Answer:
A - (2a+0)/2 ; (2b+0)/2 = ( a , b )
B - (-2a+0)/2 ; (2b+0)/2 = ( - a, b )
C - (-2a+0)/2 ; ( -2b+0)/2 = ( - a, - b )
D - (2 a+0)/2 ; (-2b+0)/2 = ( a , - b )
Step-by-step explanation:
In the population of young children eligible to participate in a study of whether or not their calcium intake is adequate, 52% are 5 to 10 years of age and 48% are 11 to 13 years of age. For those who are 5 to 10 years of age, 17% have inadequate calcium intake. For those who are 11 to 13 years of age, 54% have inadequate calcium intake. Use Bayes's rule to find the probability that a child from this population who has inadequate intake is 11 to 13 years old.
Answer:
0.7457 = 74.57% probability that a child from this population who has inadequate intake is 11 to 13 years old.
Step-by-step explanation:
Bayes Theorem:
Two events, A and B.
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]
In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.
In this question:
Event A: Inadequate intake
Event B: Is 11 to 13 years old.
48% are 11 to 13 years of age.
This means that [tex]P(B) = 0.48[/tex]
For those who are 11 to 13 years of age, 54% have inadequate calcium intake.
This means that [tex]P(A|B) = 0.54[/tex]
Probability of inadequate calcium intake:
0.17 of 0.52(5 to 10 years old)
0.54 of 0.48(11 to 13 years old). So
[tex]P(A) = 0.17*0.52 + 0.54*0.48 = 0.3476[/tex]
Find the probability that a child from this population who has inadequate intake is 11 to 13 years old.
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)} = \frac{0.48*0.54}{0.3476} = 0.7457[/tex]
0.7457 = 74.57% probability that a child from this population who has inadequate intake is 11 to 13 years old.
I did part a and b, i need help with the question that says " does the cup hold the exact volume of scoop of ice cream" and part C
Answer:
See below.
Step-by-step explanation:
Part a is correct.
The volume of part b is correct.
The volume of a scoop is 268 cm^3.
The volume of the cylindrical cup is 402 cm^3.
Part b)
Question: Does the cup hold the exact volume of the scoop? Explain.
Answer: No. The cup holds 402 cm^3 up to the brim. If you overfill it like the picture shows, it will hold even more than 402 cm^2. A scoop is only 268 cm^3, so a cup holds more than the scoop.
Part c)
volume of cone = (1/3)(pi)r^2h
V = (1/3)(3.14159)(4 cm)^2(8 cm)
V = 134 cm^3
Simplify (-9p+7)-(-9p+3)
[tex]\tt{}( - 9p + 7) - (9p + 3)[/tex]
[tex]\tt{} - 9p - 7 + 9p + 3[/tex]
[tex]\tt{}7 - 3[/tex]
[tex]\tt{}4[/tex]
Problem 5.A miner is trapped inside a mine and has access to 3 doors. The first door leads to a tunneland can take him to safety in 3 hours. The second door is a trap and brings him back to the mine againafter 5 hours through a tunnel. The third door also is a trap that brings him back to the mine after 7 hoursthrough a tunnel. The miner at all times is equally like to choose any of the doors. (In the darkness he canhardly distinguish the three). What is the expected length of time until he reaches safety
Answer:
Expected time is 15 hours for him to get to safety.
Step-by-step explanation:
We define X as the time that this miner would get to safety.
We define Y as the door he chooses initially.
P(Y= 1) = P(Y=2)=P(Y=3) = 1/3
We have E[X|Y=1] = 3
E[X|Y] = 5 hours + E[X}
E[X|Y] = 7 hours + E[X]
Then we have
E[X] = 1/3(3 + 5 + E[X] + 7 + E[X])
We cross multiply
3*E[X] = (15 + 2E[x])
3E[X] - 2E[X] = 15
E[X] = 15
So the time it would take to get him to safety is 15 hours
Can someone give me the answer and explain it to me? Pls, I’ll mark brainiest.
FOR THE SMART MATH PEOPLE
WILL GIVE BRAINLIEST
This figure shown is NOT a square because a square has all angles are 90º.
It is a rhombus and a parallelogram because they both have a parallel sides(At least 2). NOW GIVE ME BRAINLIEST!!!!
Which of the following is equivalent to
X^2 - 8x - 7 =0
A.) (x-8)^2 = 15
B.) (x-4)^2 = 15
C.) (x-8)^2 = 23
D.) (x-4)^2 = 23
Answer: it will be D
Step-by-step explanation: if You graph them you will get the same coordinate plates
In ΔQRS, the measure of ∠S=90°, the measure of ∠R=53°, and SQ = 93 feet. Find the length of RS to the nearest tenth of a foot.
Answer 70.1
Step-by-step explanation:
2/5 x 10/22 in simplest form
Answer:
2/11
Step-by-step explanation:
You would have to do 2 times 10 which equals 20. Than 5 times 22 which is 110. No to reduce you have to find the Greatest Common faction which is 10. So 20 divided by 10 equals 2 and 110 divided by 10 is 11.
According to the central limit theorem: a. The mean of a sample from a population that is not normally distributed will tend towards a normal distribution if the sample size is large b. The probability of a sample standard deviation will converge towards the population variance as the sample standard deviation increases c. The median of a sample from a population that is normally
Answer:
a. The mean of a sample from a population that is not normally distributed will tend towards a normal distribution if the sample size is large.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem estabilishes 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.
So, according to the above text, the correct answer is given by option a, that is, if the sample is large, the sampling distribution of the sample mean will be approximately normal, that is, trend towards a normal distribution.
this is my last question
Answer: B
Step-by-step explanation:because my teacher said she having trouble
Find the area of the region enclosed by the graphs of the functions
f(x)=x, g(x)=x^3
by partitioning the x- axis.
(Use symbolic notation and fractions where needed.)
Answer:
[tex]\displaystyle A = \frac{1}{2}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightEquality PropertiesAlgebra I
Terms/CoefficientsFunctionsFunction NotationGraphingCalculus
Area - Integrals
Integration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Area of a Region Formula: [tex]\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx[/tex]
Step-by-step explanation:
*Note:
Remember that for the Area of a Region, it is top function minus bottom function.
Also remember that finding area and evaluating are two different things.
Step 1: Define
f(x) = x
g(x) = x³
Bounded (Partitioned) by x-axis
Step 2: Identify Bounds of Integration
Find where the functions intersect (x-values) to determine the bounds of integration.
Simply graph the functions to see where the functions intersect (See Graph Attachment).
Interval: [-1, 1]
1st Integral: [-1, 0]
2nd Integral: [0, 1]
Step 3: Find Area of Region
Integration.
Substitute in variables [Area of a Region Formula]: [tex]\displaystyle A = \int\limits^0_{-1} {[x^3 - x]} \, dx + \int\limits^1_0 {[x - x^3]} \, dx[/tex][Area] Rewrite Integrals [Integration Property - Subtraction]: [tex]\displaystyle A = (\int\limits^0_{-1} {x^3} \, dx - \int\limits^0_{-1} {x} \, dx) + (\int\limits^1_0 {x} \, dx - \int\limits^1_0 {x^3} \, dx)[/tex][Area] [Integrals] Integrate [Integration Rule - Reverse Power Rule]: [tex]\displaystyle A = [\frac{x^4}{4} \bigg|\limits^0_{-1} - (\frac{x^2}{2}) \bigg|\limits^0_{-1}]+ [\frac{x^2}{2} \bigg|\limits^1_0 - (\frac{x^4}{4}) \bigg|\limits^1_0][/tex][Area] Evaluate [Integration Rule - FTC 1]: [tex]\displaystyle A = [\frac{-1}{4} - (\frac{-1}{2})] + [\frac{1}{2} - \frac{1}{4}][/tex][Area] [Brackets] Add/Subtract: [tex]\displaystyle A = \frac{1}{4} + \frac{1}{4}[/tex][Area] Add: [tex]\displaystyle A = \frac{1}{2}[/tex]Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Area Under the Curve - Area of a Region (Integration)
Book: College Calculus 10e
Find the slope of the line that goes through the
(-4,6) and (2.1)
Answer:
-5/6
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(1-6)/(2-(-4))
m=-5/(2+4)
m=-5/6
Suppose that a standardized biology exam has a mean score of 80% correct, with a standard deviation of 3. The school administration believes that the new class of freshmen have a different mean exam score. A sample of 65 students from the freshmen class is used and a mean score of 76% correct is obtained.
Calculate a 99% confidence interval. List the lower bound (rounded to 2 decimal places) and the upper bound (rounded to 2 decimal places).
Answer:
The 99% confidence interval is between 62.36%(lower bound) and 89.64%(upper bound).
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].
A sample of 65 students from the freshmen class is used and a mean score of 76% correct is obtained.
This means that [tex]n = 65, \pi = 0.76[/tex]
99% confidence level
So [tex]\alpha = 0.005[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.005}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.76 - 2.575\sqrt{\frac{0.76*0.24}{65}} = 0.6236[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.76 + 2.575\sqrt{\frac{0.76*0.24}{65}} = 0.8964[/tex]
0.6236*100 = 62.36%
0.8964*100 = 89.64%
The 99% confidence interval is between 62.36%(lower bound) and 89.64%(upper bound).
Describe the zeros of the graphed function.
A.
The function has three distinct real zeros.
B.
The function has two distinct real zeros and two complex zeros.
C.
The function has four distinct real zeros.
D.
The function has one distinct real zero and two complex zeros.
Answer:
A
Step-by-step explanation:
it intersects x axis at three points.
if my answer helps please mark as brainliest.
is 1/2 a solution to the equation 8 -2x = 10x + 3?
Answer yes
Step-by-step explanation:
hope this helps
An artist builds a sculpture out of metal and wood that weighs 14.9 kilograms. 3/4 of this weight is metal, and the rest is wood. How much does the wood part of the sculpture
weigh?
the length of a pool 2 km long is represented on a map with a length of 20cm. what is the map scale used?
Answer:
The scale used is 1: 10,000 cm.
Step-by-step explanation:
Given that the length of a pool 2 km long is represented on a map with a length of 20cm, to determine what is the map scale used the following calculation must be performed:
2 km = 2,000 m
1m = 100cm
2,000 x 100 = 200,000
20: 200,000
10: 100,000
1: 10,000
Thus, the scale used is 1: 10,000 cm.
Answer:
10,000
Step-by-step explanation:
Fifty people put there name
into a two different drawings
(30 males and 20 females).
One drawing is for an iPad and
the other is for a flat screen
TV. What is the probability
that a female will win the iPad
and a male win the flat
screen?
7.SP.8
2.4 x 6.7 =
I need the work too
Answer:
16.08
Step-by-step explanation:
HELP ASAP ILL GIVE BRAINLIEST
Write an expression for
The product of eleven times a number less than 12
11(n - 12)
12n - 11
11n - 12
12 - 11n
Answer:
11n - 12
Step-by-step explanation:
The answers for the March 22 Recording Check
1. Solve the following one-step equation.
x+5=−7
x = -12 This is the correct answer
x = 2
2. An expression does NOT have an equal sign
The answer would be True
Find the length of DC.
Answer:
sqart(89) in
Step-by-step explanation:
As triangle ABC is a right triangle, so sqrt(5^2 + 8^2) = sqrt(89) approximately 9.43 in.
Please help. Dont put a random answer plz.
Step-by-step explanation:
i think d x = 12 (0.42)
hope it is helpful to you
I need help on this question please and thank you that would be great
Answer:
w independant a dependant
Step-by-step explanation:
Solve 3(4x + 5) = 33
You may use the flowchart to help you if you wish.
Answer:
This is so simple omg
Expand ”4x+5” out so...
12x + 15 = 33
12x = 33 - 15 = 18
12x = 18
x = 1.5
Answer:
Step-by-step explanation:
In a group of 84 kids, three-sevenths bought their lunches. Of those who bought their lunches, 9 got a slice of pizza. What is the fraction of the students who bought their lunches got a slice of pizza. Write your fraction in simplest form.
3/7x84=36
Ans: 9/36=1/4
Which graph shows the line y = 4x - 2?
Answer:
Line A
Step-by-step explanation:
Line A is the blue line with the y-intercept of (0,-2) and positive slope of 4.
ASAP HW HELP
if you don’t know answer don’t even comment
Answer:
y=1/4x-3
Step-by-step explanation:
Find the area of each of the following
Answer:
The area of this shape is 252.
Step-by-step explanation:
Cut the right piece of the shape into a triangle of 90 degrees, which makes the shape divided into 2 triangles and 1 rectangle.
9 x 13 = 117 (rectangle part)
15 x 9 = 135, 135/2 = 67.5
15 x 9 = 135, 135/2 = 67.5
67.5 + 67.5 + 117 = 252
this question is confusing me