Based on the information provided in the table, Jack has 4h yellow marbles.
To determine the number of yellow marbles in the jar of 275 marbles, we can use the information from the table to find the proportion of yellow marbles in the first pouch.
According to the table, there are 4 yellow marbles out of a total of 25 marbles in the first pouch.
Therefore, the proportion of yellow marbles in the first pouch is 4/25.
To find the number of yellow marbles in the jar of 275 marbles, we can multiply this proportion by the total number of marbles in the jar.
Number of yellow marbles = (4/25) x 275 = 44
Therefore, there are 44 yellow marbles in the jar of 275 marbles.
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The accompanying diagram shows a revolving door with three panels, each of which is 4 feet long. What is the width, w, of the opening between x and y, to the nearest tenth of a foot?
The width, w, of the opening between x and y, is 6.9 ft.
We have,
From the diagram,
We have the radius of the circle and the angle subtended by the chord at the center of the circle.
So,
We can also use the formula.
= 2 x radius x sin(angle/2)
This is the length of the chord.
Now,
radius = 4 ft
angle = 360/3 = 120
Substituting the values.
= 2 x radius x sin(angle/2)
= 2 x 4 x sin (120/2)
= 2 x 4 x sin 60
= 2 x 4 x √3/2
= 4 x √3
= 4 x 1.732
= 6.928
Rounding to the nearest tenth.
= 6.9 ft
Thus,
The width, w, of the opening between x and y, is 6.9 ft.
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please help! thank uu ~ :)
Answer:
Unlikely.
Step-by-step explanation:
Possibility Formula: [tex]\frac{Desired Outcome}{Total Possible Outcoes}[/tex]
We want to roll a 5. On a standard six-sided die, then the odds of that happening is [tex]\frac{1}{6}[/tex]
[tex]\frac{1}{6}[/tex] is unlikely.
The Question is in the Picture, use the Pythagorean theorem to solve and show your work please
Answer:
y=8
Step-by-step explanation:
1.The volume of a triangular prism is 204cm3 . If its height is 17cm, then find the area of its base.
Answer:
12 cm ^2
Step-by-step explanation:
Using the formula
V=ABh
Solving forAB
AB=V
h=204
17=12cm²
In ΔWXY, w = 320 inches, y = 740 inches and ∠Y=169°. Find all possible values of ∠W, to the nearest 10th of a degree.
subtract these polynomials
(3x^-2x+5)-(x+3=
2x² -2x+2 is the polynomial we obtained after subtraction
The given polynomials are (3x²-2x+5)-(x²+3)
Three times of x square minus two times of x plus five minus x square plus three
We have to subtract the polynomials
3x²-2x+5 -x² - 3
Combine the like terms
2x² -2x+2
Hence, the polynomial we obtained after subtraction is 2x² -2x+2
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sin( 3pi/4 ) =
O A. 1/2
OB. -√2/2
O C. √3/2
O D. √2/2
Answer:
sin(3pi/4 ) = -√2/2
So, B.
In the following probability distribution, the random variable
represents the number of activities a parent of a 6th-8th grade student is involved in.
Please round to 2 decimal places for a-c, 3 decimal places for the probability in part d.
X 0 1 2 3 4
P(X) 0.053 0.117 0.258 0.312 0.26
a) Compute and the mean,
, of the random variable
.
2.610
Correct
b) Compute the variance,
, of the random variable
.
c) Compute the standard deviation,
, of the random variable
.
1.14
Correct
d) What is the probability that a randomly selected student has a parent involved in 4 activities?
a) The mean of the random variable is 2.610 (rounded to 2 decimal places).
b) The variance of the random variable is 1.880 (rounded to 3 decimal places).
c) The standard deviation of the random variable is 1.372 (rounded to 3 decimal places).
d) The probability that a randomly selected student has a parent involved in 4 activities is 0.260 (rounded to 3 decimal places).
To compute the variance of the random variable, we need to calculate the squared deviation of each value from the mean, weighted by their respective probabilities, and then sum them up.
b) Variance [tex](\sigma^2)[/tex] of the random variable:
Variance is given by the formula[tex]Var(X) = \sum [(X - \mu)^2 \times P(X)],[/tex] where X represents the values of the random variable, μ is the mean, and P(X) is the probability.
Using the given data:
X: 0 1 2 3 4
P(X): 0.053 0.117 0.258 0.312 0.26
μ (mean): 2.610
Calculating the squared deviations for each value:
[tex](0 - 2.610)^2 \times 0.053 = 14.152[/tex]
[tex](1 - 2.610)^2 \times 0.117 = 0.291[/tex]
[tex](2 - 2.610)^2 \times 0.258 = 0.148[/tex]
[tex](3 - 2.610)^2 \times 0.312 = 0.122[/tex]
[tex](4 - 2.610)^2 \times 0.26 = 1.429[/tex]
Summing up the squared deviations:
Var(X) = 14.152 + 0.291 + 0.148 + 0.122 + 1.429 = 16.142
Therefore, the variance of the random variable is 16.142.
c) Standard deviation (σ) of the random variable:
The standard deviation is the square root of the variance.
Taking the square root of the variance calculated above:
Standard deviation (σ) = √(16.142) ≈ 4.020 (rounded to 3 decimal places)
d) Probability of a randomly selected student having a parent involved in 4 activities:
The probability of a specific value occurring in a discrete probability distribution is given by the corresponding probability value.
From the given data:
P(X = 4) = 0.26
Therefore, the probability that a randomly selected student has a parent involved in 4 activities is 0.26 (rounded to 3 decimal places).
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Complete the square to put
y=3x²-24x + 56 in vertex form.
a) y = 3(x-8)² +4
b) y=3(x-7)² +5
c) y = 3(x-6)² +6
d) y = 3(x - 5)² +7
e) y = 3(x-4)² +8
How do you find the length of an arc expressed in terms of pi?
Ratios are often represented by the symbol. For example, 5 : 4 might mean 5 eggs are needed for every 4 batches of cookies. Select all of the ratios that are equivalent to the ratio 12:3. 6:1 1:4 4:1 246 15:6 120 : 30
The ratios that are equivalent to the ratio 12:3 are 4:1 and 120:30.
We have,
To determine the ratios that are equivalent to the ratio 12:3, we need to find ratios that have the same value when simplified.
The ratio 12:3 can be simplified by dividing both numbers by their greatest common divisor (GCD), which in this case is 3.
Dividing 12 by 3 gives us 4, and dividing 3 by 3 gives us 1. Therefore, the simplified ratio is 4:1.
Now let's check the given options:
6:1 - This ratio is not equivalent because it is different from the simplified ratio 4:1.
1:4 - This ratio is not equivalent because the order of the numbers is reversed, and it is different from the simplified ratio 4:1.
4:1 - This ratio is equivalent to the original ratio 12:3. When simplified, both ratios result in 4:1.
246 - This is not a ratio and cannot be compared to the original ratio 12:3.
15:6 - This ratio is not equivalent because it is different from the simplified ratio 4:1.
120:30 - This ratio can be simplified by dividing both numbers by their GCD, which is 30.
Dividing 120 by 30 gives us 4, and dividing 30 by 30 gives us 1.
Therefore, the simplified ratio is 4:1, which is equivalent to the original ratio 12:3.
Thus,
The ratios that are equivalent to the ratio 12:3 are 4:1 and 120:30.
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I really need help doing this. please help me.
The bisector angle is angle PQT which is equal to angle RQT.
What is angle bisector?Angle bisector or a bisector angle is a type of angle obtained after dividing the initial angle into two equal parts.
The bisected angle can be obtained using a pair of compass and a pencil attached to it.
To bisect the given angle RQP; we will take the following steps;
place the compass on exactly point Qexpand the radius of the compass such that the pencil attached to the compass will be in between R and P.strike an arc with the pencil clock wisestrike another arc with the pencil anti clock wise such that the two arc intersects.draw a line from point Q to intersect the two arcs.label the point of intersection of the two arcs Tangle PQT is equal to angle RQTLearn more about bisector angles here: https://brainly.com/question/24334771
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Write the equation of the hyperbola
Using the center and distance between co-vertex and center, the equation of the hyperbola is written below
[tex]\frac{(y + 3)^2}{49} - \frac{(x - 10)^2}{144} = 1[/tex]
What is the equation of hyperbolaA hyperbola, in analytic geometry, is a conic section that is formed when a plane intersects a double right circular cone at an angle such that both halves of the cone are intersected.
The equation of hyperbola is given as;
[tex]\frac{(y - k)^2}{a^2} - \frac{(x - h)^2}{b^2} = 1[/tex]
where (h,k) is the center of the hyperbola, a is the distance between a vertex and the center, and b is the distance between a co-vertex and the center.
In this case, the center is (10,−3), a=7, and b=12. Therefore, the equation of the hyperbola is
The equation of the hyperbola is;
[tex]\frac{(y + 3)^2}{49} - \frac{(x - 10)^2}{144} = 1[/tex]
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Quentin deposited $1,264 into a savings account that earns 2.75% simple interest annually. What will Quentin’s account balance be at the end of 2.5 years? Assume he makes no additional deposits during that time period.
Answer:
I love math
Step-by-step explanation:
The formula for simple interest is:
I = P * r * t
where:
I = interest earned
P = principal amount
r = interest rate (as a decimal)
t = time (in years)
In this case, we know that:
P = $1,264
r = 2.75% = 0.0275 (as a decimal)
t = 2.5 years
So, we can plug in these values and solve for I:
I = 1,264 * 0.0275 * 2.5 = $87.55
Therefore, the interest earned over 2.5 years is $87.55. To find the ending balance, we need to add the interest earned to the principal:
Ending balance = $1,264 + $87.55 = $1,351.55
So, Quentin's account balance will be $1,351.55 at the end of 2.5 years.
An isosceles right triangle has a third side measurement of 25 inches and a perimeter of 85 inches. The leg of the dilated triangle measures 6 inches. What is the perimeter of the dilated triangle?
The PTO is selling raffle tickets to raise money for classroom supplies. There is 1 winning ticket out of the 150 tickets sold. The winner gets a prize worth $200.
Round your answers to the nearest cent.
Make a probability distribution table and find the expected winnings of one raffle ticket. $?
If a raffle ticket costs $4, what is the expected profit or loss of one raffle ticket? (Enter a negative number for a loss) $?
Answer:
Expected winnings = $1.33
Expected profit or loss = -$2.67
Step-by-step explanation:
Winning Probability Prize Value
Yes 1/150 $200
No 149/150 $0
Expected winnings of one raffle ticket:
Expected winnings = (Probability of winning x Prize value) + (Probability of losing x Prize value)
Expected winnings = (1/150 x $200) + (149/150 x $0)
Expected winnings = $1.33
If a raffle ticket costs $4, the expected profit or loss of one raffle ticket can be calculated as:
Expected profit or loss = Expected winnings - Cost of ticket
Expected profit or loss = $1.33 - $4
Expected profit or loss = -$2.67
I WILL GIVE BRAINLIEST, square root of x, find the domain of x
The domain for the square root function is the set of all whole numbers
Calculating the domain of the square root functionFrom the question, we have the following parameters that can be used in our computation:
Function type = square root function
Equation: square root of x
This means that
f(x) = √x
The domain for x in the function is the set of input values the function can take
In this case, the square root function can take any whole number as its input
This means that the domain for f(x) is the set of all whole number
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f+90+42=180 what is the answer of this
Answer:
hello
the answer is:
f = 180 - 42 - 90 = 48
PLEASE HELP
Which of the following graphs shows an angle that would have an equivalent cosine ratio to the graph shown?
Answer: 150 deg
Step-by-step explanation:
cosine is negative in quadrants 2 and 3. the current angle, 210, is in quad 3. It will have an equal cosine value in quad 2.
that angle will be -210 degrees. in positive terms that is 360-210 = 150 degrees.
thus the answer which shows 150 degrees is correct.
in general:
[tex]cos(x) = cos(-x)[/tex]
If tanA = 60/11 and sinB = 45/53 and angles A and B are in Quadrant I, find the value of tan(A-B)
Based on the information, it should be noted that the value of tan(A-B) is 234/583.
How to calculate the valueGiven:
tanA = 60/11
sinB = 45/53
A and B are in Quadrant I
We can use the following identity to find tan(A-B):
tan(A-B) = (tanA - tanB)/(1 + tanA*tanB)
Substituting the given values, we get:
tan(A-B) = (60/11 - 45/53)/(1 + (60/11)*(45/53))
= (15/53)/(295/583)
= 234/583
Therefore, the value of tan(A-B) is 234/583.
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Please do #1 and show work
The solution to the integration of the function given, ∫√(5x - 1) dx, is:
[tex]\frac{2}{15}(5x-1)^{3/2} + C[/tex]
Understanding IntegrationTo solve the integral of:
√(5x - 1) dx
we can use a u-substitution.
Let u = 5x - 1, then:
du = 5 dx
dx = du/5
Now we can rewrite the integral in terms of u:
∫√(5x - 1) dx = ∫√u * (du/5)
Simplifying the integral:
(1/5) ∫√u du
Integrating √u:
(1/5) * (2/3) * u^(3/2) + C
Where C is the constant of integration
Substituting back u = 5x - 1:
(2/15) * (5x - 1)^(3/2) + C
Therefore, the solution to the integral of √(5x - 1) dx is:
[tex]\frac{2}{15}(5x-1)^{3/2} + C[/tex]
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i need help can everyone please help me
Since AC is the angle bisector of ∠BAD, the flowchart proof should be completed as follows;
Statement Reason
AC bisects ∠BAD Given
∠BAC ≅ ∠DAC Definition of an angle bisector.
∠BCA ≅ ∠DCA Congruent angles of a triangle (SAS).
AC ≅ AC Reflexive property
ΔABC ≅ ΔADC AAS postulate
What is an angle bisector?In Mathematics and Geometry, an angle bisector can be defined as a type of line, ray, or segment, that typically bisects or divides a line segment exactly into two (2) equal and congruent angles.
By applying the angle bisector theorem to the given triangle, we have the following statements and justifications:
AC bisects ∠BAD Given
∠BAC ≅ ∠DAC Definition of an angle bisector.
Based on side, angle, side (SA) and congruent angles of a triangle (SAS), we can reasonably infer and logically deduce that ∠BCA is congruent to ∠DCA i.e ∠BCA ≅ ∠DCA.
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un edificio de 5 metros proyecta una sombra de 4 metros determina la altura que tiene una casa que proyecta una sombra 2 metros
The height of a house that has a shadow projection of 2 meters is given as follows:
2.5 meters.
How to obtain the height of the house?The height of a house that has a shadow projection of 2 meters is obtained applying the proportions in the context of the problem.
The proportional relationship between the height of the building and the height of the shadow is given as follows:
5/4 = x/2
Hence we apply cross multiplication to obtain the height of the house, as follows:
4x = 10
x = 10/4
x = 2.5.
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Solve for X
20x+30
28x-10
Answer:
[tex]\huge\boxed{\sf x = 5}[/tex]
Step-by-step explanation:
Statement:Corresponding angles are equal.Solution:20x + 30 = 28x - 10 (Corresponding angles)
Add 10 to both sides20x + 30 + 10 = 28x
20x + 40 = 28x
Subtract 20x from both sides40 = 28x - 20x
40 = 8x
Divide both sides by 85 = x
OR
x = 5[tex]\rule[225]{225}{2}[/tex]
p: 10 > 7 q: 10 > 5
p →q
F F → T
T F → F
F T → T
T T → T
Answer: if it's true that 10 > 7 (P), then it's also true that 10 > 5 (Q).
Step-by-step explanation: In the context of logic and truth tables, p → q can be read as "if p then q." You've provided the truth values for the combinations of p and q, which I'll summarize here:
If p and q are both False (F), then p → q is True (T).
If p is True (T) and q is False (F), then p → q is False (F).
If p is False (F) and q is True (T), then p → q is True (T).
If p and q are both True (T), then p → q is True (T).
Given your propositions:
P: 10 > 7
Q: 10 > 5
P is True because 10 is indeed greater than 7. Q is also True because 10 is greater than 5.
Therefore, we're in the fourth case of your truth table: both p and q are True, so p → q is also True.
Please help. Any unnecessary answers will be reported.
If n! = (2^8)(3^4)(5^2)(7), then what is n? Note that n! = n × (n - 1) × (n - 2) × ... × 1.
Answer:
n = 10
Step-by-step explanation:
Factorial is denoted by an exclamation mark "!" placed after the number. It means to multiply all whole numbers from the given number down to 1.
Therefore, n! represents the product of all positive integers from 1 to n.
[tex]\boxed{n!=n \times(n-1) \times(n-2) \times ... \times 1}[/tex]
Given expression:
[tex]n! = (2^8)(3^4)(5^2)(7)[/tex]
The expression for n! has been given as the product of prime factors.
As n! represents the product of all positive integers from 1 to n, begin by writing out the positive integers from 1 in ascending order as the product of primes (using exponents where possible):
[tex]\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|}\cline{1-14}\vphantom{\dfrac12}n&1&2&3&4&5&6&7&8&9&10&11&12&13\\\cline{1-14}\vphantom{\dfrac12}\sf Product\;of\;primes&1&2&3&2^2&5&3\cdot 2&7&2^3&3^2&5 \cdot 2&11&2^2\cdot 3&13\\\cline{1-14}\end{aligned}\;\;\sf etc.[/tex]
If we examine the prime products of the given expression, we can see that largest prime number 7 appears only once. Therefore, n must be less than 14, since the next time 7 appears as a prime factor is when 2 · 7 = 14.
The prime number 5 appears twice in the given expression.
From the above table, we can see that the first two times the number 5 is present is (1) on its own, and (2) as a factor of 10. Therefore, n must be equal to or more than 10.
The prime number 3 appears four times in the given expression.
From the above table, we can see that the first four times the number 3 is present is (1) on its own, (2) as a factor of 6, (3) & (4) as both factors of 9.
The 5th time prime number 3 is present is as a prime factor of 12. Therefore, n must be less than 12, else 2⁵ would be a factor of n!.
Therefore, we have determined that 10 ≤ n < 12.
As 11 is a prime number and does not appear in the given expression for n!, we can conclude that n = 10.
We can check this by calculating the given expression and 10!:
[tex]\begin{aligned}n! &= (2^8)(3^4)(5^2)(7)\\&=256 \cdot 81\cdot25\cdot7\\&=20738\cdot25\cdot7\\&=518400\cdot7\\&=3628800\end{aligned}[/tex]
[tex]\begin{aligned}10!&=10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1\\&=90 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1\\&=720 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1\\&=5040 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1\\&=30240 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1\\&=151200 \cdot 4 \cdot 3 \cdot 2 \cdot 1\\&=604800 \cdot 3 \cdot 2 \cdot 1\\&=1814400 \cdot 2 \cdot 1\\&=3628800 \cdot 1\\&=3628800\end{aligned}[/tex]
Therefore, this proves that n = 10.
Find the equation of the line.
Use exact numbers.
Answer:
y = 3x + 3
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]
with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (0, 3) ← 2 points on the line
m = [tex]\frac{3-0}{0-(-1)}[/tex] = [tex]\frac{3}{0+1}[/tex] = [tex]\frac{3}{1}[/tex] = 3
the line crosses the y- axis at (0, 3 ) ⇒ c = 3
y = 3x + 3 ← equation of line
PLEASE HELPPP IM CONFUSEDDDD
Answer: C: (-4,-3)
Step-by-step explanation:
You have the correct answer selected!
The solution of a system of equations is where the graphs of the two lines intersect. we can read that point to be (-4,-3), so thats the answer :)
A spherical boulder is 28 feet in diameter and weighs almost 8 tons. Find the volume Use 3.14 for pi
Answer:
V = (4/3) × 3.14 × 14³ = 11,310.08 cubic feet
Work Shown:
d = diameter = 28
r = radius = d/2 = 28/2 = 14
V = volume of a sphere
V = (4/3)*pi*r^3
V = (4/3)*3.14*(14)^3
V = 11,488.2133 cubic feet approximately
The info "weighs almost 8 tons" is never used. It is likely an intended distraction. All we need is the radius of the sphere to get its volume.
Name the quadrant in which angle 0 must lie for the following to be true.
Answer:
d
Step-by-step explanation: