Answer:
[tex]\frac{11}{15} =0.733333333333[/tex]
Step-by-step explanation:
• Here The sample space S is the set of possible outcomes (ordered pairs of marbles) that we can draw at random (without replacement) from the bag.
Then
[tex]\text{cardS} =P^{2}_{10}=10\times 9=90[/tex]
……………………………………………
Drawing two marbles where the marbles are different colors
means
drawing (1green ,1 yellow) or (1green ,1 red) or (1yellow ,1 red)
Remark: the order intervene
=========================
•• Let E be the event “Drawing two marbles where the marbles are different colors”.
CardE = 2×3×3 + 2×3×4 + 2×3×4 = 66 (2 is for the order)
Conclusion:
[tex]p\left( E\right) =\frac{66}{90} =\frac{11}{15} =0.733333333333[/tex]
Method 2 :
[tex]p\left( E\right) =2\times \frac{3}{10} \times \frac{3}{9} +2\times \frac{3}{10} \times \frac{4}{9} +2\times \frac{3}{10} \times \frac{4}{9} =0.733333333333[/tex]
Answer:
[tex]\sf \dfrac{11}{15}[/tex]
Step-by-step explanation:
The bag of marbles contains:
3 green marbles3 yellow marbles4 red marbles⇒ Total marbles = 3 + 3 + 4 = 10
Probability Formula
[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]
First draw
[tex]\implies \sf P(green)=\dfrac{3}{10}[/tex]
[tex]\implies \sf P(yellow)=\dfrac{3}{10}[/tex]
[tex]\implies \sf P(red)=\dfrac{4}{10}[/tex]
Second draw
As the first marble is not replaced there are now 9 marbles in the bag.
If the first marble was green, the probability of drawing a yellow is now 3/9 and the probability of drawing a red is now 4/9.
If the first marble was yellow, the probability of drawing a green is now 3/9 and the probability of drawing a red is now 4/9.
If the first marble was red, the probability of drawing a green is now 3/9 and the probability of drawing a yellow is now 3/9.
To find the individual probabilities of picking 2 different colors, multiply the probability of the first draw by the probability of the second draw:
[tex]\implies \sf P(green)\:and\:P(red)=\dfrac{3}{10} \times \dfrac{4}{9}=\dfrac{12}{90}[/tex]
[tex]\implies \sf P(green)\:and\:P(yellow)=\dfrac{3}{10} \times \dfrac{3}{9}=\dfrac{9}{90}[/tex]
[tex]\implies \sf P(yellow)\:and\:P(green)=\dfrac{3}{10} \times \dfrac{3}{9}=\dfrac{9}{90}[/tex]
[tex]\implies \sf P(yellow)\:and\:P(red)=\dfrac{3}{10} \times \dfrac{4}{9}=\dfrac{12}{90}[/tex]
[tex]\implies \sf P(red)\:and\:P(green)=\dfrac{4}{10} \times \dfrac{3}{9}=\dfrac{12}{90}[/tex]
[tex]\implies \sf P(red)\:and\:P(yellow)=\dfrac{4}{10} \times \dfrac{3}{9}=\dfrac{12}{90}[/tex]
To find the probability of drawing two marbles at random and the marbles being different colors, add the individual probabilities listed above:
[tex]\begin{aligned}\implies \sf P(2\:different\:color\:marbles) &=\sf \dfrac{12}{90}+\dfrac{9}{90}+\dfrac{9}{90}+\dfrac{12}{90}+\dfrac{12}{90}+\dfrac{12}{90}\\\\ & = \sf \dfrac{66}{90}\\\\ & =\sf \dfrac{11}{15}\end{aligned}[/tex]
Given that a function, g, has a domain of -1 ≤ x ≤ 4 and a range of 0 ≤ g(x) ≤ 18 and that g(-1) = 2 and g(2) = 8, select the statement that could be true for g.
g(1) = -2
g(5) = 12
g(3) = 18
g(2) = 4
A function assigns the value of each element of one set to the other specific element of another set. The correct option is C.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Given that a function, g, has a domain of -1 ≤ x ≤ 4 and a range of 0 ≤ g(x) ≤ 18 and that g(-1) = 2 and g(2) = 8.
1.) g(1) = -2
Since the range is from 0 to 18. Therefore, this is not the correct option.
2.) g(5) = 12
Since the domain is from -1 to 4. Therefore, this is not the correct option.
3.) g(3) = 18
This is the only option that is feasible. Thus, this is the correct option.
4.) g(2) = 4
Since the value of g(2) is 8. Therefore, this is not the correct option.
Hence, the correct option is C.
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I Had 150 stickers. I gave 10 stickers to each of the 8 students in my class and kept the rest for myself. How many Stickers will I have
Answer:
70
Step-by-step explanation:
10tickets x 8students = 80tickets
150tickets-80tickets=70tickets
00
What is the volume of the following rectangular prism?
2
units
Volume=
27
5
units2
units
The volume of the rectangular prism is 27/2 square units
How to determine the volume?The volume is calculated as:
Volume = Base area * Height
This gives
Volume = 27/5 * 5/2
Evaluate the product
Volume = 27/2
Hence, the volume of the rectangular prism is 27/2 square units
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Madison drew Triangle D E F. In her triangle, Measure of angle D is represented as x degrees. The measure of Angle E is half the measure of Angle D. The measure of Angle F is 2 degrees less than twice Measure of angle D. What is Measure of angle F?
36 degrees
56 degrees
102 degrees
147 degrees
Answer:
c)102 degrees
Step-by-step explanation:
Using the following image, find QR given RS=6 and QS=7.
What is QR?
Answer:
1
Step-by-step explanation:
Knowing that the entire number line equals 7, and that the second line segment RS equals 6, we can subtract the two values to find QR.
[tex]7-6=1[/tex]
Therefore, QR equals 1.
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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:QR = 1 \:\: unit [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex] \qquad \tt \rightarrow \: QR + RS = QS[/tex]
Let QR = x
[tex]\qquad \tt \rightarrow \: x + 6 = 7[/tex]
[tex]\qquad \tt \rightarrow \: x = 7 - 6[/tex]
[tex]\qquad \tt \rightarrow \: x = 1[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Graph the exponential model
y = 3(6)^x Which point lies on the graph?
(-9 2)
(2, 9)
(- 1, - 18)
(1, 18)
Answer: (1, 18)
Step-by-step explanation:
Test each x, y pair.
Getting to the last one, plug in 1 for the x value.
y = 3 * (6 ^ x)
y = 3 * (6 ^ 1)
y = 3 * 6
y = 18
This matches with (1, 18) so it must lie on the graph.
Determine which function has a greater initial value and explain how you know.
Function 1: y = 2()*
Function 2:
xy
03
16
2 12
3 24
Answer:
Function 2
Step-by-step explanation:
An initial value of a function, aka y-intercept, is obtained by using x=0 and evaluating the function at that point. Evaluating the two functions given:
Function1: y = 2x(1/3)^x|x=0 = 2*0*1=0
with the chart
xy
03
16
2 12
3 24
Function2 has value 3 for x=0
So, Function 2 has a greater initial value
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Solve x please explain
Answer:
x = 4
Step-by-step explanation:
co interior angles add up to 180.
this means that: 48 + 34x - 4 = 180
thus 48 + 34x = 184
therefore, 34x = 136
so, x = 4.
The two angles labeled in the given diagram are interior angles on the same side of the transversal. They can also be called interior supplementary angles.
These angles have a sum of 180 degrees.
Solving the QuestionThe two angles given have measures of 48 degrees and (34x-4) degrees.
They have a sum of 180 degrees.
Form an equation:
[tex]48+(34x-4)=180\\48+34x-4=180\\44+34x=180\\34x=180-44\\34x=136\\x=4[/tex]
Answer[tex]x=4[/tex]
Please help, i can't figure this out. I'll give a brainliest, but i really need help with how to solve this.
The required linear equation is given by y=10x + 15
The data collected by Harvard Business School plots the linear relationship of business startup success vs. Time.
The statistic is the study of mathematics which deal with relations between comprehensive data.
As clearly, points represents on graph startup success vs Time
part of a straight line
so we take two points on graph at (1,25), (2,35)
now equation of line
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)[/tex]
= [tex]y-25=\frac{35-25}{2-1} (x-1)[/tex]
[tex]y=10x+15[/tex]
Thus, The required expression is given by y=10x + 15 which show the relation ship between startup success Vs time
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Solve the system of linear equations.
y=−16x+5
x+6y=30
- Please see the attached picture for full sol^! :)
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2n + 1.6 = 17.6 what is the value of n?
Answer:
n = 8Step-by-step explanation:
2n + 1.6 = 17.6 what is the value of n?
2n + 1.6 = 17.6
2n = 17.6 - 1.6
2n = 16
n = 16 : 2
n = 8
-----------------
check
2n + 1.6 = 17.6
2*8+1.6=17.6
16+1.6=17.6
17.6=17.6
the answer is good
Please Help Asap Please And Thank You!
Answer:
Rate of change: 4/3
Step-by-step explanation:
Number of sodas/Total cost
pick a number
24/18 = 4/3
Answer:
4/3
Step-by-step explanation:
Rate of change is also known as slope.
To find slope, you have to find the change in y divided by the change in x.
y2-y1 / x2-x1
The variable y in this situation is the number of sodas.
The variable x in this situation is the total cost.
28 - 24 / 21 - 18
= 4 / 3
The rate of change in this problem is 4/3.
what is the surface area of a cylinder with a radius of 9 and width of 2
what is the side view ? the rest are right like i've tried loads of combinations but they're not right, please say what the shape is you know
Answer:
it will be a rectangle mostly...
I don’t understand, please help.
A food truck did a daily survey of customers to find their food preferences. the data is partially entered in the frequency table. complete the table to analyze the data and answer the questions:
part a: what percentage of the survey respondents do not like both hamburgers and burritos? (2 points)
part b: what is the marginal relative frequency of all customers that like hamburgers? (3 points)
part c: use the conditional relative frequencies to determine which data point has strongest association of its two factors. use complete sentences to explain your answer. (5 points)
will mark brainliest if correct answers
The percentage of the survey respondents that do not like both hamburgers and burritos is 16.09%.
How to compute the percentage?The percentage of the survey respondents that do not like both hamburgers and burritos will be:
= 33/205 × 100
= 16.09%
The marginal relative frequency of all customers that like hamburgers will be:
= 134/205
= 0.65
The data point that has strongest association of its two factors will be:
Those who like hamburger and burrito = 39/134 = 0.29
Those who like hamburger and not burrito = 95/134 = 0.71
Those who like burrito but not hamburger = 38/71 = 0.53
Those who do not like hamburger or burrito = 33/71 = 0.47.
Therefore, the data point that has strongest association of its two factors will be those who like hamburgers but not burritos.
A food truck did a daily survey of customers to find their food preferences. The data is partially entered in the frequency table. Complete the table to analyze the data and answer the questions:
Likes hamburgers Does not like hamburgers Total
Likes burritos 38 77
Does not like burritos 95 128
Total 134 71
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Find the area of each rhombus.
PLS HELP!! Geometry!!!!
Answer:
A) 384
B) 576
Step-by-step explanation:
the area of a rhombus is
pq/2
First Rhombus
we have p but to find q we can cut the triangle in half to form a right triangle, that allows us to use the Pythagorean theorem
20² = 12² + b²
400 - 144 = b²
b² = 256
b = 16
since the height (b) is half the rhombus, we double it to get q
p = 24
q = 32
a = [tex]\frac{24*32}{2}[/tex]
a = 384
Second Rhombus
Since rhombuses are parallelograms, we can use its area formula (b)(h)
a = (24)(24)
a = 576
The solution to an absolute value inequality is shown on the graph below.
-5-4-3 -2 -1 0 1 2 3 4 5
What is another way to show the solution?
x> -3 or x < 2
{x|x <-3 orx <2}
[-3, 2]
O (-3, 2).
The solution to the absolute value inequality is (-3,2).
What is absolute value inequality ?Absolute Value Inequality is the expression which contains absolute function as well as inequality signs .
The absolute value inequality is represented in the form of a line
Interval of the function is -3 to 2
As the intervals are represented by open circles, so -3 and 2 are exclusive of the values of the inequality.
Therefore the another way to show the solution is
-3 < x < 2
or
(-3,2)
Therefore, the solution to the absolute value inequality is (-3,2).
The complete question is attached with the answer.
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Explain how to decide when a normal distribution can be used to approximate a binomial distribution.
A normal distribution can be used to approximate a binomial distribution when n* p and n * q are greater than 5.
What is a normal distribution?A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.
A probability bell curve is more properly described as the normal distribution.
The mean and standard deviation of a normal distribution are 0 and 1, respectively. It has a kurtosis of 3 and zero skew.
Not all symmetrical distributions are normal, but all normal distributions are symmetrical.
Natural occurrences frequently resemble the usual distribution.
However, most price distributions in finance are not exactly normal distributions.
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A new car costs $34,000 and its value depreciates at 14% of its value each year. What is the decay factor for the value of this car? What will be the price of the car after 10 years?
The price of the car after 10 years is $7524.25 if the new car costs $34,000 and its value depreciates at 14% of its value each year.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let y represent the value of the car after x years. A new car costs $34,000 and its value depreciates at 14% of its value each year. Hence:
y = 34000(0.86)ˣ
After 10 years:
y = 34000(0.86)¹⁰ = 7524.25
The price of the car after 10 years is $7524.25 if the new car costs $34,000 and its value depreciates at 14% of its value each year.
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The number line below is correctly represented by which of the following intervals?
The intervals that represent the number line are given as follows:
b. [tex](-\infty, -5] \cup [8, \infty)[/tex]
What intervals belong to the number line?The first painted interval is of numbers to the left of x = -5(inclusive due to closed circle), hence:
[tex](-\infty, -5][/tex]
The second interval is of numbers to the right of x = 8, also inclusive, hence:
[tex][8, \infty)[/tex]
Hence the union is given by:
[tex](-\infty, -5] \cup [8, \infty)[/tex]
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Answer:
B
Step-by-step explanation:
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Find the Value of z! geometry!! pls help!!! thank you :)
[tex] \frac{z + 12}{5} = \frac{3z + 3}{4} [/tex]
[tex]4(z + 12) = 5(3z + 3)[/tex]
[tex]4z + 48 = 15z + 15[/tex]
[tex]48 - 15 = 15z - 4z[/tex]
[tex]33= 11z[/tex]
[tex]z = \frac{33}{11} \\ z = 3[/tex]
: Enter your answer and show all the steps that you use to solve this problem in the space provided.
What other information do you need in order to prove the triangles congruent using the SAS Postulate?
Answer: [tex]\angle BCA \cong \angle ACD[/tex]
Step-by-step explanation:
By the reflexive property, [tex]\overline{AC} \cong \overline{AC}[/tex]. So, we just need the pair of angles between these corresponding sides to be congruent.
Absolute value of -6.2 is _________.
1. 6.2
2. 6
3. 7
4. -6
[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]
What is the absolute value of -6.2? It's _____________.
[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]
No matter what the number is, its absolute value is always positive.
The number -6.2 is not an exception, there's nothing special about that number. Its absolute value is also positive.
[tex]\cline{1-2}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{=6.2}[/tex]
[tex]\LARGE\boxed{\bf{aesthetic \not1 \theta l}}[/tex]
The absolute value of -6.2 is 6.2 (option 1).
The absolute value of a number represents its distance from zero on the number line, regardless of its sign. For the value -6.2, the distance from zero is 6.2 units. Therefore, the correct answer is 1. 6.2. Option 1 accurately reflects that the absolute value of -6.2 is indeed 6.2.
The other options (2. 6, 3. 7, and 4. -6) do not accurately represent the absolute value of -6.2. The absolute value operation ensures that the result is always a positive value, showing how far a number is from zero. In this case, the absolute value of -6.2 is 6.2.
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Richard’s checking account balance was $57.34 at the beginning of the week. During the week, he recorded the transactions below.
A 2-column table with 4 rows. Column 1 is labeled Transaction with entries groceries, credit card bill, deposit, gas. Column 2 is labeled Amount with entries negative 25.37, negative 50, 163.75, negative 13.27.
What was Richard’s account balance at the end of the week?
$
Richard’s account balance at the end of the week is $ 132.45
What is Account Balance ?The amount of money in a person's bank account is called the account balance of that person
It is given that
Account balance of Richard’s at the beginning of the week = $57.34
Deposits in the week : $ 163.75
Expenses in the week : Groceries + Credit card bill + Gas
Total Expenses in the week = 25.37 + 50 + 13.27
= $ 88.64
The Richard’s account balance at the end of the week = Account Balance +Total Deposits - Total Withdrawals
= 57.34 + 163.75 - 88.64
Therefore , Richard’s account balance at the end of the week is $ 132.45.
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ease help me and thank you so so much u are so amazing!!
[tex] \frac{36 - 40}{2 - 1} = 4[/tex]
0.3 y+\dfrac yz0.3y+
z
y
0, point, 3, y, plus, start fraction, y, divided by, z, end fraction when y=10y=10y, equals, 10 and z=5z=5
The required solution to the equation is [tex]0.3y+\frac{y}{z}[/tex] at y=10, z=5 is 5.
As we have the equation [tex]0.3y+\frac{y}{z}[/tex] and find solution At y =10 and z=5
What is equation?
The equation is the relationship between dependent and independent variables through some mathematical operators.
Now,
putting the value of y=10, z=5 in [tex]0.3y+\frac{y}{z}[/tex]
⇒[tex]0.3*10+\frac{10}{5}[/tex]
= 5
Thus the required value of the equation at y=10 and z =5 is 3.
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FIND R, Interest problem
R, which is the rate is 20%.
What is simple interest?Simple interest is the interest on a sum of money invested or borrowed for a specific period of time.
The sum invested is called the principal.
Analysis:
simple interest (I) = PRT/100 = 300
P = principal = 3000
R = rate = ?
T = 0.5 year
300 = 3000 x R x 0.5/100
R = 20%
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A rectangle has a length of 6x-5y+1. If the perimeter of the rectangle is 16x-4y-4, determine an expression for its width
Answer:
2x +3y -3
Step-by-step explanation:
The perimeter of a rectangle is the sum of the lengths of all its sides.
Perimeter of a rectangle= 2 length +2 width
16x -4y -4= 2(6x -5y +1) +2(width)
Expand:
16x -4y -4= 12x -10y +2 +2(width)
2(width)
= 16x -4y -4 -(12x -10y +2)
= 16x -4y -4 -12x +10y -2
= 4x +6y -6
2(width)= 2(2x +3y -3)
Divide both sides by 2:
width= 2x +3y -3
5 2/8 minus 1 3/8 (show work)
Answer:
[tex]\frac{31}{8} or 3\frac{7}{8}[/tex]
Step-by-step explanation:
First, these 2 fractions are proper fractions, we will convert them into improper ones.
[tex]5\frac{2}{8} = \frac{42}{8}[/tex]
[tex]1\frac{3}{8} =\frac{11}{8}[/tex]
Now to subtract fractions, we must ensure the denominators are the same, which in this case is already the same, so we can subtract straightaway.
[tex]\frac{42}{8} - \frac{11}{8} \\=\frac{31}{8} or 3\frac{7}{8}[/tex]
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\mathsf{5 \dfrac{2}{8} - 1 \dfrac{3}{8}}[/tex]
[tex]\mathsf{= \dfrac{5 \times 8 + 2}{8} - \dfrac{1 \times 8 + 3}{8}}[/tex]
[tex]\mathsf{= \dfrac{40 + 2}{8} - \dfrac{8 + 3}{8}}[/tex]
[tex]\mathsf{= \dfrac{42}{8} - \dfrac{11}{8}}[/tex]
[tex]\mathsf{= \dfrac{42 - 11}{8 - 0}}[/tex]
[tex]\mathsf{= \dfrac{42 - 11}{8}}[/tex]
[tex]\mathsf{= \dfrac{31}{8}}[/tex]
[tex]\mathsf{\approx 3 \dfrac{7}{8}}[/tex]
[tex]\huge\textsf{Therefore, your answer should be: \boxed{\mathsf{3 \dfrac{7}{8}}}}\huge\checkmark[/tex]
[tex]\huge\textsf{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040}[/tex]