Answer:
C. $32.09, since it's not the fixed cost, it changes based on how much drinks are purchased.
SAT verbal scores are normally distributed with a mean of 430 and a standard deviation of 120 (based on data from the College Board ATP). (a) If a single student is randomly selected, find the probability that the sample mean is above 500. (b) If a sample of 35 students are selected randomly, find the probability that the sample mean is above 500. These two problems appear to be very similar. Which problem requires the application of the central limit theorem, and in what way does the solution process differ between the two problems?
Using the normal distribution and the central limit theorem, it is found that there is a:
a) 0.281 = 28.1% probability that the sample mean is above 500.
b) 0.0003 = 0.03% probability that the sample mean is above 500.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, 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].In this problem:
The mean is of 430, hence [tex]\mu = 430[/tex].The standard deviation is of 120, hence [tex]\sigma = 120[/tex].Item a:
The probability is the p-value of Z when X = 500, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{500 - 430}{120}[/tex]
[tex]Z = 0.58[/tex]
[tex]Z = 0.58[/tex] has a p-value of 0.719.
1 - 0.719 = 0.281
0.281 = 28.1% probability that the sample mean is above 500.
Item b:
Sample of 35, hence [tex]n = 35, s = \frac{120}{\sqrt{35}}[/tex]
Then:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{500 - 430}{\frac{120}{\sqrt{35}}}[/tex]
[tex]Z = 3.45[/tex]
[tex]Z = 3.45[/tex] has a p-value of 0.9997.
1 - 0.9997 = 0.0003
0.0003 = 0.03% probability that the sample mean is above 500.
To learn more about the normal distribution and the central limit theorem, you can take a look at https://brainly.com/question/24663213
what is 4*6 i need help
Help me plz plllzzzz
I need help on this math question
Answer:
84
Step-by-step explanation:
7 Sizes * 3 Lengths * 4 Colors = 84
1: Solve and Graph: 5-3(x - 1)> 2
2: Solve and Graph: 2x - 3> 7 or x+5<2
3: Solve for x: |1x-5|=13
Answer:
3) x=18 , -8
Step-by-step explanation:
hi
hope it helps you
Plz help me i will give u 50pts^_^ and brainliest<3
Answer:
y/x^2=-2x+3
Step-by-step explanation:
Write a story that could represent this math problem 4 x 10/15 =
Mathew decided to have a picnic with his 4 friends. They were each assigned to bring 10 different foods. The food were to be brought in 15 bags total. How much food are there in each bag in total?
Triangle DNO has vertices at D(5, 8), N(– 3, 10), and O(– 3, 6). If vertex D is translated 4 units to the right, the best name for Triangle DNO is:
Answer Choices:
a. Scalene
b. Isosceles
c. Equilateral
d. Right
e. none of these
Using distance between two points to find the lengths of the edges of the triangle, the correct option is:
b. Isosceles
The distance between two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], is given by:
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
Vertex D is translated 4 units to the right is (9,8).
The lengths of the edges are:
[tex]DN = \sqrt{(9 - (-3))^2 + (8 - 10)^2} = \sqrt{12^2 + 2^2} = \sqrt{148}[/tex]
[tex]DO = \sqrt{(9 - (-3))^2 + (8 - 6)^2} = \sqrt{12^2 + 2^2} = \sqrt{148}[/tex]
[tex]NO = \sqrt{(-3 - (-3))^2 + (10 - 6)^2} = \sqrt{0^2 + 4^2} = 4[/tex]
Two edges of the same length, hence, it is an isosceles triangle, given by option b.
You can learn more about distance between two points at https://brainly.com/question/18345417
$145.75 marked up by 33% (round to the nearest cent)
Answer:
$189.48
Step-by-step explanation:
$145.75 + 30% × 145.75 = $145.75×1.30 ≈ $189.48
Whomever please
Find the perimeter of the triangle that has vertices at the points R(2,1), S (2,5), and T(4,
1). Round the answer to the nearest hundredth (2 decimal places).
A) 35.78
B) 32
C) 21.54
D)10.47
The perimeter of the triangle is 10.47 units
The distance between two points is given by:
[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Given the points R(2,1), S (2,5), and T(4, 1). Hence:
[tex]RS=\sqrt{(5-1)^2+(2-2)^2}=4\ units[/tex]
[tex]RT=\sqrt{(1-1)^2+(4-2)^2}=2\ units\\\\ST=\sqrt{(4-2)^2+(1-5)^2}=4.47\ units[/tex]
The perimeter of the triangle = 4 + 2 + 4.47 = 10.47 units
Find out more on triangle at: https://brainly.com/question/17335144
Help help help math math math
18
Step-by-step explanation:
X-3=15
Make X the subject of the formular by transferring the number with co-efficients in one side if the equation.
X=15+3
X=18
Answer:
18
Step-by-step explanation:
Jason considered two similar televisions at a local electronics store. The generic version was based on the brand name and was three eighths the size of the brand name. If the generic television set is 12 inches by 24 inches, what are the dimensions of the brand name television?
Answer:
Option (C) is correct, the dimensions of the brand name television = 32 inches by 64 inches.
Step-by-step explanation:
Given : The generic version was based on the brand name and was three eighths the size of the brand name and both are similar.
The dimensions of the generic television set = 12 inches by 24 inches
Let the dimensions of brand name be x by y such that
three eighth of x=12 inches
and three eighth of y=24 inches
Therefore, the dimensions of the brand name television = 32 inches by 64 inches.
Hence option (C) is correct.
Answer asap! Need help before I go to sleep.
Answer:
Step-by-step explanation:
y = (4/7)x - 1
How do I solve this and what is the answer to this?! Number 14.
Answer:
You'll have to give more information about the question or about what you need solved.
Step-by-step explanation:
Sarah opened a savings account with a $725 deposit. This account earns 3.5% annual interest compounded twice each month. How long will it take her account to reach a balance of $2000 if there are no other deposits or withdrawals.
It will take 29 years to reach $725 to $2000 compounded twice in a month.
What is compound interest?Borrowers are required to pay interest on interest in addition to principal since compound interest accrues and is added to the accrued interest from prior periods.
We know the formula for compound interest is,
A = P(1 + r/100)ⁿ.
Where, A = amount, P = principle, r = rate, and n = time in years.
The formula for compound interest compounded twice each month is,
A = P(1 +(r/24)/100)²⁴ⁿ.
Given, A = 2000, P = 725, r = 3.5.
∴ 2000 = 725(1 + (3.5/24)/100)²⁴ⁿ.
(1 + (3.5/24)/100)²⁴ⁿ = 2.76.
(1.00146)²⁴ⁿ = 2.76.
24n = [tex]log_{1.00146}2.76[/tex].
24n = 695.87.
n = 29 years.
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#SPJ2
1x10,000 + 6x1,000 + 3x100+ 7x10 + 8x 1/10 + 9/100 in a standed form
a- 163,789
b- 163,700.89
c- 16,378.9
d- 1,637.89
e- 16,370.89
Answer:
C
Step-by-step explanation:
because write in standard form hope it helps to you
Let F(x)=∫
t−3
t
2+7
for − ∞ < x < ∞
x
0
(a) Find the value of x where F attains its minimum value.
(b) Find intervals over which F is only increasing or only decreasing.
(c) Find open intervals over which F is only concave up or only concave down.
(a) It looks like you're saying
[tex]\displaystyle F(x) = \int_0^x (t - 3t^2 + 7) \, dt[/tex]
Find the critical points of F(x). By the fundamental theorem of calculus,
F'(x) = x - 3x² + 7
The critical points are where the derivative vanishes. Using the quadratic formula,
x - 3x² + 7 = 0 ⇒ x = (1 ± √85)/6
Compute the second derivative of F :
F''(x) = 1 - 6x
Check the sign of the second derivative at each critical point.
• x = (1 + √85)/6 ≈ 1.703 ⇒ F''(x) < 0
• x = (1 - √85)/6 ≈ -1.370 ⇒ F''(x) > 0
This tells us F attains a minimum of
[tex]F\left(\dfrac{1-\sqrt{85}}6\right) \approx \boxed{-6.080}[/tex]
(b) Split up the domain of F at the critical points, and check the sign of F'(x) over each subinterval.
• over (-∞, -1.370), consider x = -2; then F'(x) = -7 < 0
• over (-1.370, 1.703), consider x = 0; then F'(x) = 7 > 0
• over (1.703, ∞), consider x = 2; then F'(x) = -3 < 0
This tells us that
• F(x) is increasing over ((1 - √85)/6, (1 + √85)/6)
• F(x) is decreasing over (-∞, (1 - √85)/6) and ((1 + √85)/6, ∞)
(c) Solve F''(x) = 0 to find the possible inflection points of F(x) :
F''(x) = 1 - 6x = 0 ⇒ 6x = 1 ⇒ x = 1/6
Split up the domain at the inflection point and check the sign of F''(x) over each subinterval.
• over (-∞, 1/6), consider x = 0; then F''(x) = 1 > 0
• over (1/6, ∞), consider x = 2; then F''(x) = -11 < 0
This tells us that
• F(x) is concave up over (-∞, 1/6)
• F(x) is concave down over (1/6, ∞)
Solve
5 + 3 ( x - 1 ) = 5x - 6
which measures form a triangle
[tex]\huge \rm༆ Answer ༄[/tex]
Measure of each side of a triangle can't be greater than the sum of the other two sides and can't be smaller than the difference between the two other sides. therefore the most appropriate choice is ~
4 cm , 7 cm and 9 cmI hope it helps ~
We have:
1) 3 + 5 = 8 ⇒ wrong
2) 4 + 7 > 9 ⇒ right
3) 2 + 11 < 15 ⇒ wrong
ANSWER: 4 cm, 7 cm, 9 cm
Ok done. Thank to me :>
20 is 25% of what number?
Enter your answer in the box.
Answer:
80
Step-by-step explanation:
25 percent is equal to 1/4
1/4 of 80 is 20
Answer:
80
Step-by-step explanation:
Activity 1.
Direction. Using the diagram below, form ratios. Express them in lowest term to
To form a proportion
Answer:
6:3 =2:12:2=1:16:13:24:14=2:7Which of the following statements correctly uses the distributive property?
-2(15 - 3) = -2(15) + (-2)(3)
7(9 - 8) = 7(9) - 8
9(-7 + 6) = 9(-7) + 9(6)
-3(12 + 5) = -3(12) - (-3)(5)
Step-by-step explanation:
9(-7 + 6) = 9(-7) + 9(6)
Hope it help !
Question
Each data point on the scatter plot represents last month’s necklace and earring sales, in thousands of dollars, at one of the fourteen locations in a nationwide jewelry store chain. The correlation coefficient between necklace sales and earring sales is 0.98.
Wes says that an increase in necklace sales must cause an increase in earring sales. Ann says that an increase in earring sales must cause an increase in necklace sales. Who is correct?
Answer:
Wes
Step-by-step explanation:
This represents a positive correlation, meaning that when x increases, so does y. Because of x, y increases meaning that Wes is correct
If the mean of five values is 8.2 and four of the valuesare 6, 10, 7, and12, find the fifth value.
Answer:
6
Step-by-step explanation:
→ Do the 8.2 × 5
41
→ Minus the answer from the sum of the values
41 - ( 6 + 10 + 7 + 12 ) = 6
Write and solve an absolute value inequality.
18. Students are guessing the number of jelly beans in a jar. Each student who guesses
within 15 of the correct amount will win a prize. The correct amount of jelly beans in the
jar is 389. Write and solve an absolute value inequality to represent this situation.
Express your solution as a compound inequality.
Compound inequalities are used to combine several inequalities
The solution as a compound inequality is [tex]374<x <404[/tex]
Assume the correct amount of jelly beans in the jar is x.
15 away from x can be represented as 15 - x or x - 15
The correct number of jelly beans is given as 389.
So, when the statement is represented as an absolute inequality, we have:
[tex]|x - 15| < 389[/tex]
Express as compound inequality:
[tex]389 - 15<x <389 + 15[/tex]
Evaluate like terms
[tex]374<x <404[/tex]
Hence, the solution as a compound inequality is [tex]374<x <404[/tex]
Read more about compound inequalities at:
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Stan's favorite cereal provides 20% of the Vitamin A and 30% of the Vitamin C he needs daily. How many servings of this cereal must he consume before he gets the recommended daily requirement of both vitamins?
Answer:
Step-by-step explanation:
100 %/ 20 % = 5 servings
100 %/ 30 % = 3⅓ servings
He must consume 5 servings to get 100% of Vitamin A
In those servings he will consume 150% of Vitamin C
the question in the picture
Answer:
the answer is
[tex] {3}^{5} [/tex]
Can you please help me with number 16
Solve for x: 5x + 15 = 28
A: 43/5
B: 13/5
C: 13
D: 43
[tex]\mathfrak{5x + 15 = 28} [/tex]
[tex]\mathfrak{5x = 28-15} [/tex]
[tex]\mathfrak{5x = 13} [/tex]
[tex]\boxed{\mathfrak{x = \dfrac{13}{5}}} [/tex] → option B.
[tex]\mathbb{MIREU} [/tex]
Answer:
B
Step-by-step explanation:
The first thing you need to do is,
28 - 15
which is 13.
Now look at the answer choices and multiply them by 5.
It cannot be C or D because it would not fit the equation.
If anyone of them equal 13 then it is the answer.
Now lets try it.
43/5 = 8.6
13/5 = 2.6
8.6 times 5 is way to big so A is not it.
2.6 times 5 is 13.
So it is B.
BraniliestBraniliestBraniliestBraniliest Braniliest
Answer:
-20.54 C
Step-by-step explanation:
Form an equation
-12.94 C = initial temperature
changes -1.9 per hour = -1.9h
h = hour
x = temperature after 4 hours
-12.94 -1.9h = x
substitute 4 for "h"
-12.94-1.9(4) = x
x = -20.54C
Answer:
-20.54Step-by-step explanation:
Just multiply -1.9 by 4 then add it to 12.94