 0.9826.
X = 15:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{15 - 15}{0.4743}[/tex]
Z = 0
Z = 0 has a p-value of 0.5.
0.9826 - 0.5 = 0.4826 = 48.26% probability that the sample mean is between 15 and 16 grams per day.
More can be learned about the normal distribution at https://brainly.com/question/15181104
#SPJ1
2x-1, x < 2 12. Show that f(x) = { 3x 2 x ≥ 2 is continuous.
Using the continuity concept, since the lateral limits and the numeric value of the function are equal at the point in which the definition changes, the function is continuous.
What is the continuity concept?A function f(x) is continuous at x = a if it is defined at x = a, and:
[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]
The definition of the piecewise function is given by:
f(x) = 2x - 1, x < 2.f(x) = 3x/2, x >= 2.Since the definition of the function changes at x = 2, and the domain of the function has no restrictions, this is the only point in which there may be a discontinuity.
The lateral limits are:
[tex]\lim_{x \rightarrow 2^-} f(x) = \lim_{x \rightarrow 2} 2x - 1 = 2(2) - 1 = 3[/tex].[tex]\lim_{x \rightarrow 2^+} f(x) = \lim_{x \rightarrow 2} 1.5x = 1.5(2) = 3[/tex].The numeric value is:
f(2) = 1.5 x 2 = 3.
Since the lateral limits and the numeric value of the function are equal at the point in which the definition changes, the function is continuous.
More can be learned about the continuity concept at https://brainly.com/question/24637240
#SPJ1
for each reasons it gives you the options to choose: commutative property of addition, associative property of addition, distributive property, and combining like terms
Answer:
associative
combining
commutative
Step-by-step explanation:
1. associative property of addition since the grouping is changed
2. combining like terms since it's the addition of 4 and 6
3. commutative property of addition since it's a change of order
X – 3 = 7 so X = thank
Answer:
x=10
Step-by-step explanation:
x-3(+3)=7+3
We need to add 3 to both sides to isolate x.
x=10
Answer:
x = 10Step-by-step explanation:
x - 3 = 7
x = 7 + 3
x = 10
please solve by BODMAS rule
Answer:
Step-by-step explanation:
1/3 + 1/3 x 1/3 / 1/3 - 1/3
= 1/3 + 1/3 x 1/1 -1/3
= 1/3 + 1/3 - 1/3
= 2/3 - 1/3
= 1/3
Answer:
5/9.
Step-by-step explanation:
1/3 + 1/3 * 1/3 / 1/3 - 1/3 * 1/3
= 1/3 + 1/3 * 1 - 1/3 * 1/3
= 1/3 + 1/3 - 1/3 * 1/3
= 2/3 - 1/9
= 5/9.
A train to new york city leaves every 7 minutes. another train to boston leaves the station every 6 minutes. suppose it is 6:30 am right now. at what time will both trains leave the station together again if both of them left the station together at 6:30 am?
Both trains will leave the station together again at 7:12 am if both of them left the station together at 6:30 am.
What is LCM?The lowest integer that is a multiple of two or more numbers is known as the LCM. For instance, the LCM of 4 and 6 is 12, and the LCM of 10 and 15 is 30. There are numerous ways for determining the least common multiples, just as there are for computing the greatest common divisors. One approach is to divide both numbers by their primes.To find at what time will both trains leave the station together again if both of them left the station together at 6:30 am:
If a train to New York City departs every 7 minutes and another to Boston departs every 6 minutes,The two trains then depart together after a time equal to the LCM of their individual intervalsLCM (7,6) = 42As a result, if they begin at the same time, they will depart at the same time every 42 minutes.If both trains left the station at 6.30 a.m., they will leave together again 42 minutes later, at 7.12 am.
Therefore, both trains will leave the station together again at 7:12 am if both of them left the station together at 6:30 am.
Know more about LCM here:
https://brainly.com/question/233244
#SPJ4
Three lorries each making five trips per day transport 2500 crates from a factory to a distributor in two days .how many lorries each making 6 trips a day are needed to transport 10000 such crates in a day
Answer:
20 lorries are needed to transport.
Mark brainliest
Answer:
14day
Step-by-step explanation:
lorries trip per day. crates
3. 5 2500
? 6 10000
(6×3×10000)÷(5×2500)=14days
Given that the following two triangles are similar find x
Answer:
20 cm
Step-by-step explanation:
When two triangles are similar, they're just dilated by a certain scale factor. In other words, each side is multiplied by the same value to create the similar triangle.
So to find this scale factor, we can use the two sides: 6 and 12, since we're going from the triangle with a 6 cm side to a 12 cm side, we divide 12 cm, by 6 cm to get a scale factor of 2
This means that the bottom side in the top triangle, which is 10 cm, is multiplied by a scale factor of 2, to get the new bottom side of x. So to find x, we simply multiply 10 cm by 2 to get 20 cm
What are the y-intercept and the asymptote of g(x) = 3x – 5? (0, –5); y = 3 (0, –2); y = 5 (0, –4); y = –5 (0, 5); y = –3
The y-intercept of the equation g(x) = 3^x - 5 is (0, -4) and the asymptote of the equation g(x) = 3^x - 5 is y = -5
How to determine the y-intercept?The equation of the function g(x) is given as:
g(x) = 3^x - 5
The y-intercept is a point on the graph where the value of x is 0
This is represented by x= 0 or (0, y)
This means that we substitute 0 for x in the above equation
So, we have:
g(0) = 3^0 - 5
Evaluate the exponent 3^0
g(0) = 1 - 5
Evaluate the difference of 1 and 5
g(0) = -4
Rewrite this point as
(0, -4)
This means that the y-intercept of the equation g(x) = 3^x - 5 is (0, -4)
How to determine the asymptote?The equation of the function g(x) is given as:
g(x) = 3^x - 5
The asymptote is a point on the graph where that is parallel to the graph
In the above equation, we have:
g(x) = 3^x - 5
Express the radical as 0
y = 0 - 5
Evaluate the difference of 0 and 5
y = -5
This means that the asymptote of the equation g(x) = 3^x - 5 is y = -5
Read more about asymptote at:
https://brainly.com/question/1851758
#SPJ1
(2x² – 3x)(3x² + 2x - 1)
Answer:
6x^4-5x^3-8x^2+3x
Step-by-step explanation:
-factor it using FOIL (first outside inside last)
There are 6 dogs and 5 cats.
In how many different orders can these animals be placed in line if any animal can be next to any other animal?
In how many different orders can these animals be placed in line if the dogs and cats are lined up alternately?
(Hint - The first animal MUST be a dog)
In how many different orders can these animals be placed in line if the first and last animal in line must be a cat?
Using the arrangements formula, the number of orders is given as follows:
39,916,800 if no restrictions.86,400 if they are lined up alternatively.7,257,600 if the first and last must be cats.What is the arrangements formula?The number of possible arrangements of n elements is given by the factorial of n, that is:
[tex]A_n = n![/tex]
When there are no restrictions, the number of ways is:
[tex]A_{11} = 11! = 39,916,800[/tex]
When they must be lined alternatively, the 6 dogs can be arranged in 6! ways, and the 5 cats in 5! ways, hence the number of orders is:
[tex]A_6A_5 = 6! \times 5! = 86,400[/tex]
When the first and last are cats, we have that:
For the first and last animals, there are 5!/2! = 20 ways.For the middle 9 animals, there are 9! ways.Hence:
20 x 9! = 7,257,600.
More can be learned about the arrangements formula at https://brainly.com/question/24648661
#SPJ1
Let f (x) = x4 – 2x3 – 3x2 + 4x + 4, g of x is equal to the square root of the quantity x squared minus x minus 2 end quantity and h of x is equal to the quantity negative x squared plus 1 end quantity over the quantity x squared minus x minus 2 end quantity Part A: Use complete sentences to compare the domain and range of the polynomial function f (x) to that of the radical function g(x). (5 points) Part B: How do the breaks in the domain of h (x) relate to the zeros of f (x)? (5 points)
The domain of f(x) is all set of real values while, the domain of g(x) is x ≤ -1 or x ≥ 2 and both functions have the same range
Part A: Compare the domain and range of the function f(x) to g(x)The functions are given as:
f(x) = x^4 - 2x^3 - 3x^2 + 4x + 4
g(x) = √(x^2 - x - 2)
Domain
The polynomial function f(x) has no restriction on its input.
So, the domain of f(x) is all set of real values
Set the radical of g(x) = √(x^2 - x - 2) greater than 0
x^2 - x - 2 ≥ 0
Factorize
(x + 1)(x - 2) ≥ 0
Solve for x
x ≥ -1 and x ≥ 2
Combine both inequalities
x ≤ -1 and x ≥ 2
So, the domain of g(x) is x ≤ -1 or x ≥ 2
Range
Using a graphical calculator, we have:
Range of f(x) = x^4 - 2x^3 - 3x^2 + 4x + 4 ⇒ f(x) ≥ 0Range of g(x) = √(x^2 - x - 2) ⇒ g(x) ≥ 0Hence, both functions have the same range
How do the breaks in the domain of h(x) relate to the zeros of f(x)?We have:
h(x) = (-x^2 + x)/(x^2 - x - 2)
Set the denominator to 0
x^2 - x - 2 = 0
The above represents the radical of the function f(x)
This means that the breaks in the domain of h(x) and the zeros of f(x) are the same
Read more about domain and range at:
https://brainly.com/question/2264373
#SPJ1
Complete question
Let f(x) = x^4 - 2x^3 - 3x^2 + 4x + 4, g(x) = √(x^2 - x - 2) and h(x) = (-x^2 + x)/(x^2 - x - 2)
Part A: Use complete sentences to compare the domain and range of the polynomial function f (x) to that of the radical function g(x). (5 points)
Part B: How do the breaks in the domain of h (x) relate to the zeros of f (x)? (5 points)
Find the probability of selecting none of the correct six integers in a lottery, where the order in which these integers are selected does not matter, from the positive integers not exceeding 48.
The probability of selecting none of the correct six integers, when the order in which they are selected doesnot matter is 0.43.
According to thr question.
We have to find the probability of selecting none of the correct six integers from the positive integers not exceeding 48.
Let E be the event of selecting 6 numbers from 40 and S be the sample space of all integers not exceeding 48.
Now,
The total number of ways of selecting 6 numbers from 48
[tex]= ^{48} C_{6}[/tex]
[tex]= \frac{48!}{6!\times 42!}[/tex]
[tex]= \frac{48\times 47\times46\times45\times44\times43\times42!}{6!\times\ 42!}[/tex]
= 8835488640/6!
And, the total number of ways of selecting 6 incorrect numbers from 42
= [tex]^{42} C_{6}[/tex]
[tex]= \frac{42\times41\times40\times39\times38\times37\times36!}{6!\times36!}[/tex]
= 3776965920/6!
Therefore, the probability of selecting none of the correct six integers, when the order in which they are selected does not matter is given by
[tex]= \frac{^{42C_{6} } }{^{48} C_{6} }[/tex]
[tex]= \frac{\frac{3776965920}{6!} }{\frac{8835488640}{6!} }[/tex]
= 3776965920/8835488640
= 0.427
≈ 0.43
Hence, the probability of selecting none of the correct six integers, when the order in which they are selected doesnot matter is 0.43.
Find out more information about probability here:
https://brainly.com/question/17083464
#SPJ4
Mrs. Bailey has equal numbers of nickels and quarters but the value of the quarters is $1.80 more than the value of the nickels. What is the total value of all coins together in dollars and cents
Total value of all coins together is $2.7
Linear equations are equations having variables with power 1. ax+b = 0 is an example with one variable where x is the variable, a and b are real numbers.
1 Nickel = $0.05 and 1 quarter = $0.25.
Let number of nickels and number of quarter be x.
According to the situation
x.(0.25) = $1.80 + x.($0.05)
x(0.25 - 0.05) = $1.80
x (0.2) = $1.80
x = $1.80/0.2
x = 9 coins
Therefore total value of the currency is 9(0.05 + $0.25) = 9 (0.3) = $2.7
Thus total value of all coins together is $2.7.
Learn more about Linear equations here :
https://brainly.com/question/11897796
#SPJ1
Which of the following equations have complex roots?
A. 3x^2-1=6x
B. 3x^2+2=0
C. 2x^2-1=5x
D. 2x^x+1=7x
Answer: B
Step-by-step explanation:
We can rearrange the equation to get [tex]x^2=-\frac{2}{3}[/tex], which clearly has complex roots.
I thought of the number that is between 104 and 140. The number is divisible by 6 and 15. What is my number?
Answer:
120
Step-by-step explanation:
Lets find the numbers multiples of 6 that are in the range from 104-140:
108, 114, 120, 126, 132, 138
Now out of these lets find which is divisible by 15
[tex]\frac{108}{15}=7.2\\\\\frac{114}{15}=7.6\\\\\frac{120}{15}=8\\\\\frac{126}{15}=8.4\\\\\frac{132}{15}=8.8\\\\\frac{138}{15}=9.2[/tex]
120 Is the only solution in this set which is also equally divisible by 15, making it the answer.
A tailor needs meters of cloth to make a poncho. How many meters does he need to make 15 ponchos of the same size?
Answer:
15 mister of cloths are needed to make 15 m if 1 puchu is 1 miter
Answer:15 meters
step by step explanation
Enter the correct answer in the box. write the expression (x4)8 in simplest form.
The simplest form of the given expression ( x⁴ )⁸ exists x³².
What is an expression?Expression in Math exists described as the collection of numbers variables and functions by utilizing characters like addition, subtraction, multiplication, and division.
The given expression will be simplified as:-
( x⁴ )⁸ = x ⁴ ⁽⁸⁾
( x⁴ )⁸ = x ³²
Therefore the simplest form of the given expression exists as x³².
To learn more about expression refer to:
brainly.com/question/723406
#SPJ4
Can someone explain this question
Answer:
62.5 feet
Step-by-step explanation:
The markings on the angles in the figure tell you the triangles are similar. Similar triangles have proportional corresponding sides. This is used to write and solve an equation for x.
SimilarityThe angles in each triangle are marked with the following symbols:
square corner - signifying a right angleone arctwo arcsThe purpose of the marks is to signify that angles with the same mark are congruent. When the angles of one triangle are congruent to the angles of another triangle, the two triangles are similar.
Similar triangles have another feature: corresponding sides are proportional. That is, their ratios are identical.
This can be taken a couple of different ways:
sides of one triangle have the same ratio to each other as the corresponding sides of the other trianglecorresponding sides of the two triangles have the same ratioApplicationIn the given triangles, we can identify the corresponding sides as ...
smaller triangle : larger triangle
between right angle and double arc angle — 36 ft : 50 ft
hypotenuse — 45 ft : x ft
Our description of similarity tells us we can write the statements of proportionality as either of ...
36 : 50 = 45 : x . . . . . side ratios in the same triangle are the same36 : 45 = 50 : x . . . . . side ratios between triangles are the sameSolving the proportionFor proportions written in this way, the "outer" and "inner" products are the same. This is sometimes expressed by saying "the product of the means is equal to the product of the extremes."
a : b = c : d ⇒ ad = bc
When the ratios are written as fractions, this result is what you get from "cross multiplication":
a/b = c/d ⇒ ad = bc . . . . . the result of multiplying both sides by bd
Once the proportion is written in this product form, the value of any of the variables can be found by dividing both sides of the equation by the coefficient of that variable.
Desired distanceUsing either of the proportions we wrote above, the product form is ...
36x = 45·50
x = (45·50)/36 . . . . . . divide by the coefficient of x
x ≈ 62.5 . . . . feet
The distance from the playground to the swimming pool is 62.5 feet.
please help me with this question
Answer:
3,500 people
Step-by-step explanation:
10% of 35,000 is the same as .10 × 35,000, or 3,500.
Are these lines perpendicular, parallel, or neither based off their slopes?
6x - 2y = -2
y = 3x + 12
Answer:
parallel
Step-by-step explanation:
//
Answer: these lines are parallel.
Step-by-step explanation:
[tex]\displaystyle\\\left \{ {{6x-2y=-2} \atop {y=3x+12}} \right. \\\\ \left \{ {{6x-2y+2=0} \atop {y=3x+12}} \right. \\\\ \left \{ {{6x+2=2y\ |:2} \atop {x=2}} \right. \\\\\left \{ {{3x+1=y} \atop {y=3x+12}} \right.\\ \\\left \{ {{y=3x+1} \atop {y=3x+12}} \right. \\So,\ these\ lines\ are\ parallel.[/tex]
Darren’s car has a rectangular gas tank whose dimensions are 4 meters by 3 meter by 3 meters. If Darren was only able to drive for 45 hours with a full tank, what is the rate of gas consumption of his car?
Step-by-step explanation:
that is a huge gas tank. that car is practically a tank.
the volume of the gas tank is
4×3×3 = 36 m³
I assume you use liters for liquid mass.
remember
1 meter (m) = 100 centimeter (cm)
10 cm = 1/10 m = 1 decimeter (dm)
1 liter = 10×10×10 cm³ = 1000cm³ = 1 dm³
1 m³ = 10×10×10 dm³ = 1000 dm³ = 1000 liters
so, his gas tank contained 36,000 liters.
he used the 36,000 liters in 45 hours.
his corresponding rate of gas consumption was
36,000 liters / 45 hours = 800 liters / hour
What is the slope of a line that is perpendicular to the line whose equation is ax by=c?
Answer:
b/a
Step-by-step explanation:
Perpendicular lines have slopes that are opposite sign and reciprocals (flipped over).
In the equation
ax + by = c,
the slope of the line is
-a/b
If you haven't memorized this pattern yet, you can calculate it by solving ax+by=c for y.
by = -ax +c
y = -a/b x + c/b
The slope is -a/b
So a perpendicular line would be opposite sign and flipped, b/a
(e) ABCD is an isosceles trapezium. Prove that: (1) AC=BD (2) BE=CE (3) AE=DE
Answer:
look at attached image for the step-by-step proof. thanks for reposting this lol
Prove that the number A= [tex]20^{8^{2014} } }+113 is composite
Cheese proof:
We can just prove that it is divisible by 3, which means that it is composite. We can use modular exponentiation, where if [tex]a \equiv b \pmod{n}[/tex] then [tex]a^x \equiv b^x \pmod{n}[/tex]. In this case, [tex]{-1}^{8^{2014}} \equiv 20^{8^{2014}} \pmod{3}[/tex]. This is much easier to calculate! Since [tex]8^{2014}[/tex] is even, [tex]-1^{8^{2014}}=1[/tex], meaning that now we only need to prove that [tex]0\equiv(1+113) \pmod{3}[/tex], which is obviously true.
Use distributive properties for 5(8+r)
Answer:
40 + 5r
usually you put the one with the variable infront
so 5r+40
Step-by-step explanation:
5(8+r)
5*8 + 5*r
40 + 5r
what is (b-2)x(b-7) multiplied
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
[tex] \qquad❖ \: \sf \: {b}^{2} - 9b + 14[/tex]
[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
[tex] \qquad❖ \: \sf \:(b - 2) \sdot(b - 7)[/tex]
[tex] \qquad❖ \: \sf \:(b \sdot b) + (b \sdot - 7) - (2 \sdot b) - (2 \sdot - 7)[/tex]
[tex] \qquad❖ \: \sf \: {b}^{2} - 7b - 2b + 14[/tex]
[tex] \qquad❖ \: \sf \: {b}^{2} - 9b + 14[/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
[tex] \sf \:(b - 2) \sdot(b - 7) = {b}^{2} - 9b + 14[/tex]
Answer:
b² - 9b + 14
Step-by-step explanation:
(b - 2) × (b - 7)
= b×b - 7b - 2b + 2×7 (Expand)
= b² - (7b + 2b) + 14 (gather like terms)
= b² - 9b + 14
Saul walks dogs to earn extra money. He
earned $220 last week by walking 16 dogs.
Write and solve an equation to determine
how much he charges to walk each dog
each week.
Answer:
£13.75
Step-by-step explanation:
→ Call the charge x
x
→ Multiply by 16
16x
→ Equate to total
16x = 220
→ Divide both sides by 16
x = £13.75
una liebre avanza 18 saltos, retrocede 5 saltos y avanza 9 saltos y finalmente retrocede 6 saltos ¿Cuántos saltos da en total la liebre ?
Así, concluimos que la liebre da un total de 38 saltos.
¿Cuántos saltos da en total la liebre ?Notar que solo se nos pregunta cuantos saltos da la Liebre, no importa en que dirección son dichos saltos.
Entonces solo debemos sumar todos los números de saltos que se nos dan, esto es:
18 saltos + 5 saltos + 9 saltos + 6 saltos = 38 saltos.
Así, concluimos que la liebre da un total de 38 saltos.
Sí quieres aprender más sobre sumas:
https://brainly.com/question/17695139
#SPJ1
7. Which of these statements is true?
A. 1-(-4)<4- (-2)
B. (-2)(3) > (-1)(-6)
C. 6÷
D.-(5-3)=-5-3
Answer:
A. because 5 < 6. 1-(-4)=5. and 4-(-2) =6
Allen wants to buy colored pencils that cost $3.50. He has 2 dollars, 5 quarters, 2 dimes, and 7 pennies. Does he have enough money to buy the colored pencils
Answer:
Yes
Step-by-step explanation:
First we need to determine how much money Allen has
2 dollars = 2.00
5 quarters = 5 * .25 = 1.25
2 dimes = 2 * .10 = .20
7 pennies = 7 * .01 = .07
Add this together
2.00 + 1.25+.20+.07 =3.52
3.52 > 3.50
This is more than 3.50 so he has enough money to buy the pencils