Answer:
a) The probability that a randomly chosen specimen has an acceptable hardness is 0.7938.
b) If the acceptable range of hardness is (70-c, 70+c), then the value of c would 95% of all specimens have an acceptable hardness of 5.88.
c) Expected number of acceptable specimens among the ten is 7.938.
d) Binomial with n = 10 and p = P(X < 73.84)
[tex]p = P(Z <(73.84 - 70) / 3 ) = P(Z < 1.28) = 0.8997\\\\P(X <= 8) = 1 - P(X = 9) - P(X = 10)\\= 0.2650635[/tex]
Step-by-step explanation:
a )
[tex]P(67 < X< 75) = P( (67 - 70) / 3 < X < (75 - 70) / 3 )\\\\= P( - 1 < Z < 1.67) = 0.9525 - 0.1587 = 0.7938[/tex]
b )
[tex]c = 1.96 * 3 = 5.88[/tex] { Since Z = 1.96 for 95% CI refer table.}
c )
Expected number of acceptable specimens among the ten [tex]= 10 * P(67 < X< 75) \\\\= 10 * 0.7938 = 7.938[/tex]
d )
Binomial with n = 10 and p = P(X < 73.84)
[tex]p = P(Z <(73.84 - 70) / 3 ) = P(Z < 1.28) = 0.8997\\\\P(X <= 8) = 1 - P(X = 9) - P(X = 10)\\= 0.2650635[/tex]
Someone please help with the questions on this picture!! URGENT!!!
Answer:
A) Independent
B) Dependent
Step-by-step explanation:
A) If we take a marble out and put the marble back, it means we have restored the sample to what it was initially and thus it doesn't affect probability of making another selection.
Thus, this is an independent event.
B) A card is taken from a deck of cards without replacement and set aside. Then after that another card is taken from the first sample, this means that the first sample size has now reduced and thus the first card taken affects the probability of the second card to be picked. Thus, this is a dependent event.
Help. Urgent. Skenekeks
Answer:
D
Step-by-step explanation:
Plug in the numbers for the x-value and solve the equation.
| 3(80/3)/4 + 1 | = 16
| 3(-40/3)/4 + 1 | = 16
if ABCD is a cyclic quadrilateral and A,B,C,D are its interior angles , then prove that
tanA/2+tanB/2=cotC/2+cotD/2
answer the question plz
dont spam or else i will report that
9514 1404 393
Explanation:
In a cyclic quadrilateral, opposite angles are supplementary. This means ...
A + C = 180° ⇒ A/2 +C/2 = 90° ⇒ C/2 = 90° -A/2
B + D = 180° ⇒ B/2 +D/2 = 90° ⇒ D/2 = 90° -B/2
It is a trig identity that ...
tan(α) = cot(90° -α)
so we have ...
tan(A/2) = cot(90° -A/2) = cot(C/2)
and
tan(B/2) = cot(90° -B/2) = cot(D/2)
Adding these two equations together gives the desired result:
tan(A/2) +tan(B/2) = cot(C/2) +cot(D/2)
x( 3x - 2y + 4z)x = -2, y = 4, and z = -3
Based on the Pythagorean theorem , find the missing length for each of the given right triangles
Answer:
See Explanation
Step-by-step explanation:
The question is incomplete, as the right trianglea are not given. The general explanation is as follows.
Using Pythagoras Theorem, we have:
a² = b² + c²
Where:
a => hypotenuse
Assume that the opposite and the adjacent sides are given as 3 and 4, respectively.
The hypotension becomes
a² = 3² + 4²
a² = 9 + 16.
a² = 25
Take square roots.
a = 5
If any of the other side lengths is missing; you make that side the subject and then solve.
Use a net to find the surface area of the cone
to the nearest square centimeter. Use 3.14 for
20 cm
TT.
Answer:
4444
Step-by-step explanation:
Answer:
819
Step-by-step explanation:
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Discount Comics is running a special: 20 comics for $5.00. Seth purchases 30 comics for $7.50. What is the sale price per comic?
$ per comic?
Answer:
$0.25
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
The senior classes at High School A and High School B planned separate trips to Yellowstone National Park. The senior class at High School A rented and filled 9 vans and 14 buses with 710 students. High School B rented and filled 13 vans and 5 buses with 371 students. Each van and each bus carried the same number of students. Find the number of students in each van and in each bus.
Answer:
Buses - 43 people
Vans - 12 people
19. Which of the following would best be solved using factoring the difference of squares?
O x^3 + 5x^2 - 9x - 45 = 0
O 3x² + 12x = 8
O x^2 - 25 = 0
O x^2 + 3x – 10 = 0
Please hurry!
Answer:
x² + 3x - 10 = 0
x² - 25 = 0
b. If you take one spin, what is your expected value?
Answer:
3/7
Step-by-step explanation:
Expected Value:
3(1/7) + 1(2/7) + 0(2/7) - 1(2/7) = 3/7
Expected value when we take one spin = 3/7
What is the expected value?It is the sum of values multiplied by their respective probabilities.
How do we calculate the expected value after one spin?We have 2 red, 2 purple, 2 yellow, and 1 blue sector.
Total number of Sectors = 7
∴Probability of landing on red sector = 2/7
∴Probability of landing on purple sector = 2/7
∴Probability of landing on yellow sector = 2/7
∴Probability of landing on blue sector = 1/7
Points on blue sector = 3, on yellow sector = 1, on purple sector = 0, and on red sector = -1.
X 3 1 0 -1
P(X) 1/7 2/7 2/7 2/7
Expected Value = ∑X.P(X)
=3.(1/7) + 1(2/7) + 0(2/7) - 1(2/7)
= 3/7
Learn more about Expected Values on
https://brainly.com/question/15858152
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*PLEASE HELP ASAP I WILL MARK BRAINLIST*
(Questions and Answers pictured)
Answer:
The first equation, sorry can’t explain.
Answer:
g(x)=3f(2x)
I think
The square below represents one whole.
What percent is represented by the shaded area?
%
The anwser is 6%
Answer:
the answer is 6%
hdhxbxcbxbxszznzj
Find the Value of x
Answer:
42
Step-by-step explanation:
(adjacent straight angles sum up to 180)
3x+54=180
x=42
I’ve been stuck on this problem I can’t seem to get 7 9/4 into the ABC form
Answer:
7 square root 9^4
Step-by-step explanation:
Pa help po plssssss
Sana po meron Ang maka-sagot ☺️☺️
Answer:
The answer is below
Step-by-step explanation:
a) the volume of the pit = length * width * depth = 9 dm * 6 dm * 7 dm = 378 dm³
Hence to fil the pit, 378 dm³ of sand is needed.
b) Volume of the room = length * width * height = 2.3 m * 0.59 m * 3.74 m = 5.08 m³
The cabinet would occupy 5.08 m³ of space.
c) volume = length * width * height
210 dm³ = 3.5 dm * 6 dm * width
width = 210 dm³ / (3.5 dm * 6 dm) = 10 dm
d) Volume of the room = length * width * height = 15 m * 15 m * 15 m = 3375 m³
The stockroom has a space of 3375 m³
e) volume = length * width * height = 5 dm * 5 dm * 5 dm = 125 dm³
The container has a space of 125 dm³
f) volume = length * width * height = 41 cm * 13 cm * 24 cm = 12792 cm³
The box has a space of 12792 cm³
g) volume of prism = length * width * height
72 m³ = 4 m * 3 m * length
length = 72 m³ / (4 m * 3 m) = 6 m
h) volume = length * width * height = 8 cm * 8 cm * 8 cm = 512 cm³
The figure has a volume of 512 cm³
i) volume = length * width * height = 5 ft * 2 ft * 3 ft = 30 ft³
The cabinet has a space of 30 ft³
find the equation of the line passing through points A(3,4) and B(1,10)
Answer:
y = -3x + 13
Step-by-step explanation:
First, find the slope:
[tex]m=\frac{y_1-y_2}{x_1-x_2}\\\\m=\frac{4-10}{3-1}\\\\m=\frac{-6}{2}\\\\m=-3[/tex]
Finally, find the equation:
[tex]y-y_1=m(x-x_1)\\\\y-4=-3(x-3)\\\\y-4=-3x+9\\\\y=-3x+13[/tex]
What’s the solution
Answer:
x ≥ 12
Step-by-step explanation:
-3/4x +2 ≤ -7
Subtract 2 from each side
-3/4x +2-2 ≤ -7-2
-3/4x ≤ -9
Multiply each side by -4/3, remembering to flip the inequality
-3/4x * -4/3 ≥ - 9 *(-4/3)
x ≥ 12
Answer:
x>=12
Step-by-step explanation:
-3/4x + 2<=-7
-3/4x <= -7 -2
-3/4x<=-9
cross multiply
-3x<=-36
dividing throughout by -3
x>=12
Which function of x has a y-intercept of -3?
Answer:
C. y = 2x - 3
Step-by-step explanation:
you look at the number without the x. and the minus three means it's negative. But if it's a plus three then it's positive
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Khan Academy
Dependent probability
In a class of 7, there are 4 students who play soccer.
If the teacher chooses 3 students, what is the probability that none of the three of them play soccer?
Answer:
[tex]\frac{12}{49}[/tex]
Step-by-step explanation:
[tex]\frac{4}{7} *\frac{3}{7} = \frac{12}{49}[/tex]
Hope this helps.
Neglecting air resistance and the weight of the propellant, determine the work done in propelling a five-ton satellite to a height of (a) 100 miles above Earth and (b) 300 miles above Earth.
Answer:
a) the work done in propelling a five-ton satellite to a height of 100 miles above Earth is 487.8 mile-tons
b) the work done in propelling a five-ton satellite to a height of 300 miles above Earth is 1395.3 mile-tons
Step-by-step explanation:
Given the data in the question;
We know that the weight of a body varies inversely as the square of its distance from the center of the earth.
⇒F(x) = c / x²
given that; F(x) = five-ton = 5 tons
we know that the radius of earth is approximately 4000 miles
so we substitute
5 = c / (4000)²
c = 5 × ( 4000 )²
c = 8 × 10⁷
∴ Increment of work is;
Δw = [ ( 8 × 10⁷ ) / x² ] Δx
a) For 100 miles above Earth;
W = ₄₀₀₀∫⁴¹⁰⁰ [ ( 8 × 10⁷ ) / x² ] Δx
= (8 × 10⁷) [tex][[/tex] [tex]-\frac{1}{x}[/tex] [tex]]^{4100}_{4000[/tex]
= (8 × 10⁷) [tex][[/tex] [tex]-\frac{1}{4100}[/tex] [tex]+\frac{1}{4000}[/tex] [tex]][/tex]
= (8 × 10⁷ ) [ 6.09756 × 10⁻⁶ ]
= 487.8 mile-tons
Therefore, the work done in propelling a five-ton satellite to a height of 100 miles above Earth is 487.8 mile-tons
b) For 300 miles above Earth.
W = ₄₀₀₀∫⁴³⁰⁰ [ ( 8 × 10⁷ ) / x² ] Δx
= (8 × 10⁷) [tex][[/tex] [tex]-\frac{1}{x}[/tex] [tex]]^{4300}_{4000[/tex]
= (8 × 10⁷) [tex][[/tex] [tex]-\frac{1}{4300}[/tex] [tex]+\frac{1}{4000}[/tex] [tex]][/tex]
= (8 × 10⁷ ) [ 1.744186 × 10⁻⁵ ]
= 1395.3 mile-tons
Therefore, the work done in propelling a five-ton satellite to a height of 300 miles above Earth is 1395.3 mile-tons
y+4x=7 find the missing coordinates for a(-3,) and b (5,)
Answer:
-3 1
Step-by-step explanation:
If 12 girls can sweep a room in 20hours, how many hours will it take 8 girls to perform the same task, assuming they are sweeping at the same rate?
Answer:
30 hour
Step-by-step explanation:
girls time
12 20 hour
8 x(let)
now,
12/8=x/20
12×20=8×x
240=8x
x=240/8
x=30,,
Exhibit 11-10 n = 81 s2 = 625 H0: σ2 = 500 Ha: σ2 ≠ 500 At 95% confidence, the null hypothesis _____. a. should not be rejected b. should be revised c. should be rejected d. None of these answers are correct
Answer:
Option C
Step-by-step explanation:
n = 81
s2 = 625
H0: σ2 = 500
Ha: σ2 ≠ 500
Test Statistics X^2 = (n-1)s^2/ σ2 = (81-1)*625/500
X^2 = 100
P value = 0.0646 for degree of freedom = 81-1 = 80
And X^2 = 100
At 95% confidence interval
Alpha = 0.05 , p value = 0.0646
p < alpha, we will reject the null hypothesis
At 95% confidence, the null hypothesis
Lydiagrace33
Image attached
A) 1 point Write an inequality for this graph . Use the shift key and the key or key to type the < or > symbol . *
B) Water boils when the temperature is at least 212 degrees F. Which inequality shows this situation ?
C) When the temperature drops below 50 degrees F , crickets usually stop chirping . Which inequality shows this situation ?
D) Explain the difference between the meaning of a closed
circle and an open circle on a graph of an inequality .
x^3y+2x^2y^2+xy^3 and 2x^3+4x^2y+2xy^2 Find the HCF.
Answer:
[tex]x(x+y)^2[/tex]
Step-by-step explanation:
We are given that
[tex]x^3y+2x^2y^2+xy^3[/tex] and [tex]2x^3+4x^2y+2xy^2[/tex]
We have to find HCF.
[tex]x^3y+2x^2y^2+xy^3=xy(x^2+2xy+y^2)[/tex]
=[tex]xy(x+y)^2[/tex]
By using the formula
[tex](x+y)^2=x^2+2xy+y^2[/tex]
[tex]xy(x+y)^2=x\times y\times (x+y)^2[/tex]
[tex]2x^3+4x^2y+2xy^2=2x(x^2+2xy+y^2)[/tex]
[tex]=2x(x+y)^2[/tex]
[tex]2x(x+y)^2=2\times x\times (x+y)^2[/tex]
HCF of ([tex]x^3y+2x^2y^2+xy^3,2x^3+4x^2y+2xy^2[/tex])
[tex]=x(x+y)^2[/tex]
The following data represents the number of days absent and the final grade for a sample of college students in a general education course at a large state university.
No. of absences 0 1 2 3 4 5 6 7 8 9
Final Grade 89.2 86.4 83.5 81.1 78.2 73.9 64.3 71.8 65.5 66.2
a) Which variable is the explanatory variable?
b) Draw a scatter plot and describe your scatter plot (Direction, Strength, Form).
c) Compute the correlation coefficient
d) Does a linear relation exist between the number of absences and the final grade? Justify your answer.
e) Write out the least-squares regression line equation.
f) Compute and draw the residual (on your scatter plot) for a student who misses 5 class meetings.
g) Explain the slope in context.
h) Is the y-intercept meaningful in this situation? Explain.
i) Compute and interpret the coefficient of determination.
j) Construct a residual plot to verify the requirements of the least-squares regression model.
Defined the total variation distance to be a distance TV(P,Q) between two probability measures P and Q. However, we will also refer to the total variation distance between two random variables or between two pdfs or two pmfs, as in the following.
Compute TV(X,X+a) for any a∈(0,1), where X∼Ber(0.5).
TV(X,X+a) = ?
Answer:
1
Step-by-step explanation:
Computing Tv(X, X + a ) for any a∈(0,1)
Given that : X∼Ber(0.5)
∴ The probability mass function
P(X = 1 ) = 0.5
P(X = 0) = ( 1 - 0.5 )
and expectation E[X] = 0.5
hence ; TV ( X, X + a ) = 1
Mô hình quy hồi tuyến tính và ứng dụng
Answer:
where are you from Korea or not
Hope it helps you!
-miraculousfanx-
What is the cube root of -1,000p12q3?
O-1004
O - 10pta
O 1004
O 10pta
Answer:
Your options are not clear
Step-by-step explanation:
[tex]\sqrt[3]{-1000 \times p^{12} \times q^3} \\\\(-1 \times 10^3 \times p^{12} \times q^3)^{\frac{1}{3} }\\\\(-1^3)^{\frac{1}{3} }\times 10^{3 \times \frac{1}{3} } \times p^{12 \times \frac{1}{3}} \times q^{3 \times \frac{1}{3}} \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ (-1)^3 = - 1 \ ] \\\\- 1 \times 10 \times p^4 \times q\\\\-10p^4q[/tex]
Question
At a certain university, intramural volleyball is chosen as an activity by 50% of the student population. How likely is it that a
randomly chosen student will or will not participate in intramural volleyball?
Answer:
50%
Step-by-step explanation:
50% of the student population chooses instramural volleyball, meaning 50% doesn't. So if a random student is chosen, then it is a 50% chance that they will choose volleyball and 50% chance they won't.
