The situation can be solved by determining the probability of the selecting a certain color marble.
Probability is the ratio of a favorable outcome x to the total number of outcomes n of an event. In the give case, if the prediction is correct, you get a dollar.
Probability=x/n
On the first draw, the chance that predicted color is drawn is:
Probability=2/4=1/2
Amount you may get is ½*1=1/2
On the second draw, the chance the color with two left balls is predicted and come out:
Probability=2/3
Amount you may get is 2/3*1=2/3
On the third draw, you predicted a color with no same color balls left:
Probability=1/3
Amount you may get is 1/3*1=1/3
Or you predicted a color with two different color balls left
Probability=2/3*1/2=2/6=1/3
Amount you may get is 1/3*1=1/3
On the fourth draw, the probability of correct predicted ball is 1
Amount you may get is 1=1
If you played the game optimally, summing up the amount=1/2+2/3+1/3+1/3+1=17/6≈2.88
Hence, by playing the game optimally, the expected value of the game is $2.88.
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What is the solution of √4 x-23 -3 = 2 ?
The solution of the given equation √(4x-23) - 3 = 2 is (x = 14.25).
What is meant by square numbers?A 'Square Number' is the result of multiplying a number or integer (not really a fraction) by itself.
For instance, 3 multiplied by 3 equals 3 squared, or 3 x 3 = 32. So, in essence, a square number is really the exponential form of multiplying a number or integer by itself. Also, if we multiply the number on its own again, we get the integer's cube, a x a x a = a³.Now, as per the given equation;
√(4x-23) - 3 = 2
This could also be written as;
√(4x-23) = 2 + 3
√(4x-23) = 5
Now, squaring on the both side;
(4x-23) = 25
Open the brackets;
4x - 32 = 25
4x = 25 + 32
4x = 57
x = 14.25
Therefore, the solution of the given equation √(4x-23) - 3 = 2 is calculated as (x = 14.25).
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Find the tenth term of each arithmetic sequence. 15,23,31, ...........
The 10th term of an Arithmetic Progression (AP) is (a₁₀ = 87.)
What is the sequence of AP arithmetic progression?In Arithmetic Progression, the difference between the two mathematical orders is a constant value (AP). Arithmetic Sequence is another name for it.
We'd come across a few important words in AP that were denoted as:
The first term (a)Common difference (d)Term nth (an)The total of first n terms (Sn)As shown below, the AP also can be described in aspects of common differences.
The following is the formula for evaluating an AP's n-th term: an = a + (n − 1) × dThe arithmetic progression sum is as follows: Sn = n/2[2a + (n − 1) × d].Common difference 'd' of an AP: d = a2 - a1 = a3 - a2 = a4 - a3 = ...... = an - an-1.Now, the given sequence is; 15,23,31, ...........
Consider the first term is'a₁' = 15
Consider 'a₂' = 23 is the second term.
Consider the third term is 'a₃' = 31
Calculate the common difference;
d = a₂ - a₁
Put the values in the above obtained equation;
d = 23 - 15 = 8
Now, to estimate the value of the 10th term using the formula of nth term.
an = a + (n − 1) × d , n = total number of terms = 10.
Put all the values;
a₁₀ = 15 + (10 - 1) × 8
a₁₀ = 15 + 9 × 8
a₁₀ = 15 + 72
a₁₀ = 87
Therefore, the value of the 10th term is calculated as a₁₀ = 87.
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help, please!!!!!!!!!!
Given that triangle GHI and JKL are similar, the measure of side JK to the nearest tenth is 43.7
What is the measure of side JK?Similar triangles are triangles that have the same shape and are proportional, but their sizes may vary.
Given that;
Triangle GHI is similar triangle JKLSide IH = 13Side GH = 9.8Side LK = 58Side JK = ?Since the triangle are similar;
IH/GH = LK/JK
Plug in the given values and solve for side JK.
13/9.8 = 58/JK
Cross multiply
13 × JK = 58 × 9.8
13 × JK = 568.4
JK = 568.4 / 13
JK = 43.7
Given that triangle GHI and JKL are similar, the measure of side JK to the nearest tenth is 43.7.
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question is in the picture
Answer:
18 tables: $143
t tables: $35 + $6t
Step-by-step explanation:
35 + 6t
35 + 6(18) = 35 + 108 = 143
Find a slope-intercept form equation for the line through the points (-10,6) and (5,3) HELP ILL GIVE BRAINLIES
Answer:
[tex]y = - \frac{1}{5} x + 4[/tex]
Step-by-step explanation:
The slope-intercept form equation of a line is given by y= mx +c, where m is the slope and c is the y-intercept.
Start by finding the slope.
[tex]\boxed{\text{Slope}= \frac{y_1 - y_2}{x_1 - x_2} }[/tex]
Slope of line, m
[tex] = \frac{6 - 3}{ - 10 - 5} [/tex]
[tex] = \frac{3}{ - 15} [/tex]
[tex] = - \frac{1}{5} [/tex]
Substitute value of m into equation:
[tex]y = - \frac{1}{5} x + c[/tex]
Substitute any point the line passes through into the above equation:
When x= 5, y= 3,
[tex]3 = - \frac{1}{5} (5) + c[/tex]
3= -1 +c
c= 3 +1
c= 4
Substitute the value of c into the equation:
[tex]y = - \frac{1}{5} x + 4[/tex]
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Solve for the value of s (3s-2)°
(4s-6)°
Answer:
(3s-2)°+(4s-6)°=90
3s-2+4s-6=90
7s-8=90
7s=90+8
7s=98
Dividing both sides by 7
S=98/7
S=14
find the volume of the given shape
Answer:
[tex]{ \tt{volume = base \: area \times height \times length}} \\ \\ { \tt{v = \frac{1}{2} (a + b) \times h \times l }} \\ \\ { \tt{v = \frac{1}{2} (1.7 + 2.3) \times 1.3 \times 1.5}} \\ \\ { \tt{v = 2 \times 1.3 \times 1.5}} \\ \\{ \tt{v = 3.9 \: {m}^{3} }}[/tex]
Answer:
3.9 m³
Step-by-step explanation:
To find the volume of a right prism, multiply its base area by its height.
For the given shape:
Base = trapezoid ABCDHeight = 1.5 mArea of a trapezoid
[tex]\boxed{A = \dfrac{1}{2}(a+b)h}[/tex]
Where a and b are the bases and h is the height.
From inspection of the given diagram:
a = BC = 1.7 mb = AD = 2.3 mh = CD = 1.3 mSubstitute the given values into the formula to find the area of the trapezoid base (ABCD):
[tex]\begin{aligned}A & = \dfrac{1}{2}(a+b)h\\\implies ABCD & = \dfrac{1}{2}(BC+AD)CD\\ &=\dfrac{1}{2}(1.7+2.3)(1.3)\\&=\dfrac{1}{2}(4)(1.3)\\&=(2)(1.3)\\&=2.6\; \sf m^2\end{aligned}[/tex]
Therefore:
[tex]\begin{aligned}\textsf{Volume of prism} & = \textsf{Area of base} \times \sf height\\\implies V & = ABCD \times 1.5\\V & = 2.6 \times 1.5\\V & = 3.9\;\sf m^3\end{aligned}[/tex]
Approximate:
A. √370
B. √71
Given: AB CD
CF EB
Prove: AE FD
Proof:
AB CD
given
AB=CD
definition of
congruent segments
AE+EB-CFFD
segment addition
AE-FD
AE=FD
definition of
congruent segments
AB AE+EB
CD-CF FO
segment addition
CF = EB
given
CF EB
defation of
congruent segments
9
What is the missing reason in the proof?
OA segment addition
OB.
Congruent Segments Theorem
OC.
Transitive Property of Equality
OD. Subtraction Property of Equality
The figure have AE = FD
given,
AB =CD
AB = AE + EB
CD = CF + FD
AE + EB = CF + FD
CF = EB given,
AE = FD
if the triangle ABC and triangle DEF are identical. More specifically their side lengths and their angle measures are all the same, therefore we can consider them congruent figures. And that's exactly how you prove two figures are congruent by matching their corresponding parts.
SSS (Side-Side-Side) SAS (Side-Angle-Side) ASA (Angle-Side-Angle) AAS (Angle-Angle-Side).
Triangles that have exactly the same size and shape are called congruent triangles.
Identifying Congruent Figures in the Real World
Two figures are congruent if and only if they have the exact same shape and the exact same size.2.If the corresponding sides of two figures with the same shape have the same length, then the two figures are congruent.
They are the same shape but not the same size. Non-congruent rectangles. These two polygons have matching sides equal but their matching angles are not equal and so they are not congruent. They are different shapes even though the sides are the same size.
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Write an algebraic expression that models each situation.
Jenny had 130 , but she is spending 10 per week.
The algebraic expression of the situation "Jenny had $130, but she is spending $10 per week is 130-10x
Given,
The total amount she had = $130
Amount she spend per week = $10
Consider the number of weeks as x
Then the algebraic expression = 130-10x
Hence, the algebraic expression of the situation "Jenny had $130, but she is spending $10 per week" is 130-10x.
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A new cell phone sold for $200, which was 200% of the actual cost. What is the actual price of the cell phone?
Answer:
Step-by-step explanation:
200 / 2 = $100
7. Nina has 2/3 cup of shampoo left in the shampoo bottle. She uses 1/8 cup of shampoo to wash her hair. If nina washes her hair every day, how many days can she wait before opening a new bottle of shampoo?
Answer:
5 days
Step-by-step explanation:
Make 1/8 and 2/3 have the same denominator
the Least common multiple is 24
1/8 becomes 3/24 and 2/3 becomes 16/24
she can use it 5 more times with a remainder of 1/24 of a cup of shampoo remaining
Find the missing term of each geometric sequence. 2,□ ,0.5, . . . .
The missing term of the given geometric sequence can be 1 or -1
Given a geometric sequence,
2, □ ,0.5, . . . .
Hence, we know that
a(1) = 2
a(3) = 0.5
and the missing term is a(2).
The formula for the nth term of a geometric sequence is:
a(n) = a(1) . rⁿ⁻¹
Substitute a(1) =2 and n = 3
a(3) = 2 . r³⁻¹
0.5 = 2 . r²
r² = 0.5/2 = 0.25
r = 0.5 or r = -0.5
Take r = 0.5, then
a(2) = a(1) . r
= 2 . (0.5) = 1
Take r = -0.5, then
a(2) = a(1) . r
= 2 . (-0.5) = -1
Therefore, the missing term, a(2) can be 1 or -1
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Which situation shows causation?
When the number of people in a bus increases, the number of animals in a zoo also increases.
When the number of hours worked each week by an hourly employee decreases, the amount of money earned
by the employee also decreases.
When the amount of a discount for a sale increases, the number of items sold during the sale decreases.
6 When the number of bike trails in a city decreases, the amount of rainfall in the city increases.
Statements (B) and (D):
"(B) When the number of hours worked each week by an hourly employee decreases, the amount of money earned by the employee also decreases.(D) When the number of bike trails in a city decreases, the amount of rainfall in the city increases."shows causation.
What do we mean by Causation?Causation denotes that one event is the result of the other event's occurrence; that is, there is a causal relationship between the two events. This is also known as cause and effect. Causation is the process by which one variable causes another to change, implying that one variable is dependent on the other. It is also known as cause and effect. For example, as the weather warms, people get more sunburned. In this instance, the weather resulted in sunburn.In the given questions statements (B) and (D) shows causation.
Therefore, statements (B) and (D):
"(B) When the number of hours worked each week by an hourly employee decreases, the amount of money earned by the employee also decreases.(D) When the number of bike trails in a city decreases, the amount of rainfall in the city increases."shows causation.
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The correct question is given below:
Which situation shows causation?
(A) When the number of people in a bus increases, the number of animals in a zoo also increases.
(B) When the number of hours worked each week by an hourly employee decreases, the amount of money earned by the employee also decreases.
(C) When the amount of a discount for a sale increases, the number of items sold during the sale decreases.
(D) When the number of bike trails in a city decreases, the amount of rainfall in the city increases.
Samuel wants to buy a snake for $288 and the pet store owner wants him to make 6 equal payments of $49.
6 StartLongDivisionSymbol 288 EndLongDivisionSymbol minus 240 = 48. 48 minus 48 to get a remainder of 0 and a quotient of 49.
What error did the pet store owner make?
There is a multiplication error. The payment should be $48 per month.
There is a multiplication error. The payment should be $58 per month.
6 goes into 288 forty-six times. The answer is $46.
6 goes into 48 nine times. $49 is correct. PTS WORTH: 12
ima be up all night please help
The pet store owner made a multiplication error.
The payment should be $48 per month.
How do we calculate an equal periodic payment?An equal periodic payment can be calculated using the following formula:
P = T / N ............................................. (1)
Where, from the question:
P = periodic payment or the amount required to be paid periodically = ?
T = Total amount payable or the amount Samuel bought the snake = $288
N = Number of periods = 6
Substituting all the relevant values into equation (1), we have:
P = $288 / 6
P = $48
The P = $48 implies that $48 has to be multiplied by 6 to obtain $288.
Therefore, the pet store owner made a multiplication error.
The payment should be $48 per month.
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answer this please (will give brainliest)
Answer:
Step-by-step explanation:
Me personally, thinks that p is 9, and M is one or 4.
Think about it this way; 40-4p = _ SO, 40-4(9) = 4 because its like
40- 4 x 9 (40-36=4).
Next thing; m(p) 1(9) OR 4(9)
I HOPE YOU FIGURE IT OUT GOOD LUCK BYE!
solve for x : 15x - 3(3x+4)=6
Expand each binomial. (3-x)⁵
The expand each binomial. (3-x)⁵ is:
-x⁵ + 15x⁴ -90x³ + 270x² - 243x + 243
We solve first by perfect square trinomial, then we apply the distributive property.
(3 - x)⁵ = (3 - x)²(3 - x)²(3 - x)
(3 - x)²= 9 - 6x + x²
(9 - 6x + x²)(9 - 6x + x²)81 - 54x + 9x² - 54x + 36x² - 6x³ + 9x² - 6x³ + x⁴
x⁴ - 12x³+ 54x² - 108x + 81
(x⁴ - 12x³+ 54x² - 108x + 81)(3 - x)
3x⁴ - 36x³+ 162x² - 324x + 243 - x⁵ + 12x⁴ - 54x³ + 108x² - 81x
-x⁵ + 15x⁴ -90x³ + 270x² - 243x + 243
What is a polynomial?A polynomial is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms.
Depending on the number of terms it can be :
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Read the problem. Identify what you need to know. Then organize the data to solve the problem.
Find the probability that a point chosen at random lies in the shaded region.
A. 0.22
B. 0.25
C. 0.28
D. 0.32
The probability that a point is chosen at random will lie in the shaded area will be 0.32.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
Here favorable outcomes will be the shaded portion and the total outcome will be the total circular portion.
Favorable Outcome = Area of shaded portion = 1/2 x 18 x 18/2
= 81 inch sq.
Total Outcome = Total area = 81 π inch sq.
Probability, P(E) = 81/ 81 π = 1/32
Hence, the probability that a point chosen at random will lie in the shaded area is 0.32.
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solve the inequality
Answer:
the inequality solution is -19
the difference of six and two divided by 4 in numerical expression
Answer: 1 thank you
Step-by-step explanation:
Write this from least to greatest:
0.2, 1/4, 1/12, 22%
Answer:
1/12, 0.2, 22%, 1/4
Step-by-step explanation:
1/12 = 0.083333
1/4 = 0.25
22% = 0.22
0.2
So: 1/12, 0.2, 22%, 1/4
4y+20x-12=0 solve for y, would appreciate some help, in struggling a bit
Answer:
y = 3 - 5x
Step-by-step explanation:
Answer:
Step-by-step explanation:
4y+20x−12=0
4y−12=−20x
4y=−20x+12
4y=12−20x
4/4y = 12−20x / 4
y= 12−20x / 4
y=3−5x
Helpp, practice problems.
By comparing the intercepts of the linear equation with the ones in the graph, we conclude that the given graph corresponds with the linear equation.
How to know if the graph represents the given equation?
Here we have the linear equation:
1.5*s + 3.5*c = 21
And we have a graph, which we want to see if it is the graph of the linear equation.
To check this, we just need to look at the intercepts, the variable "c" is on the vertical axis and the variable "s" is on the horizontal axis.
The "s" intercept is what we get when we take c = 0, replacing that we will get:
1.5*s + 3.5*0 = 21
1.5*s = 21
s = 21/1.5 = 14
This means that the line should pass through the point (14, 0), and we can see that this happens.
The other intercept is what we get when we take s = 0.
1.5*0 + 3.5*c = 21
c = 21/3.5 = 6
The other intercept is at (0, 6), which we also can see on the graph.
With that is enough to conclude that the given graph represents the given linear equation.
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3x - 1 = 4x+8-х what is the answer
Answer:
No Solutions
Step-by-step explanation:
Hello!
Solve for x by isolating the variable.
Solve for x3x - 1 = 4x + 8 - x3x - 1 = 3x + 8 Combine like terms-1 = -8 Subtract 3x from both sidesSince -1 does not equal to -8, there are no solutions for x that makes this equation true.
Answer:
no solution
Step-by-step explanation:
3x-1=4x+8-x
add like terms
3x-1=3x+8
add 1 to both sides
3x=3x+9
subtract 3x from both sides
0=9
no answer!
In a telephone poll, 31 people said they like shopping and 6 people said they do not like shopping. What is the ratio of the number of people who do not like shopping to the number of people who like shopping?
Answer:
31 to 6
Step-by-step explanation:
31 to 6,
Which equation does NOT represent a direct variation?
a. y=x
b. 2 x-y=5
c. 2 x-y=0
d. 2 x-5 y=0
The graph of 2x - y = 5 does not represent a direct variation.
Direct variation is variation in which the quotient of the two variables is constant. A constant ratio of two quantities means that one quantity varies directly with the other or that the two quantities vary directly. In symbols, the direct variation formula is y=k*x or k=y/x.
k is known as the constant of variation or the constant of proportionality.
This means that as x increases, y increases, and as x decreases, y decreases, and their ratio is always the same.
The graph of the direct variation equation is a straight line through the origin.
The graph of 2x-y =5 does not pass through the origin, so it does not represent a direct variation. (consult the images attached below).
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Write an equation in standard form for the line that is perpendicular to the
graph of 1/5x + 2/5y = 0.05 and has y-intercept -0.5.
first look at the equation you’re given. It’s in y-intercept form. The slope is 5.
A line perpendicular to it has a slope that is the opposite reciprocal, -1/5. You are told that the y-intercept of the line is 4, so the equation for the Since the slope of the line is -1/5, and the y-intercept is 4, the equation of the line is,
y = (-1/5)x + 4
Multiply both sides by 5 and put into standard form,
x + 5y = 20line in y-intercept form is y= -1/5x+4
When we have a linear equation in standard form, we can find the x- and y-intercepts of the corresponding line. This also allows us to graph it.
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A diver is 25 feet below sea level. After he swims up 15 feet toward the surface, what is his elevation?
Answer:
-10.
Step-by-step explanation:
-25+15=-10.
Natalie works as a playground supervisor for 8 weeks during the summer at a rate of
$15.27/h. She works a 40-hour week but averages 3 hours of overtime each week,
paid at time and a half. How much will she earn each week, and for the whole
summer?
Natalie will receive a weekly salary of $656.61 and a summer salary of $10505.76.
What is an expression?The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.
Given that Natalie earns $15.27 per hour while working as a playground supervisor for 8 weeks throughout the summer. Although she works a 40-hour week, she typically puts in 3 hours of overtime.
For a week = ( 40 + 3 ) x 15.27 = $656.61
For a summer = 4 x 4 = 16 weeks
For a summer = 16 x $656.61 = $10505.76
Therefore, Natalie will be paid $656.61 for a week and for summer $10505.76.
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