The required probability of randomly selecting a white marble, replacing it, then randomly selecting another white marble is 4/25.
The probability of randomly selecting a white marble from the bag is 8/20, or 2/5, since there are 8 white marbles out of a total of 20 marbles (5 red, 8 white, and 7 green).
After replacing the first marble, there are still 8 white marbles and a total of 20 marbles in the bag. Therefore, the probability of randomly selecting another white marble is also 2/5.
To find the probability of both events happening (selecting a white marble, replacing it, and then selecting another white marble), we multiply the probabilities of the two events:
The probability of selecting a white marble and replacing it, then selecting another white marble = (2/5) x (2/5) = 4/25
Therefore, the probability of randomly selecting a white marble, replacing it, then randomly selecting another white marble is 4/25.
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if you roll a 6 sided die 66 times what is the best prediction possible for the number of times you will roll a five
Answer:
11/66, or 11 times
The ability of lizards to recognize their predators via tongue flicks can often mean life or death for lizards. Seventeen juvenile common lizards were exposed to the chemical cues of the viper snake. Their responses, in number of tongue flicks per 20 minutes, are presented below.
523, 455, 693, 574, 370, 642, 336, 387, 727, 370,
302, 268, 693, 472, 710, 285, 744
Preliminary data analyses indicate that you can reasonably apply the z-interval procedure. Find a 90% confidence interval for the mean number of tongue flicks per 20 minutes for all juvenile common lizards. Assume a population standard deviation of 190.0. Note: The sum of the data is 8551.
Confidence interval:
We can see here that the 90% confidence interval will be: 420.2 to 585.8.
What is confidence interval?An interval of values known as a confidence interval is one that is likely to include the real value of a population parameter. A confidence interval of 95%, for instance, indicates that there is a 95% likelihood that the population parameter's real value falls inside the interval.
We will find the sample mean first:
Sample mean = sum of data points / number of data points
Sample mean = 8551 / 17 = 503
Then the standard error will be:
Standard error = population standard deviation / square root of number of data points
Standard error = 190 / √(17) = 41.7
Confidence interval = Sample mean ± 1.645 × standard error.
where 1.645 is the z-score for a 90% confidence interval.
Confidence interval = 503 ± 1.645 * 41.7 = 420.2 to 585.8
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How many solutions does the system of equations below have?
y=-x-3
2y + 2x = -6
OA. No solution
B. Exactly 1 solution
C. More than 1 solution
D. At least 1 solution
There are more than one solution for the given system.
Hence the correct option is C.
The given system of equations is,
y=-x-3
2y + 2x = -6
Write the equation in the form of ax + by = c,
Therefore, the system be
x + y = -3
2x + 2y = -6
We know that,
The system of equations a₁x + b₁y = c₁ and a₂x + b₂y = c₂
If [tex]\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}[/tex]
Then the system has more than one solution.
Therefore,
1/2 = 1/2 = -3/-6
= 1/2
Hence, this has more than one solution or roots.
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URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS!!!!
Fill in the blanks please!
Answer:
How could the intersection of the graphs of the two equations be located on a coordinate grid?
-From the origin, move three units right and nine units up
What does the solution to a system of two linear equations mean on a graph?
-The point of intersection of the two lines
Can you have more than one solution to a system of linear equations?
-Yes, if both lines are the same exact line
Can you have exactly two solutions to a system of linear equations?
-No, because lines are straight
Can you have no solutions to a system of linear equations?
-Yes, if the lines are parallel
Step-by-step explanation:
Please look at the images attached. Sorry for the bad handwriting, I'm on a computer.
Basically, a linear system of equations has one solution if the equations yield two lines that intersect exactly once.
A linear system of equations has no solutions if the lines are parallel, because they will never intersect.
A linear system of equations has infinite solutions if the system of equations yields two lines that are the same, because they will forever intersect.
If you have any questions about these answers, please tell me in the comments below my answer. I'll be happy to answer them :)
what is 4/m + 1 at m=1
Answer:
5
Hope this helps!
Step-by-step explanation:
Plug in m = 1 into the equation.
m = 1 : [tex]\frac{4}{m} +1[/tex] => [tex]\frac{4}{(1)} +1[/tex] = 4 + 1 = 5
25-40x = x - 10
solve this radical equation
the 25-40x is supposed to be in a square root
The functions f(x) and h(x) share a common x-intercept.
f(x) = x2+4x
It is true that the functions f(x) and h(x) share a common x-intercept.
How to obtain the x-intercepts of a function?On the definition of a function, the x-intercept is given by the value/values of x for which the function assumes a value of zero.
Function f(x) is defined as follows:
x² + 4x.
Hence the x-intercepts are obtained as follows:
x² + 4x = 0
x(x + 4) = 0
x = 0 and x + 4 = 0 -> x = -4.
On a graph, the x-intercept of a function is the value of x at which the graph of the function crosses the x-axis.
Hence the x-intercept of function h(x) is given as follows:
x = -4.
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Ms Smith has 45 apples that she wants to divide equally among 5 learners. However, she realises that she only has small baskets that hold a maximum of 8 apples each.
How many small baskets will Ms Smith need to divide the apples equally among her learners
Answer:
6 small baskets
Step-by-step explanation:
Ms smith has decided to split 45 apples among 5 learners. So, 45/5=9 apples.
However, she realizes only 8 apples can be held in a small basket, She will need to use at least two baskets to give 9 apples to each learner.
So, the number of baskets required can be calculated as:
45 apples ÷ 8 apples per basket = 5.625 baskets
Since we can't use a fraction of a basket, 5.625 is approximately equal to 6.
Therefore, Ms. Smith will need 6 small baskets to divide the apples equally among her learners
The aquarium, measuring 23 cm and 15 cm, is filled with water up to half its height. If we insert sand with a volume of 2350 cm3, by how much will the water level in the aquarium rise.
10.th grade
" tutors , went offline ....?
The water level in the aquarium will rise by 18 cm.
Volume calculationThe volume of water in the aquarium before adding the sand is given by:
Volume = (1/2) x 23 cm x 15 cm = 172.5 cm³
When the sand is added, its volume is 2350 cm³. Therefore, the new volume of water and sand in the aquarium is:
= 172.5 cm³ + 2350 cm³
= 2522.5 cm³
Let h be the height of the water level after adding the sand. The new volume of water in the aquarium is given by:
Volume = (1/2) x 23 cm x 15 cm x h
Setting this equal to the new total volume, we can solve for h:
(1/2) x 23 cm x 15 cm x h = 2522.5 cm³
h = 2522.5 cm³ / (1/2 x 23 cm x 15 cm) = 18 cm
Therefore, the water level in the aquarium will rise by 18 cm.
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The answer choices are:
A. 4
B. 2 radical 5
C. 4 radical 2
D. 2 radical 10
The length of segment WK is given as follows:
B. [tex]2\sqrt{5}[/tex]
How to calculate the distance between two points?Suppose that we have two points of the coordinate plane, and the ordered pairs have coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex].
The shortest distance between them is given by the equation presented as follows, derived from the Pythagorean Theorem:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
The endpoints of the segment in this problem are given as follows:
K(-2,0) and W(-6,-2).
Hence the length of the segment is given as follows:
[tex]\sqrt{(2 - (-6))^2 + (0 - (-2))^2} = \sqrt{20} = \sqrt{4 \times 5} = 2\sqrt{5}[/tex]
Meaning that option B is the correct option in the context of this problem.
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Martin a une table ronde de 1 ,10m de diamètre il peut ajouter jusqu'à 5 rallonge de 40 cm chacune pour son repas d'anniversaire 10 personne seront présentes autour de cette table En comptant 60 cm par personne quel est le nombre minimal de rallonge qu'il doit installé
Solve the triangle and round
B to C is 15.2 cm
C to A is 6.6 cm
A to B is 15.6 cm
Answer:
Step-by-step explanation:
This is a triangle with sides 15.2 cm, 6.6 cm, and 15.6 cm. To solve for the angles, we can use the Law of Cosines:
c^2 = a^2 + b^2 - 2ab cos(C)
where a = 6.6 cm, b = 15.6 cm, c = 15.2 cm, and C is the angle opposite side c.
Using this formula, we can solve for the cosine of angle C:
cos(C) = (a^2 + b^2 - c^2) / 2ab
cos(C) = (6.6^2 + 15.6^2 - 15.2^2) / (2 * 6.6 * 15.6)
cos(C) = 0.748
Taking the inverse cosine of 0.748, we get:
C = 41.5 degrees
To find the other angles, we can use the Law of Sines:
a/sin(A) = b/sin(B) = c/sin(C)
Using this formula, we can solve for angle B:
sin(B) = (b/sin(C)) * sin(A)
sin(B) = (15.6/sin(41.5)) * sin(A)
sin(B) = 0.614 * sin(A)
Using the fact that sin(A) + sin(B) + sin(C) = 1, we can solve for sin(A) and sin(B):
sin(A) = (sin(C) - sin(B)) / (1 + cos(C))
sin(A) = (sin(41.5) - 0.614 * sin(A)) / (1 + cos(41.5))
Solving for sin(A), we get:
sin(A) = 0.266
Using this value of sin(A), we can solve for sin(B):
sin(B) = 0.614 * sin(A)
sin(B) = 0.157
Taking the inverse sine of these values, we get:
A = 15.4 degrees
B = 123.1 degrees
Therefore, the triangle has angles of approximately 15.4 degrees, 123.1 degrees, and 41.5 degrees.
In 2005 an area vocational school had an enrollment of 325 men and 123 women. In 2006 there were 149 women. what was the percent increase of women students. The answer should be rounded to the nearest whole percent
The nearest Whole percent, the percent increase of women students is approximately 21%.
The percent increase of women students, we need to compare the number of women students in 2005 and 2006.
In 2005, the number of women students was 123.
In 2006, the number of women students was 149.
To find the increase, we subtract the initial value (2005) from the final value (2006):
Increase = Final Value - Initial Value
Increase = 149 - 123
Increase = 26
Next, we need to calculate the percent increase. The percent increase is given by the formula:
Percent Increase = (Increase / Initial Value) * 100
Plugging in the values:
Percent Increase = (26 / 123) * 100
Calculating the percent increase:
Percent Increase ≈ 21.14%
Rounding to the nearest whole percent, the percent increase of women students is approximately 21%.
Therefore, the answer is 21%.
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A standard number cube has 6 faces, labeled 1 through 6. If you roll a standard number cube, what is the probability of a rolling a number other than 1? Write your answer as a fraction.
The probability of rolling a number other than 1 on a standard number cube is 5/6.
When rolling a standard number cube, there are six equally likely outcomes, one for each face of the cube. To find the probability of rolling a number other than 1, we need to determine the number of favorable outcomes and divide it by the total number of possible outcomes.
In this case, the favorable outcomes are rolling any number from 2 to 6, which gives us five possibilities. Therefore, the probability of rolling a number other than 1 is 5 out of 6.
Expressing this as a fraction, the probability can be written as 5/6. This means that out of all the possible outcomes, there is a 5/6 chance of rolling a number that is not 1.
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An experimental calculation of the specific heat of aluminum was found in a lab to be 0.174 cal/g*f. Based on the calibration of the equipment it is known that maximum percent error in the readings is 20%. Which of the following readings is not possible?
A. 0.102cal/g*f
B. 0.1398cal/g*f
C. 0.1953cal/g*f
D. 0.2020cal/g*f
A reading that is not possible is given as follows:
A. 0.102cal/g*f
How to obtain the possible readings?The possible readings are obtained applying the proportions in the context of the problem.
The percent error is of 20%, hence the minimum reading is given as follows:
0.8 x 0.174 = 0.1392 cal/gf
The maximum reading is given as follows:
1.2 x 0.174 = 0.2088 cal/gf.
The reading from option A is the only reading that is not between the minimum and the maximum values.
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Supermarkets Agreement 2012 Adult Rate The normal weekly pay for an adult aged 21 and over is $565.90 Junior Rates The wage rates for a junior employee are based on a percentage of the adult rate.
How many people aged 16 and under 17 years can be employed for the same cost as one adult employee?
Based on the Supermarkets Agreement 2012, the normal weekly pay for an adult aged 21 and over is $565.90.
The wage rates for a junior employee are based on a percentage of the adult rate, but the exact percentage is not provided. Therefore, it is impossible to determine how many people aged 16 and under 17 years can be employed for the same cost as one adult employee without knowing the specific percentage and calculating the wages accordingly Based on the Supermarkets Agreement 2012, the normal weekly pay for an adult aged 21 and over is $565.90. To determine how many people aged 16 and under 17 years can be employed for the same cost as one adult employee, we need to know the percentage of the adult rate for junior employees. Once we have that information, we can calculate the number of junior employees that can be employed for the same cost as one adult employee.
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!! I’ll give brainlist !!
Can someone please help
Determine the measure of each arc.
The measures of the arcs are: 16. m(MN) = 72°; 17. m(NQR) = 180°; 18. m(NQ) = 108°; 19. m(MRP) = 265°; 20. m(QR) = 72°; 21. m(MR) = 108°; 22. m(QMR) = 288°; 23. m(PQ) = 13°; 24. m(PRN) = 265°; 25. m(MQN) = 288°
How to Determine the Measure of Arcs?To determine the measures of each of the arcs, note that the central angle will have the same measure as the arc.
16. m(MN) = m<QRN
Substitute:
m(MN) = 72°
17. m(NQR) = 180° [semicircle is equal to 180 degrees]
18. m(NQ) = 180 - 72
m(NQ) = 108°
19. m(MRP) = 180 + (180 - 95)
m(MRP) = 180 + 85
m(MRP) = 265°
20. m(QR) = 72° [central angle is equal to intercepted arc measure)
21. m(MR) = 180 - 72
m(MR) = 108°
22. m(QMR) = 360 - 72 = 288°
23. m(PQ) = 180 - 95 - 72 = 13°
24. m(PRN) = 360 - 95
m(PRN) = 265°
25. m(MQN) = 360 - 72
m(MQN) = 288°
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Determine the equation of the circle with radius 9 and center ( − 1 , − 8 ).
The equation of the circle with radius 9 and center ( -1,-8 ) is( x + 1 )² + ( y + 8 )² = 81.
What is the equation of the circle?The standard form equation of a circle with center (h, k) and radius r is:
( x - h )² + ( y - k )² = r²
Given that the circle has a center of (-1, -8) and the radius is 9.
Hence; from the standard form of the equation of the circle:
Center ( h , k ) = ( -1, -8 )
h = -1
k = -8
And radius r = 9
Plug these values into the above formula and simplify.
( x - h )² + ( y - k )² = r²
( x - ( -1 ) )² + ( y - ( -8 ) )² = 9²
Simplify
( x + 1 )² + ( y + 8 )² = 81
Therefore, the equation of the circle is ( x + 1 )² + ( y + 8 )² = 81.
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If the distance from 3rd base to home plate is 60 feet, and the average speed of a pitch is 40mph, how many seconds would you have to get to home from 3rd before the ball reaches the catcher?
You would need to reach home plate in 1.02 seconds before the ball reaches the catcher.
we need to convert the speed from mph to feet per second, since the distance is given in feet.
40 mph = 58.7 feet per second (rounded to one decimal place)
To calculate the time it takes to get from 3rd base to home plate, we can use the formula:
time = distance / speed
Plugging in the given values, we get:
time = 60 feet / 58.7 feet per second
time = 1.02 seconds
Therefore, you would need to reach home plate in 1.02 seconds before the ball reaches the catcher.
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A ___does not have an apex.
1. pyramid
2. prism
3. cone
Answer: 3. Prism
explanation: An apex is basically, the point where all lines meet at one point, and a prism is the one shape that doesn't have a apex. Hope this helps!
100 Points! Algebra question. Photo attached. Thank you!
Answer:
a₁ = 121.5-------------------------
Use the formula for the sum of n terms of a GP:
Sₙ = a₁(1 - rⁿ) / (1 - r)And use the nth term formula:
aₙ = a₁*rⁿ⁻¹ = a₁*rⁿ/r ⇒rⁿ = aₙ*r/a₁We can rearrange the sum formula to solve for the first term:
Sₙ = a₁(1 - aₙ*r/a₁) / (1 - r) ⇒Sₙ = ( a₁ - aₙ*r) / (1 - r)Plugging in the given values, we get:
4860 = (a₁ - 3280.5*3)/(1 - 3)4860 = (a₁ - 9841.5)/ (-2)a₁ - 9841.5 = -2*4860a₁ - 9841.5 = -9720a₁ = 9841.5 - 9720a₁ = 121.5Therefore, the first term of the GP is 121.5.
please help me with my geometry i cant fail this class or i’ll have to move out of my parents house :(
Applying the tangent and the circle theorems, we have:
22. x ≈ 9.4; 23. Perimeter of triangle GHI = 168 units
24. m<NSR = 110°; 25. x = 10
How to Find the Missing Measures Using Circle and Tangent Theorems?22. Based on the tangent theorem, the triangle is a right triangle since the line is tangent to the radius of the circle. Therefore, based on the Pythagorean theorem, we have:
x = √[(7.4 + 4.6)² - 7.4²]
x ≈ 9.4
23. JH and HK are tangents, therefore they are equal. Thus:
7x + 4 = 13x - 20
7x - 13x = -4 - 20
-6x = -24
x = 4
Perimeter = GI + GJ + JH + HK + KI
GI = 52
HK = JH = 7x + 4 = 7(4) + 4 = 32
KI = 15
GJ = 52 - 15 = 37
Perimeter of triangle GHI = 52 + 37 + 32 + 32 + 15 = 168 units
24. Based on the angle of intersecting chords theorem, we have:
m<NSR = 1/2(170 + 50)
m<NSR = 110°
25. Based on the inscribed angle theorem, we have:
2(4x - 5) + 290 = 360
Solve for x:
8x - 10 + 290 = 360
8x = 360 - 280
8x = 80
x = 10
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(Ratios MC) Michelle had 6 paperback books and 5 hardcover books on the shelf by her bed. Write a ratio to represent the ratio of paperback books to hardcover books. 05:11 5:6 06:11 6
_
5
The ratio which represents the ratio of paperback books to hardcover books is 6 : 5.
Given that,
Michelle had 6 paperback books and 5 hardcover books on the shelf by her bed.
We have to find the ratio of the paperback books to hardcover books.
We have,
Number of paperback books = 6
Number of hardcover books = 5
We need to find the ratio of the paperback books to hardcover books.
Ratio = Number of paperback books / Number of hardcover books
= 6/5
Hence the ratio is 6/5.
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a
E
Calculator
Given that cos=, what is sin ?
Enter your answer, as a simplified fraction, in the boxes.
URGENT
The trigonometric value equation is solved and sin θ = 24/25
Given data ,
Let the triangle be represented as ΔABC
Now , the measure of sides of the triangle are
From the trigonometric relations , we get
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
And , sin² θ + cos² θ = 1
where the measure of cos θ = 7/25
On simplifying the equation , we get
sin θ = √ ( 1 - cos² θ )
sin θ = √ ( 1 - 49/625 )
sin θ = √576/625
sin θ = 24/25
Hence , the trigonometric relation is sin θ = 24/25
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What conclusion can be determined from the dot plot below?
Answer: Most Data takes 10 seconds to download. (sorry if this answer is very vague its hard to explain)
write answers that are not integers rounded to the nearest tenth
The value of x is 12.82, the value of z is 40.25.
Using Pythagorean theorem
50²= 39² + y²
y²= 2500- 1521
y= 32.28
Again Using Pythagorean theorem
z²= y²+ x²
z²- x²= 979
and, (39 + x)² = 50² + z²
(39 + x)² = 50² + (x² + 979)
1521 + 78x + x² = 2500 + x² + 979
78x = 1000
x ≈ 12.82
Substituting this value of x back into the first equation, we get:
z² - x² = 979
z² - (12.82)² = 979
z² ≈ 1620.12
Taking the square root of both sides, we get:
z ≈ 40.25
Therefore, the value of x is 12.82, the value of z is 40.25.
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a certain patcch of land sustains a population of heffalump. If the heffalump is presently 42 and expected to double every six years, how many heffalumps will be living on this patch of land fifty years from now?
The population of the patch land in 50 years is given as follows:
13,547.
How to define an exponential function?An exponential function has the definition presented as follows:
[tex]y = ab^\frac{x}{n}[/tex]
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.n is the time needed for the rate of change.The parameter values in this problem are given as follows:
a = 42, b = 2, n = 6.
Hence the function for the population after x years is given as follows:
[tex]y = 42(2)^\frac{x}{6}[/tex]
The population in 50 years is given as follows:
[tex]y = 42(2)^\frac{50}{6}[/tex]
y = 13,547.
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If a is an inversely proportional to b and a =1.5 when b =30,what is a when b =5
The proportion is solved and value of a = 9 and constant is k =45
Given data ,
If a is inversely proportional to b, it means that their product remains constant
a * b = k
where "k" is the constant of proportionality.
Given that a = 1.5 when b = 30, we can substitute these values into the equation:
1.5 * 30 = k
k = 45
Now, we can use the value of k to determine the value of "a" when b = 5:
a * 5 = 45
Dividing both sides by 5:
a = 45 / 5
a = 9
Hence , proportionality constant is k = 45 and when b = 5, the value of "a" is 9
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Part A
A data set is normally distributed with a mean of 27 and a standard deviation of 3.5. Find the z-score for a value of 25, to the nearest hundredth.
z-score =
Part B
In Part A, about what percent of the data is greater than 34?
A. 48%
B. 2%
C. 4%
D. 0.2%
a. The z-score for a value of 25 is -0.57, to the nearest hundredth.
b. The percent of the data is greater than 34 is about 2%.
What is the z-factor of the data set?To find the z-score for a value of 25, we can use the following formula;
z = (x - μ) /σ
where;
x is the valueμ is the meanσ is the standard deviationz = (25 - 27) / 3.5
z = -0.57
Rounding to the nearest hundredth, we get the z-score of -0.57.
The z-score for x = 34 is calculated as follows;
z = (x - μ) / σ
z = (34 - 27) / 3.5
z = 2
Using a standard normal distribution table, we find that the percentage of data that is greater than 34 = 2.28%.
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Match the given slope (m) and y-intercept (b) with the equation of the line in slope-intercept form.
The general equation is y=mx+b
where m is the slope and b is the y intercept.
So substitute the m and the b for the equation.
m=2, b = 5 : y = 2x+5
m=3 b = 5: y = 3x + 5
m = 5 b = 4: y = 5x + 4
