Answer:
The sampling distribution of the sample mean is approximately normal with mean 72 and standard deviation 1.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Normally distributed with mean 72 and standard deviation 6.
This means that [tex]\mu = 72, \sigma = 6[/tex]
A random sample of size 36
This means that [tex]n = 36, s = \frac{6}{\sqrt{36}} = 1[/tex]
The sampling distribution of the sample mean is
By the Central Limit Theorem, it is approximately normal with mean 72 and standard deviation 1.
find the amount on 800 for one year at 10%
Answer:
80
Step-by-step explanation:
You mean the "interest on"
I=800×.1×1=80
Help me plz I can’t figure it out
Answer:
m = 60
Step-by-step explanation:
The context is very important, the 'm' represents the minutes late the parents are and from this we can eliminate some options :
- The last one because then a parent would drop their child off earlier
- The first one and the third one because it is too long
What is the m GE bisects Find m
Answer:
DGF = 106
Step-by-step explanation:
Bisects means to divide in half, with two equal parts
DGF = DGE + EGF
DGE = EGF
DGF = DGE + DGE
DGF = 53+53
DGF = 106
GE bisects ∠DGF, so it divides ∠DGF into 2 equal parts.
So, m∠EGF = m∠DGE
=> m∠EGF = 53°
m∠DGF = m∠EGF + m∠DGE
=> m∠DGF = 53° + 53°
=> m∠DGF = 106°
If the bearing of P and
Q is
145°. What is the bearing of
Q from P?
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Answer:
325°
Step-by-step explanation:
The bearing in the reverse direction is 180° more (or less) than the bearing in the forward direction.
145° +180° = 325°
The bearing of Q from P is 325°.
If the bearing of P and
Q is 145°
Soo,
the bearing of Q from P is 145+180=325°
Because it is reserve in the forward direction
[tex]\sf{ }[/tex] [tex]\sf{ }[/tex] [tex]\sf{ }[/tex]
if y = k where k is a constant and y =24 when x =6 what is the value of y when x= 5
Answer:
20
Step-by-step explanation:
y=kx
24=6k
k=4
y=4*5=20
Given a parametric curve
{x = 2 cost
{y = 4 sint 0 <= t <= π
a. Set up but do NOT evaluate an integral to find the area of the region enclosed by the curve and the x-axis.
b. Set up but do NOT evaluate an integral to find the area of the surface obtained by rotating the curve about the x-axis.
(a) The area of the region would be given by the integral
[tex]\displaystyle\int_0^\pi y(t)\left|x'(t)\right|\,\mathrm dt = 8 \int_0^\pi \sin^2(t)\,\mathrm dt[/tex]
(b) The area of the surface of revolution would be given by
[tex]\displaystyle\int_0^\pi y(t)\sqrt{x'(t)^2+y'(t)^2}\,\mathrm dt = 4\int_0^\pi\sin(t)\sqrt{4\sin^2(t)+16\cos^2(t)}\,\mathrm dt[/tex]
After heating a fixed volume of gas at 50 psia from 300° R to 600°R, its pressure will be:
Answer:
100 psia
Step-by-step explanation:
Applying,
Pressure law,
P/T = P'/T'................. Equation 1
Where P = initial pressure, P' = Final pressure, T = initial temperature, P' = Final temperature.
make P' the subject of the equation
P' = PT'/T............ Equation 2
From the question,
Given: P = 50 psia, T = 300°R = (300×5/9)K = 166.66 K, T' = 600°R = (600×5/9)K = 333.33 K
Substitute these values into equation 2
P' = (50×333.33)/166.66
P' ≈ 100 psia
P ≈ 100 psia
Pls help this is rlly important!! You’ll get branliest bc this is hard and I’m stuck.
the median of restaurant b's cleanliness ratings is 2.
the median of restaurant b's food quality ratings is 4.
the median of restaurant b's service ratings is 3.
:))
15×115-(-3)}(4-4)÷3{5+(-3)×(-6
Answer:
15×115+3{0÷3}5-3×(-6)
15×115+3of 0 of 5-3×(-6)
15×115+0 of 5-3×(-6)
15×115+0+18
1725+0+18
1743
The sum of 7/3 and four times a number is equal to 2/3 subtracted from five times the number?
Answer:
-3
Step-by-step explanation:
625^1+1 *125^-1-1 *25^-1+2
Answer:
626.968
Step-by-step explanation:
EMDAS rule
HELP PLSSSS I will GIVE BRAINLYEST!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
If one card is drawn from a deck, find the probability of getting these results.
Enter your answers as fractions or as decimals rounded to 3 decimal places.
Answer:
Face card= 12/52
(52 cards in a deck and 12 are face cards)
Red face card= 6/12
(12 face cards in a deck cards in a deck and 6 are red face cards)
Black face card= 6/52
(6 are black)
Black card= 26/52
(52 cards in a deck and 26 are black)
Red card= 26/52
(26 are red)
Restaurants sales totaled $38,676 for the week your customer count was $7,325 what did the average customer spend for the week
Which table represents a direct variation function?
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Answer:
(b) the correct table is marked
Step-by-step explanation:
Direct variation is characterized by the ratio of y to x being a constant for all values in the table. That constant is the constant of proportionality. For the values in the second table (marked), the ratio is ...
y/x = 8/6 = 12/9 = 16/12 = 4/3
The constant of proportionality is 4/3.
Suppose you choose a marble from a bag containing 3 red marbles, 5 white marbles, and 4 blue
marbles. You return the first marble to the bag and then choose again. Find P (red and blue).
Answer:
P(red and blue) = 1/12
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
Probability of independent events:
If two events, A and B, are independent, the probability of both happening is the multiplication of the probabilities of each event happening, that is:
[tex]P(A \cap B) = P(A)P(B)[/tex]
P (red and blue).
Probability of choosing a red marble, then a blue marble. The marbles are replaced, so the trials are independent.
Probability of a red marble:
3 out of 3 + 5 + 4 = 12. So
[tex]P(A) = \frac{3}{12} = \frac{1}{4}[/tex]
Probability of a blue marble:
4 out of 12, so:
[tex]P(B) = \frac{4}{12} = \frac{1}{3}[/tex]
P (red and blue).
[tex]P(A \cap B) = P(A)P(B) = \frac{1}{4} \times \frac{1}{3} = \frac{1}{4*3} = \frac{1}{12}[/tex]
So
P(red and blue) = 1/12
The graph below has the same shape as the graph of G(x) = x, but it is
shifted three units to the left. Complete its equation. Enter exponents using
the caret (-); for example, enter x as x^4. Do not include "G(x) =" in your
answer.
G(x) =
Answer:
G(x) = x+3
Step-by-step explanation:
The equation of the graph is G (x) = (x - 3)⁴
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
A relation between a set of inputs having one output each is called a function.
An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
The graph of function G (x) is shown in image.
Here, the graph is 3 units left to function F (x) = x⁴.
The equation of the graph is G (x) = (x - 3)⁴
Hence, the equation of the graph is G (x) = (x - 3)⁴
To learn more on Graph click:
https://brainly.com/question/17267403
#SPJ7
Can someone help me please..
An irrigation system (sprinkler) has a parabolic pattern. The height, in feet, of the spray of water is given by the equation h(x) = -x^2+10x+7.5 where x is the number of feet away from the sprinkler head (along the ground) the spray is.
The irrigation system is positioned____ feet above the ground to start.
The spray reaches a maximum height of ____feet at a horizontal distance of feet away from the sprinkler head.
The spray reaches all the way to the ground at about_____ feet away
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Answer:
7.5 ft32.5 ft, 5 ft10.7 ftStep-by-step explanation:
a) The starting height is h(0) = 7.5 feet, the constant in the quadratic function.
The irrigation system is positioned 7.5 feet above the ground
__
b) The axis of symmetry for quadratic ax^2 +bx +c is x = -b/(2a). For this quadratic, that is x=-10/(2(-1)) = 5. This is the horizontal distance to the point of maximum height. The maximum height is ...
h(5) = (-5 +10)(5) +7.5 = 32.5 . . . feet
The spray reaches a maximum height of 32.5 feet at a horizontal distance of 5 feet from the sprinkler head.
__
c) The maximum distance will be √32.5 + 5 ≈ 10.7 ft.
The spray reaches the ground at about 10.7 feet away.
Answer:
7.5
32.5
5
maximum
10.7
Step-by-step explanation:
Help asap please!!..
Answer:
9x² - 4/3x + ¼
Step-by-step explanation:
(3x - ½)²
(3x - ½)(3x -½)
9x² - ⅔x - ⅔x + ¼
9x² - 4/3x + ¼
Ed decided to build a storage box. At first, he was planning to build a cubical box with edges of length n inches. To increase the amount of storage, he decided to make the box 1 inch taller and 2 inches longer while keeping its depth at n inches. The volume of the box Ed built has a volume how many cubic inches greater than the box he originally planned to build?
Answer:
The new volume is 3n^2+2n inches greater.
Step-by-step explanation:
Volume of a cube = s^3 where s is side of cube
Original volume = n^3
Volume of a Rectangular Prism = LBH
New Volume = (n+1)(n+2)(n)= n^3+3n^2+2n
DIfference = New- original = 3n^2+2n
Can someone help me please! Thanks
Answer:
hello again.. I think you have a problem about figures
Step-by-step explanation:
please be brave when you try to solve..try to draw new lines to get angle and then look at the overall of shape.. the photo helps you good bye
The highway department is testing two types of reflecting paint for concrete bridge end pillars. The two kinds of paint are alike in every respect except that one other is yellow. The orange paint is applied to 12 bridges, and the yellow paint is applied to 12 bridges. After a period of 1 year, reflectometer readings were made end pillars. (A higher reading means better visibility.) For the orange paint, the mean reflectometer reading was x19.4, with standard deviation s1-2.5. For the mean was X2-6.5, with standard deviation S2-2.4. Based on these data, can we conclude that the yellow paint has less visibility after 1 year?
Use a 10% level What are we testing in this problem?
a. difference of means
b. single proportion
c. difference of proportions
d. single mean
e. paired difference
Answer:
a. difference of means
Step-by-step explanation:
Given that :
Mean , x = 9.4
Standard deviation, [tex]s.d_1[/tex] = 2.5
Number, [tex]n_1[/tex] = 12
Mean, y = 6.5
standard deviation, [tex]s.d_2[/tex] = 2.4
Number, [tex]n_2[/tex] = 12
The null hypothesis is : [tex]$H_0: \mu_1=\mu_2$[/tex]
The alternate hypothesis is : [tex]$H_1: \mu_1>\mu_2$[/tex]
Level of significance, [tex]\alpha[/tex] = 0.1
From the [tex]\text{standard normal table, right tailed,}[/tex] [tex]$t_{1/2}$[/tex] = 1.363
Since out test is right tailed.
Reject [tex]H_0[/tex], if [tex]$T_0>1.363$[/tex]
We use the test statics,
[tex]$t_0=\frac{(x-y)}{\sqrt{\frac{s.d_1}{n_1}+\frac{s.d_2}{n_2}}}$[/tex]
[tex]$t_0=\frac{(9.4-6.5)}{\sqrt{\frac{6.25}{12}+\frac{5.76}{12}}}$[/tex]
[tex]$t_0=2.899$[/tex]
[tex]$|t_0|=2.899$[/tex]
[tex]\text{Critical value}[/tex]
The value of [tex]$|t_{1/2}|$[/tex] with minimum [tex]$\left(n_1-1,n_2-1)$[/tex] that is 11 df is 1.363
We go [tex]$|t_0|=2.899$[/tex] and [tex]$|t_{1/2}|$[/tex] = 1.363
Decision making:
Since the value of [tex]|t_0|>|t_{1/2}|$[/tex] and we reject the [tex]H_0[/tex]
The p-value : right tail [tex]H_a:(p>2.8988)[/tex]
= 0.00724
Therefore the value of [tex]$p_{0.1} > 0.00724$[/tex], and so we reject the [tex]H_0[/tex]
Thus we are testing 'the difference of means" in this problem.
Use sigma notation to represent the sum of the first seven terms of the following sequence: −4, −6, −8, …
Answer:
[tex]\sum_{n = 1}^{7} -2 -2n[/tex]
Step-by-step explanation:
Arithmetic sequence:
In an arithmetic sequence, the difference of consecutive terms is always the same, called common difference.
The nth term of a sequence is given by:
[tex]a_{n} = a_1 + (n-1)d[/tex]
In which [tex]a_1[/tex] is the first term and d is the common difference.
Sigma notation to represent the sum of the first seven terms
Sum going from the index starting at 1 and finishing at 7, that is:
[tex]\sum_{n = 1}^{7} f(n)[/tex]
Now we have to fund the function, which is given by an arithmetic sequence.
−4, −6, −8,
First term -4, common difference - 6 - (-4) = -6 + 4 = -2, so [tex]a_1 = -4, d = -2[/tex]
Then
[tex]f(n) = a_{n} = a_1 + (n-1)d[/tex]
[tex]f(n) = -4 + (n-1)(-2)[/tex]
[tex]f(n) = -4 - 2n + 2 = -2 - 2n[/tex]
Sigma notation:
Replacing f(n)
[tex]\sum_{n = 1}^{7} -2 -2n[/tex]
Express the following composite numbers as products of prime factors 64
Answer:
64 is a composite number, and it is 8 squared. 64 = 1 x 64, 2 x 32, 4 x 16, or 8 x 8. Factors of 64: 1, 2, 4, 8, 16, 32, 64. Prime factorization: 64 = 2 x 2 x 2 x 2 x 2 x 2, which can also be written 64 = 2⁶.
Lena and Ras drive to work. Lena drives 24 miles in 1.5 hours. Ras drives 36 km in 1 hour 15 min. Work out the difference between their average speeds in km/h. 1 mile = 1.6 km
Answer:
Difference = 3.2 km/h
Step-by-step explanation:
Given that,
Lena drives 24 miles in 1.5 hours. Ras drives 36 km in 1 hour 15 min.
For average speed of Lena,
d = 24 miles = 38.4 km
t = 1.5 h
[tex]v=\dfrac{38.4}{1.5}= 25.6\ km/h[/tex]
For average speed of Ras,
d = 36 km
t = 1h 15 min = 1.25 h
[tex]v=\dfrac{36}{1.25}=28.8\ km/h[/tex]
Difference = 28.8-25.6
= 3.2 km/h
So, the difference between their average speed is 3.2 km/hr.
Answer:
3.2 km/h
Step-by-step explanation:
Chloe is working two summer jobs, landscaping and clearing tables. She must work no less than 12 hours altogether between both jobs in a given week. Write an inequality that would represent the possible values for the number of hours landscaping, ll, and the number of hours clearing tables, cc, that Chloe can work in a given week.
Answer:
[tex] L + C \ge 12 [/tex]
Step-by-step explanation:
L = hours landscaping
C = hours clearing tables
The sum of the hours must be no less than 12, so it must be 12 or more.
[tex] L + C \ge 12 [/tex]
what was the original price of the car? MUST SHOW ALL STEPS OF THE PROCESS.
Answer:
19219.48
Step-by-step explanation:
16540x0.162+16540
The original price would be 100%
It was marked down 16.2%
100 % - 16.2% = 83.8%
The price you paid was 83.8% of the original price.
To find the original price divide the amount you paid by the percentage of the original price:
16,540 / 0.838 = 19.737.47
Original price: $19,737.47
Graph the solution set to this Inequality.
-2x + 9 < 51 12
Answer:
X<-2551.5
Step-by-step explanation:
-2x<5112-9
-2x/-2<5103/-2
x<-2551.5
3x7 I need help with this i do not know the answer pls help.
Answer:
21
Step-by-step explanation:
7+7+7=21
