Since two-way table shows the distribution of high school students The correct option is C: No, events A and B are not independent because P(A) ≠ P(A|B).
What is the distribution about?To determine whether events A and B are independent, we need to compare the probability of event A occurring without any knowledge of event B (i.e., P(A)) to the probability of event A occurring given that event B has occurred (i.e., P(A|B)).
From the table, we see that P(A) = 8/32 = 1/4, since there are 8 juniors out of a total of 32 students. Also, P(B) = 8/32 = 1/4, since there are 8 students who prefer earbuds out of a total of 32 students.
From the table, we see that the probability of both events A and B occurring is P(A and B) = 4/32 = 1/8, since there are 4 juniors who prefer earbuds out of a total of 32 students.
Now, to calculate P(A|B), we use the formula:
P(A|B) = P(A and B) / P(B)
Substituting the values we have, we get:
P(A|B) = (1/8) / (1/4) = 1/2
Since P(A) = 1/4 and P(A|B) = 1/2, we can see that P(A) ≠ P(A|B). Therefore, events A and B are not independent.
Therefore, the answer is No, P(A) ≠ P(A|B).
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What is the greatest number of unit cubes that would fit in a rectangular prism that is 12 units tall, 5 units long, and 7 units wide?
A 420
B 84
C 60
D 7
Answer:
A or 420
Step-by-step explanation:
Remember Length x Width x Height. 12 * 5 is 60, then 60 * 7 is 420.
three numbers m,n,p are in the ratio 3:6:4.which of the following is the value
[tex] \frac{4m - n}{n + 2p} [/tex]
Answer:
the value of (4m-n)/(n+2p) is 3/7.
Step-by-step explanation:
Let's substitute the given ratio in terms of a common multiplier, k:
m = 3k
n = 6k
p = 4k
Now we can substitute these values in the expression:
(4m-n)/(n+2p) = (4(3k) - 6k)/(6k + 2(4k)) = (12k - 6k)/(6k + 8k) = 6k/14k = 3/7
Therefore, the value of (4m-n)/(n+2p) is 3/7.
HELP ME! PLEASE!! . . .
Step-by-step explanation:
that makes ORQ a right-angled triangle, and we can use Pythagoras
c² = a² + b²
c being the Hypotenuse (the side opposite of the 90° angle), a and b are the legs.
OQ is the radius of the circle = OM = LM/2 = 20/2 = 10 cm.
RQ = PQ/2 = 16/2 = 8 cm.
so, our Pythagoras equation looks like :
OQ² = RQ² + OR²
10² = 8² + OR²
100 = 64 + OR²
36 = OR²
OR = 6 cm
RM = OM - OR = 10 - 6 = 4 cm
Please answer this question with the following proofs.
Answer:
Line DB and AC intersect at point E.
∠AEB = ∠DEC because they are vertical angles.
∠EAB and ∠ECD are alternate interior angles because AB and CD are parallel lines and line AC crosses through both parallel lines.
m∠EAB = m∠ECD because they are alternate interior angles.
ΔABE ≅ ΔCDE because there are two sets of congruent angles.
someone help pls i’m confused
Answer:
CF = 12
DE = 23
CD = 23
DF = 23.9
Step-by-step explanation:
We can see that there are 2 right-angled triangles: DEF and CDF with common side FD.
They are right angled triangles because the EF and CF are radii of the circle and these segments intersect the tangents at 90°
The common side DF is the hypotenuse for both triangles
The sides EF and CF are radii of the circle so EF = CF
We have two triangles which have two sides equal and one of the angles equal to the corresponding angle of the other
By the SSA theorem, the two triangles are similar
SSA Theorem
if two sides and an angle not included between them are respectively equal to two sides and an angle of the other then the two triangles are equal
Therefore by the law of similar triangles,
CD = EF
Plugging in the expressions we get
13x - 16 = 4x + 11
Subtract 4x from both sides:
13x - 4x - 16 = 11
9x - 16 = 11
Add 16 to both sides:
9x - 16 + 16 = 11 + 16
9x = 27
x = 27/9 = 3
Therefore
ED = 4x + 11 = 4(3) + 11 = 12 + 11 = 23
and this is equal to CD
Using the Pythagorean theorem for right triangles,
For ΔDEF,
DF² = EF² + DE²
DF² = 12² + 23²
= 144 + 529
= 673
DF = √673
= 25.9422
= 25.9 rounded to the nearest tenth
So the measures of the segments are
CF = 12
DE = 23
CD = 23
DF = 23.9
number that multiplys into -144 ans adds into -10
Answer:
-12 and 2
Step-by-step explanation:
1. Notice that both numbers have to be negative. This means that one number has to be negative, and the number with the largest value has to be negative.
2. Think of numbers that multiply to -144
3. Check and see if they add to -10
4. The only numbers that satisfy this are -12 and 2
What is the length of TR?
Answer:
2x + 30
Step-by-step explanation:
assuming there is no other data
4x + 6 + 24 - 2x =
2x + 30
A video company randomly selected 100 of its subscribers and asked them how many hours of shows they watch per week. Of those surveyed, 45 watch more than 10 hours per week. Based on the data, if the company has 2,500 subscribers, then how many watch more than 10 hours per week?
Answer:
11205 is correct answer
A jeweler had a fixed amount of gold to make bracelets and necklaces. The amount of gold in each bracelets is 7 grams And the amount of gold in each necklace is 24 grams. The jeweler used 172 grams of gold and made 2 more necklaces than bracelets. Write a system of equations that could be used to determine the number of bracelets made and the number of necklaces made. Define variabkes
The jeweler made 4 bracelets and 6 necklaces using 172 grams of gold.
What is equations ?An equation is a mathematical statement that shows that two expressions are equal. It contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Equations are used to solve problems by finding the values of the variables that make the equation true.
According to given information :Let x be the number of bracelets made, and y be the number of necklaces made.
Then, we can create the following system of equations:
Equation 1: 7x + 24y = 172 (the total amount of gold used is 172 grams)
Equation 2: y = x + 2 (the number of necklaces made is 2 more than the number of bracelets made)
So, the variables are x (the number of bracelets made) and y (the number of necklaces made).
We can solve this system of equations to find the values of x and y. We can use substitution or elimination to solve for one variable and then plug it into the other equation.
Substitution method:
From Equation 2, we have y = x + 2. Substituting this into Equation 1, we get:
7x + 24(x+2) = 172
7x + 24x + 48 = 172
31x = 124
x = 4
So, the jeweler made 4 bracelets.
Plugging this into Equation 2, we get:
y = x + 2 = 4 + 2 = 6
So, the jeweler made 6 necklaces.
Therefore, the jeweler made 4 bracelets and 6 necklaces using 172 grams of gold.
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The line joiningA(1,4)to B(5,p) has a gradient of 1/2. Find
Answer:
p = 6
Step-by-step explanation:
The table shows the number of minutes in different numbers of days.
Number of days 4 7 11
Number of minutes 5760 10,080 15,840
Which equation expresses the relationship between the number of days, d, and the number of minutes, m?
Responses
m=d1440
m equals frqaction d over 1440 end fraction
A.m = d + 1440
B.m, = , d, + 1440
C.m = 1440d
D.d = 1440m
Answer:
C. m = 1440d
Step-by-step explanation:
You want to know the equation that represents the relationship between days (d) and minutes (m) given the table of values (d, m) = (4, 5760), (7, 10080), or (11, 15840).
Proportional relationshipOn the off chance you don't already know that the number of days must be multiplied by minutes per day to find the number of minutes (m = 1440d), you can always try the table values in the response choices to see what works:
A. 5760 = 4/1440 . . . . . . nope
B. 5760 = 4 + 1440 . . . . . nope
C. 5760 = 1440·4 . . . . . . . yep
D. 4 = 1440·5760 . . . . . . . nope
The equation that works is m = 1440d.
__
Additional comment
Fractions work the same way with units that they do with numbers. Common factors in numerator and denominator cancel.
[tex]\dfrac{2}{3}\times 3=2\\\\\dfrac{\text{minutes}}{\text{day}}\times \text{days}=\text{minutes}[/tex]
The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $7 and each adult ticket sells for $11.50. The drama club must make at least $980 from ticket sales to cover the show's costs. Write an inequality that could represent the possible values for the number of student tickets sold, � s, and the number of adult tickets sold, � a, that would satisfy the constraint.
Using inequality, x < 63.33, Student take 62 and adult take 68.
By utilizing the "equal tο" symbοl in mathematics, equatiοns are nοt necessarily balanced οn bοth sides. Sοmetimes it can be abοut a "nοt equal tο" relatiοnship, which denοtes that οne thing is better than οr wοrse than anοther.
A relatiοnship between twο numbers οr οther mathematical expressiοns that yields an unfair cοmparisοn is referred tο as an inequality in mathematics. Certain algebraic mathematical expressiοns are referred tο as inequalities.
The student's ticket sells fοr $5,
adult ticket sells fοr $950,
Tοtal auditοrium = 130,
If x represents the number οf student, then adult = 130 - x,
∴ 5x + 9.5y > 950
insert y = 130 - x5x + 9.5(130 - x) > 950,
5x + 1235 - 9.5 x > 950
x < 63.33
∴ Student take 62 and adult take 68.
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Billy and Joey collect baseball cards. Billy has 25 more cards than Joey.
Write an expression in simplest form to represent the total number of cards
(c) in both collections.
12x(x+3)=0 using zero product property
Answer:
0, -3.
Step-by-step explanation:
12x(x+3)=0
Either 12x = 0 or (x + 3) = 0
x = 0/12 or x = -3
So, x = 0 or x = -3
I don't know What 5 + x + 3 simplified is, help me please?
Answer:
5+x+3 simplified is x+8
Step-by-step explanation:
when you simplify something, you combine terms and write it in the simplest way you can. So combine 5 and 3 to get 8, and then the final answer of x+8
Answer: x+8
Step-by-step explanation:
"5 + x + 3" can be simplified by combining the numerical terms, which are 5 and 3, to get 8.
Then, just rewrite the expression as "x + 8." Therefore, "5 + x + 3" simplified is just "x + 8".
Divide 14x3 − 21x2 − 7x by −7x.
A) −2x2 + 3x + 1
B) −2x2 + 3x − 1
C) −2x3 − 3x2 − x
D) −2x2 + 3x
Answer:
A
Step-by-step explanation:
simply divide each ter by -7x ..
I think account has a balance of $120 on January 1. Describe a situation in which the account balance for each month February 1 March 1 forms the following sequences in exercise one and two. Write the first three terms of each sequence.
In exercise 1:
Situation: The account holder saves $30 each month
The first three terms of the sequence are: $120, $150, $180.
In exercise 2:
Situation: The account earns 25% interest each month.
The first three terms of the sequence are: $120, $150, $187.50.
What is a sequence?A sequence in mathematics is described as an enumerated collection of objects in which repetitions are allowed and order matters.
Explaining exercise 1:
In this exercise, the account balance for each month should form an arithmetic sequence with a common difference of $30
February 1 balance: $150
March 1 balance: $180
Hence, we have the first three terms of the sequence as: $120, $150, $180.
Explaining exercise 2:
In this exercise, the account balance for each month should form a geometric sequence with a common ratio of 1.25.
The account earns 25% interest each month is the situation here.
February 1 balance: $150
March 1 balance: $187.50
The first three terms of the sequence are: $120, $150, $187.50.
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The data represent the results for a test for a certain disease. Assume one individual from the group is randomly selected. Find the probability of getting someone who tested positive given that he or she had the disease.
The probability of getting someone who tested positive, given that he or she had the disease, is 0.9.
What is probability?The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
The probability of getting someone who tested positive, given that he or she had the disease, is equal to the probability that the individual has the disease and tests positive ( P(positive | disease) ).
This can be calculated using the formula P(A|B) = P(A∩B) / P(B)
P(positive | disease) = P(positive ∩ disease) / P(disease)
= 141 / (141+16)
= 0.898
Therefore, the probability of getting someone who tested positive, given that he or she had the disease, is 0.898, which is 0.9.
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Sharon paid $32,400 in Social Security taxes over a 25-year period. The total contribution to her account is
The total contribution to Sharon's account over the 25-year period is $64,800.
How to solve
To find the total contribution to Sharon's account, we need to consider both her contribution and her employer's contribution.
Social Security taxes are generally split evenly between the employee and the employer, with each paying half of the tax.
Sharon paid $32,400 in Social Security taxes over the 25-year period, which represents her share (half) of the total Social Security taxes paid.
To find the total contribution to her account, we simply need to double her share to include the employer's contribution:
Total contribution = Sharon's contribution + Employer's contribution
Total contribution = $32,400 + $32,400
Total contribution = $64,800
The total contribution to Sharon's account over the 25-year period is $64,800.
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You deposit $1,000 into a bank account. The account pays 3.75% annual interest compounded monthly. Find the balance after 6 years.
Your answer:
O $14,162.62
O 1,471.92
O $1,251.88
O $1,018.90
The answer of the given question based on the compound interest is the balance after 6 years is $14,162.62 (option a).
What is Amount?Amount refers to total value of something, usually in terms of a money. It can also be used in context of a quantity of something, such as an amount of the time or an amount of the material.
formula for the compound interest is :
A = P(1 + r/n)^(nt)
Where,
A = final amount
P = principal amount
r = annual interest rate
n = the number of times interest is to be compounded per year
t = time in years
In this case, we have:
P = $1,000
r = 3.75% = 0.0375 (annual interest rate as a decimal)
n = 12 (monthly compounding)
t = 6 years
Substituting the values into formula, we will get:
A = 1000(1 + 0.0375/12)⁽¹²*⁶⁾
A = $1,4162.62
Therefore, the balance after 6 years is $14,162.62 (option a).
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The shape ABC in the quilt block shown is an isosceles triangle, where AB = AC. The perimeter of the triangle is 27.3 inches. Find the values of x and y. Then, find the length of each side of the triangle. Enter the correct answers in the boxes. AB= BC = AC=
The values of the variables and the side lengths are
(x, y) = (3, 5)AB = AC = 8 and BC = 11.3How to determine the values of the variables and the side lengthsFrom the question, we have the following parameters that can be used in our computation:
AB = AC
Perimeter = 27.3
Using the attached figure, we have
6x - 2y = x + 5
Evaluate
5x = 2y + 5
For the perimeter, we have
AC + AB + BC = 27.3
So, we have
6x - 2y + x + 5 + y + 6.3 = 27.3
Simplify
7x = y + 16
Multiply by 2
14x = 2y + 32
Subtract from 5x = 2y + 5
9x = 27
So, we have
x = 3
This means that
2y + 32 = 14 * 3
2y + 32 = 42
Evaluate
2y = 10
y = 5
For the side lengths, we have
AC + AB + BC = 27.3
So, we have
AC = 6(3) - 2(5) = 8
AB = 3 + 5 = 8
BC = 5 + 6.3 = 11.3
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Find the Area of the figure below, composed of a rectangle and a semicircle. Round to the nearest tenths place.
The area of the figure is obtained to be approximately 74.1 units².
What is area?
An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.
The rectangle has the length of 6 units.
The rectangle has the breadth of 10 units.
The semicircle has a diameter of 6 units.
The semicircle has the radius of 3 units.
The formula for area of rectangle is -
Area (r) = l × b
Substitute the values into the equation -
Area (r) = 6 × 10
Area (r) = 60 units²
The formula for area of semicircle is -
Area (r) = πr² / 2
Substitute the values into the equation -
Area (s) = [3.14 × (3)²] / 2
Area (s) = 28.26 / 2
Area (s) = 14.13 units²
The total area of the diagram is -
Total Area = Area (r) + Area (s)
Substitute the values into the equation -
Total Area = 60 + 14.13
Total Area = 74.13 units²
Therefore, the area of the figure is 74.1 units².
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A spinner is divided into 4 equal sections. The probability of landing on A is 1/4. Brandy spins the spinner 24 times. How many times can she expect the spinner to land on A?
Answer:
6 times
Step-by-step explanation:
24/4 = 6
I need help answering this
The first five term of the sequence are -12, -24, -36, -48 and -60.
How to find the value of a sequence?A sequence is an enumerated collection of objects that follows are particular pattern.
The explicit formula of the sequence is aₙ = -12n
where
n = number of termsTherefore, let's find the first five terms of the sequence as follows:
a₁ = -12(1) = -12
a₂ = -12(2) = - 24
a₃ = -12(3) = -36
a₄ = -12(4) = -48
a₅ = -12(5) = - 60
Therefore, the sequence are -12, -24, -36, -48 and -60.
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I need help with this please
Answer: A. Nikko by 2 inches
Step-by-step explanation: Because 82 inches = 6ft 10in, which is 2 inches taller than Ricco.
i need help with the question pls
The area of the region bounded by the curves y = x² + 6x + 9 and y = 4 is 16 ² / ₃ square units.
How to find the area of the region?First, we need to find the points of intersection between the two curves. Set y = x² + 6x + 9 equal to y = 4:
x² + 6x + 9 = 4
Now, solve for x:
x² + 6x + 5 = 0
Factor the quadratic equation:
(x + 5)(x + 1) = 0
This gives us the solutions x = -5 and x = -1. These are the x-coordinates of the points of intersection.
Now, to find the area of the region bounded by the curves, we'll integrate the difference between the two functions with respect to x, from x = -5 to x = -1:
Area = ∫[4 - (x² + 6x + 9)]dx from -5 to -1
Area = ∫[5 - x² - 6x]dx from -5 to -1
Now, integrate:
Area = [5x - (x³/3) - 3x²] from -5 to -1
Plug in the limits:
Area = (5(-1) - (-1)³/3 - 3(-1)²) - (5(-5) - (-5)³/3 - 3(-5)²)
Area = (-5 - 1/3 - 3) - (-25 + 125/3 - 75)
Area = (-8 1/3) - (- 25/3)
Area = 16 ² / ₃ square units
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How do l do this??? Please help
Answer:
69
Step-by-step explanation:
69
5. A rock is thrown directly upward with an initial velocity of 79 feet per second from a cliff 50 feet above a beach. The height of the rock above the beach (h) after t seconds is given by the equation h = -16t² + 79t + 50. The graph below shows the rock's height as a function of time.
5. The quadratic function for the height of the rock, h = -16·t² + 79·t + 50, indicates;
a. The height of the rock will be 125 feet above the beach at 1.28 seconds and 3.66 seconds after it is thrown
b. The maximum height reached is about 147.5 feet
The time it takes the rock to reach the maximum height is about 2.47 seconds
What is a quadratic function?
A quadratic function is a function of the form; f(x) = a·x² + b·x + c, where, a, b, and c are numbers, and a ≠ 0.
The initial velocity of the rock = 79 ft/s
Height of the cliff above the beach from which the rock is thrown = 50 feet
The function for the height of the rock above the beach is; h = -16·t² + 79·t + 50
Please find attached the graph of the height of the rock as a function of time, created with MS Excel.
Required; When the height of the rock will be 125 feet above the beach
When the height of the rock is 125 feet, we get;
h = 125 = -16·t² + 79·t + 50
-16·t² + 79·t + 50 - 125 = 0
-16·t² + 79·t - 75 = 0
The value of t obtained using an online tool are;
t = (79 + √(1441))/32 ≈ 3.66 and t = (79 - √(1441))/32 ≈ 1.28
The times at which the height of the rock will be 125 feet above the beach are; 1.28 seconds and 3.66 seconds after the rock is thrown
b. The maximum height of the rock can be obtained from the formula for finding the maximum height of a quadratic equation of the form; f(x) = a·x² + b·x + c, which is;
At the maximum point, x = -b/(2·a)
The function for the height; h = -16·t² + 79·t + 50, indicates that we get;
a = -16, b = 79, and c = 50
Therefore;
The time it takes the rock to reach the maximum height, t(max), is therefore;
t(max) = -79/(2 × (-16)) ≈ 2.47
It takes about 2.47 seconds for the rock to reach the maximum height
The maximum height, h(max) = -16 × 2.46875² + 79×2.46875 + 50 ≈ 147.5
The maximum height reached by the rock is about 147.5 feet
Possible part of the question, obtained from a similar online question, includes;
a. The time it takes the rock to reach a height of 125 feet above the beach
b. The maximum height reached by the rock and the duration it takes the rock to reach the maximum height.
Please find attached the possible graph in the question, created with MS Excel, using the function for the height of the rock.
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Assume that the data has a normal distribution and the number of observations is
greater than fifty. Find the critical z value used to test a null hypothesis.
a = 0.05 for a two-tailed test.
O±2.575
O±1.764
O±1.645
O±1.96
-1.96 and 1.96 are the essential z values for a two-tailed test with a significance level of 0.05.
A null hypothesis is what?A null hypothesis is a statistical hypothesis that presupposes that there is no link between two variables in a population or that there is no meaningful difference between two populations. It serves as the beginning point of a statistical hypothesis test and is typically marked as H0. A null hypothesis serves as a reference point against which the alternative hypothesis may be compared. The alternative hypothesis is accepted if there is sufficient evidence from the data to reject the null hypothesis. The null hypothesis is not rejected if there is insufficient evidence in the data to support it.
Using a significance threshold of 0.05, we may use a conventional normal distribution table or calculator to get the essential z value. The value that corresponds to the 0.025 percentile is the crucial z value (or the 0.975 percentile, depending on the direction of the alternative hypothesis).
The z value for the 0.025 percentile, as determined by a typical normal distribution table, is -1.96.
Hence, -1.96 and 1.96 are the essential z values for a two-tailed test with a significance level of 0.05.
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A city has cone-shaped buildings for storing salt and sand for icy roads. Each
building has a radius of 30 feet and a height of 20 feet. Find the volume of the
building. Use 3.14 for π.
OA. 1884 ft³
OB. 18,840 ft³
OC. 628 ft3
OD. 56,520 ft³
The volume of the building is approximately 18,840 cubic feet.
So the answer is (B) 18,840 ft³
What is volume of cone ?
The volume of a cone is a measure of the amount of space that the cone occupies and can be calculated using the formula:
[tex]V = (1/3)\pi r^2h[/tex]
where V is the volume of the cone, r is the radius of the base of the cone, h is the height of the cone, and π is a mathematical constant approximately equal to 3.14.
According to the question:
The volume V of a cone can be calculated using the formula:
[tex]V = (1/3)\pi r^2h[/tex]
where r is the radius of the base of the cone, h is the height of the cone, and π is a constant approximately equal to 3.14.
In this case, the radius r is 30 feet and the height h is 20 feet. Substituting these values into the formula, we get:
[tex]V = (1/3)\pi (30)^2(20)[/tex]
[tex]V = (1/3)\pi (900)(20)[/tex]
[tex]V = (1/3)(56,520)[/tex]
[tex]V = 18,840[/tex]
Therefore, the volume of the building is approximately 18,840 cubic feet.
So the answer is (B) 18,840 ft³.
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