Answer:
Step-by-step explanation:
A player puts 3 balls of different color into 4 empty baskets. What is the probability that the maximum number of balls in a single basket is 2?
Answer:
3/8
Step-by-step explanation:
For each of the 3 balls, there are 4 options of baskets to put the ball.
The Probability is 3/4.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Given:
Total sample space for 3 balls= 4 x 4 x 4 = 64
So, Favorable events such that a basket has 3 balls = (\(^4C_1\)) x (\(^3C_1\))
Favorable events such that a basket has 4 balls = (\(^4C_1\))
Then,
= 1- Probability that any basket has 3 or 4 balls
= 1- ((\(^4C_1\)) x (\(^3C_1\)) + (\(^4C_1\))) / (4 x 4 x 4)
= 1- ((4!/ 3!) x (3!/2!) + (4!/3!) / 64
= 1- (12 + 4)/ 64
= 1- 16/64
= 1-1/4
= 3/4
Hence, the probability is 3/4
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Noncollinear points are points that do not lie on the same line. A. Undefined Terms B. Defined Terms C. Postulates D. Theorems
The statement noncollinear points are points that do not lie on the same line is a postulate. Option C
What are postulates?Postulates are ideas suggested or accepted as a basic principle before a further idea is formed or developed from it.
It is generally known that non -collinear points are points that do not lie on the same line
Some postulates about non -collinear points are:
a line contains at 2 points at least a plane contains at least 3 non-collinear points space contains at least 4 non-collinear Two points are found in one and only one line non-collinear points are contained in one and only one planeThus, the statement noncollinear points are points that do not lie on the same line is a postulate. Option C
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Use function notation to write the equation of the line
please asap
Answer:
b
Step-by-step explanation:
b
Find the derivative of ln(xe^x).
Answer:
\(\frac{dy}{dx} =\frac{1}{x} +1\)
Step-by-step explanation:
\(y=ln(xe^x)\)
\(=ln(x)+ln(e^x)\)
\(=ln(x)+x\)
Therefore,
\(\frac{dy}{dx} =\frac{1}{x} +1\)
help.........................................................
Answer:
C and D have the same slope of 1
F. Why would a linear function describing an investment made at a bank have a minimum
value but no maximum value? Explain your reasoning.
Answer: The function would have a minimum value because the least you will ever have is 0$. It cannot go below 0, so that is the minimum. However, depending on how much time has passed, the maximum amount of money you have can change. It can always go up more, so there is no set maximum.
Step-by-step explanation:
Use the relationship represented in this Venn diagram to identify the true statement.
A. All trapezoids are rhombuses
B. All rhombuses are trapezoids
C. No trapezoids are rhombuses
D. No rhombuses are trapezoids
The true statement based on the relationship depicted in the Venn diagram is that no rhombuses are trapezoids (option D).
To identify the true statement using the relationship represented in the Venn diagram, we need to analyze the overlapping regions and the properties of the shapes involved.
A trapezoid is a quadrilateral with at least one pair of parallel sides, while a rhombus is a quadrilateral with all sides of equal length. Let's evaluate the options:
A. All trapezoids are rhombuses: This statement is not true based on the diagram. The overlapping region between the trapezoids and rhombuses shows that there are trapezoids that are not rhombuses. Therefore, option A is incorrect.
B. All rhombuses are trapezoids: This statement is true based on the diagram. The entire region representing rhombuses is also included within the region representing trapezoids. Every rhombus can be considered a trapezoid because it has at least one pair of parallel sides. Thus, option B is correct.
C. No trapezoids are rhombuses: This statement is not true based on the diagram. The overlapping region indicates that there are trapezoids that are indeed rhombuses. Therefore, option C is incorrect.
D. No rhombuses are trapezoids: This statement is true based on the diagram. There is no overlap between the regions representing rhombuses and trapezoids, implying that no rhombus can be considered a trapezoid. Hence, option D is correct.
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1. Do 4x and 15+x have the same value when x is 5?
Answer:
yes
Step-by-step explanation:
if x=5
4(5)=20
15+5=20
hence they are the same
Find the slope (-1,-1) (-6,-5)
Answer:
The slope is \(\frac{4}{5}\)
Step-by-step explanation:
Hi there!
We are given the points (-1, -1) and (-6, -5).
We want to find the slope between them.
We can use the slope formula for this, which is \(\frac{y_2-y_1}{x_2-x_1}\), where \((x_1, y_1)\) and \((x_2, y_2)\) are points
We do have two points, which is what we need to find the slope, but let's label their values to avoid any confusion.
\(x_1=-1\\y_1=-1\\x_2=-6\\y_2=-5\)
Now substitute those values into the slope formula (m is the slope, and remember: the formula contains SUBTRACTION, even though we have negative numbers):
m=\(\frac{y_2-y_1}{x_2-x_1}\)
m=\(\frac{-5--1}{-6--1}\)
Simplify:
m=\(\frac{-5+1}{-6+1}\)
m=\(\frac{-4}{-5}\)
Divide again:
m=\(\frac{4}{5}\)
The slope is \(\frac{4}{5}\)
Hope this helps!
4 Millimeters decrease to 3 millimeters what's the percent of decrease
Answer:
Now first we have to found the decrease length.
which is:4mm-3mm=1mm
Now
we have to use formula to calculate the percentage which is
= decrease length/total length ×100%
=. 1/4×100%
=. 25 %
Therefore,the decrease rate is 25%.
Please help me understand!Problem:Two identical number cubes are shown in the picture. The edge length of these number cubes is 3 centimeters.Question:What is the combined volume of the number cubes in cubic centimeters?A.27 cm^3B.18cm^3C.9 cm^3D.54 cm^3
The volume of a cube is given by
\(V=l^3\)Since the lenght in this case is 3 cm, each cube has a volume of:
\(V=(3)^3=27\)Now, the combined volume is the sum of the volume of each cube.
Therefore, the combined volume of the cubes is 54 cm^3.
Francium is an element with a half-life of 22 minutes. 1000 grams of francium is placed into a bowl determine how much Francium (in grams) will be left after 2 hours
The amount of the element, Francium, that will remain after 2 hours is 31.25 grams.
Half-life problemTo determine how much francium will be left after 2 hours, we need to calculate the number of half-lives that occur within that time period.
Given that the half-life of francium is 22 minutes, we can calculate the number of half-lives in 2 hours (120 minutes):
Number of half-lives = (Total time elapsed) / (Half-life)
Number of half-lives = 120 minutes / 22 minutes ≈ 5.4545
Since we can't have a fraction of a half-life, we take the integer part, which is 5.
Each half-life represents a halving of the amount of francium. So, after 5 half-lives, the remaining amount of francium can be calculated using the formula:
Remaining amount = Initial amount * (1/2)^(Number of half-lives)
Given that the initial amount is 1000 grams, we can calculate the remaining amount after 2 hours:
Remaining amount = 1000 grams * \((1/2)^5\)
Remaining amount ≈ 1000 grams * 0.03125
Remaining amount ≈ 31.25 grams
Therefore, after 2 hours, approximately 31.25 grams of francium will be left.
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3x-4y=7,-3x+4y=2
system of equations
step by step
Answer:
{x,y} = {1,1}
Step-by-step explanation:
// Solve equation [2] for the variable x
[2] 3x = 4y - 1
[2] x = 4y/3 - 1/3
// Plug this in for variable x in equation [1]
[1] 3•(4y/3-1/3) + 4y = 7
[1] 8y = 8
// Solve equation [1] for the variable y
[1] 8y = 8
[1] y = 1
// By now we know this much :
x = 4y/3-1/3
y = 1
// Use the y value to solve for x
x = (4/3)(1)-1/3 = 1
Solution :
{x,y} = {1,1}
100 Points ! ! !
Exploiting points will be reported.
Brain deposited $9,824 into a savings account for which interest is compounded daily at a rate of 3.62%. How much interest will he earn after 8 years?
SHOW WORK AND WILL GIVE BRAINLIST
$3299.62
compounded daily interest : \(\sf A = P(1 + \dfrac{r}{n})^{nt}\)\(\sf 9,824.00(1 + \dfrac{3.62\%}{365})^{(365)(8)}\)\(\sf \$13,123.62\)
total money he will have : $13,123.62
amount earned : $13,123.62 - $9,824 = $3299.62Answer:
Interest = $3,299.64 (nearest cent)
Step-by-step explanation:
Compound interest formula: \(\sf I=P(1+\frac{r}{n})^{nt}-P\)
where:
I = total interest earned over time periodP = initial principal balancer = interest rate (in decimal form)n = number of times interest applied per time periodt = number of time periods elapsedGiven:
P = $9,824r = 3.62% = 0.0362n = 365t = 8 yearsSubstituting given values into the formula and solving for I:
\(\sf \implies I=9824(1+\frac{0.0362}{365})^{365 \times8}-9824\)
\(\sf \implies I=13123.62461-9824\)
\(\sf \implies I=3299.62 \ (nearest \ hundredth)\)
Simplify 2x^2-7x-4/x^2
Answer:
Option 1
Step-by-step explanation:
\(\frac{2x^2 - 7x-4}{x^2 - 5x+4}=\frac{(x-4)(2x+1)}{(x-4)(x-1)}=\frac{2x+1}{x-1}\)
One of the legs of a right triangle measures 2 cm and the other leg measures 7 cm. Find the measure of the hypotenuse. If necessary, round to the nearest tenth.
Answer:
Hypotenuse = 7.3 cm
Step-by-step explanation:
We can find the hypotenuse using the Pythagorean Theorem, which is:
\(a^2+b^2=c^2\), where a and b are the legs of the right triangle and c is the hypotenuse.
By plugging in 2 and 7 for a and b, we have:
\(2^2+7^2=c^2\\4+49=c^2\\53=c^2\\7.2801=7.3=c\)
Part 1 of 2
Find the numerical value of the rational expression when x = 2 and x = -3.
11x+6
2
2x + 28x + 48
Answer:
28, -27, 108, -42
Step-by-step explanation:
when x=2, 11x+6 = 22+6=28,
2x+28x+48= 30x+48=60+48=108
when x=-3, 11x+6 = -33+6=-27,
2x+28x+48= 30x+48=-90+48=-42
Answer:
I got 28, -27, 108, and -42. See explanation for the answer for which problems
Step-by-step explanation:
11x + 6 = ?
2x + 28x + 48 = ?
x = 2 and x = -3
Let's start with the first equation
Using x = 2
11(2) + 6 = ?
22 + 6 = 28
Using x = -3
11(-3) + 6 =?
-33 + 6 = -27
Second equation
Using x = 2
2(2) + 28(2) + 48 = ?
4 + 56 + 48 = 108
Using x = -3
2(-3) + 28(-3) + 48 = ?
-6 - 84 + 48 = -42
HELP PLEASE I’m having troubles!!!
1. The velocity at time t , v(t) = (18t² + 3 ) m/s
2. The velocity at time t = 3 seconds = 165 m/s
3. The acceleration at time t, a(t) =( 36t )m/s²
4. The acceleration at time t = 3 seconds = 108 m/s²
What is instateanou velocity and acceleration?The quantity that tells us how fast an object is moving anywhere along its path is the instantaneous velocity.
Instantaneous acceleration is defined as the ratio of change in velocity during a given time interval such that the time interval goes to zero.
1. s(t) = 6t³ + 3t +9
to find the velocity at time t, we differentiate s(t)
= 18t² + 3
2. at t = 3s
= 18(3)² +3
= 165 m/s²
3. v(t) = 18t² + 3
to get the acceleration at time t, we differentiate v(t)
= 36t
4. when t = 3
a = 36 × 3
= 108 m/s²
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How would you solve
"if f(x) / (x - 2) = x ^ 3 + 2x - 4 + 13/(x - 2) what is f(2)"
and
"if f(x) / (x + 3) = 3x ^ 2 - 4x + 2 what is f(-3)"
The denominator is zero (0/0 is undefined), we cannot determine the exact value of f(-3) using this equation.
To solve the given equations, we need to find the value of the function f(x) for specific values of x.
"If f(x) / (x - 2) = x³ + 2x - 4 + 13/(x - 2), what is f(2)?"
To find f(2), we can substitute x = 2 into the equation and solve for f(2).
Plugging in x = 2, we get:
f(2) / (2 - 2) = 2³ + 2(2) - 4 + 13/(2 - 2)
Since the denominator is zero (2 - 2 = 0), the equation is undefined. Therefore, there is no solution for f(2) in this case.
"If f(x) / (x + 3) = 3x² - 4x + 2, what is f(-3)?"
To find f(-3), we can substitute x = -3 into the equation and solve for f(-3).
Plugging in x = -3, we get:
f(-3) / (-3 + 3) = 3(-3)² - 4(-3) + 2
Simplifying, we have:
f(-3) / 0 = 3(9) + 12 + 2
f(-3) / 0 = 27 + 12 + 2
f(-3) / 0 = 41
Additional information or context is needed to solve for f(-3).
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Find all points on the x-axis that are 16 units from the point (5,-8)
To find all points on the x-axis that are 16 units away from the point (5, -8), we can use the distance formula. The distance between two points (x₁, y₁) and (x₂, y₂) is given by the formula:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
In this case, the y-coordinate of the point (5, -8) is -8, which lies on the x-axis. So, any point on the x-axis will have a y-coordinate of 0. Let's substitute the given values and solve for the x-coordinate.
d = √((x - 5)² + (0 - (-8))²)
Simplifying:
d = √((x - 5)² + 64)
Now, we want the distance d to be equal to 16 units. So, we set up the equation:
16 = √((x - 5)² + 64)
Squaring both sides of the equation to eliminate the square root:
16² = (x - 5)² + 64
256 = (x - 5)² + 64
Subtracting 64 from both sides:
192 = (x - 5)²
Taking the square root of both sides
√192 = x - 5
±√192 = x - 5
x = 5 ± √192
Therefore, the two points on the x-axis that are 16 units away from the point (5, -8) are:
Point 1: (5 + √192, 0)
Point 2: (5 - √192, 0)
In summary, the points on the x-axis that are 16 units away from the point (5, -8) are (5 + √192, 0) and (5 - √192, 0).
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It cost $36.75 for three tickets to visit the science center. It cost $51 for 4 tickets to visit the zoo. Which attraction will cost more money for a group of 12 students to visit? How much more?
After you place the order for 15 shirts, one of the members asks if he can order 2 more shirts, how much will it cost for the 2 extra shirts.
Answer:
???
Notes:
Hi, sorry, but I can't really do this if I don't know what 15 shirts cost, or if there isn't an equation of some sort. (Sorry again...)
6 = 30 divided by blank
Answer:30 divided by 5 = 6
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
6 = 30/x
multiply both sides by x
6x = 30
divide both sides by 6
x = 30/6 = 5
Please Solve, Thank you!
Answer:
1711
Step-by-step explanation:
\(4\cdot(14+8)^2-9\cdot(9-4)^2\\=4\cdot(22)^2-9\cdot(5)^2\\=4(484)-9(25)\\=1936-225\\=1711\)
Make sure to follow order of operations!
I'll be there tomorrow thank you so very sweet for the reminder of my day
we are told to complete the tables using the same ratio. To do that we need to multiply each number in the upper row by the same number to get the number in the lower row. Or divide the same number in the lower row to get the number in the upper row. In the case of table 4 we have that in the first column the numbers:
\(\begin{gathered} 1 \\ 9 \end{gathered}\)Therefore, we need to multiply the number in the first row by 9, to get the number in the lower row. Therefore, for the second column we have:
\(\begin{gathered} 3 \\ 27 \end{gathered}\)Since 9x3 = 27. In the third column:
\(\begin{gathered} 5 \\ 45 \end{gathered}\)Since 9x5 = 45. In the fourth row:
\(\begin{gathered} 7 \\ 63 \end{gathered}\)Since 9x7=63. In the final row:
\(\begin{gathered} 9 \\ 81 \end{gathered}\)Since 9x9 = 81. And thus we complete the table.
The complete table would be:
\(\begin{bmatrix}{1} & 3 & {5} \\ {9} & {27} & {45} \\ {} & {} & {}\end{bmatrix}\begin{bmatrix}{7} & {9} & {} \\ {63} & {81} & {} \\ {} & {} & {}\end{bmatrix}\)
the note payable relating to the june 2, and 10 transactions is a five-year note, with interest at the rate of 12 percent annually. interest expense should be computed based on a 360 day year. [important note: the original note on the computer equipment purchased on june 2 was $124,000. on june 10, eight days later, $23,750 was repaid. interest expense must be calculated on the $124,000 for eight days. in addition, interest expense on the $100,250 balance of the loan ($124,000 less $23,750
The initial note on the computer hardware bought on June 2 was $128,000.
What is the note payable relating to the June 2 and 10 transactions?The payable note for the transactions on June 2 and June 10 has a term of five years and carries interest of 12 percent a year. A 360-day year should be used to calculate interest expenses. (CRITICAL NOTE: The initial note on the computer hardware bought on June 2 was $128,000.
The note payable is a promissory note that the borrower issues pledging to pay the lender according to the terms set forth in their mutual agreement. If the note payable is due in less than a year, it can be recorded as a current liability on the liability side. If the note payable is due in more than a year, it is recorded as a non-current liability.
The complete question is:
The note payable relating to the June 2, and 10 transactions is a five-year note, with interest at the rate of 12 percent annually. Interest expense should be computed based on a 360 day year. (IMPORTANT NOTE: The original note on the computer equipment purchased on June 2 was $128,000. On June 10, eight days later, $24,500 was repaid. Interest expense must be calculated on the $128,000 for eight days. In addition, interest expense on the $103,500 balance of the loan ($128,000 less $24,500 = $103,500) must be calculated for the 20 days remaining in the month of June.)
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find g(x+5): g(x)=3x^2+2 simplify as much as possible
The answer of the given question based on the expression is , the simplified expression for g(x+5) is 3x² + 30x + 73.
What is Expression?An expression is combination of numbers, variables, and operators (such as +, -, ×, ÷) that represents value or quantity. Expressions can be as simple as a single number or variable, or they can be complex with multiple terms and operations. Expressions can be evaluated or simplified by performing the indicated operations according to the rules of arithmetic and algebra.
To find g(x+5), we replace every occurrence of x in the expression for g(x) with x+5:
g(x+5) = 3(x+5)² + 2
Expanding the square and simplifying, we get:
g(x+5) = 3(x² + 10x + 25) + 2
g(x+5) = 3x² + 30x + 73
Therefore, the simplified expression for g(x+5) is 3x² + 30x + 73.
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What 3 dimensional solid will be formed by rotating the given figure around the given line of symmetry?
Answer:
option D)
Step-by-step explanation:
when a equilateral triangle is rotated about x-axis
rotating equilateral triangle about x-axis will lead to the formation of cone in.
the height of the equilateral triangle will represent height of the cone.
the base of the equilateral triangle will represent the circular base of the cone
and the slant height of the cone will represented by the sides.
hence, the correct answer will cone which is option D)
Determine whether the equation is true or false. Where possible, show work to support your conclusion. If the statement is false, make the necessary change(s) to produce a true statement.
log(x+3)-log(8x)=log(x+3)/log(8x)
if false make necessary changes to produce a true statement
So the RHS of the given equation is incorrect.
How many distinct ways are there to arrange 2 orange marbles, 2 clear marbles, and 3 yellow marbles in a row? Give your
answer as an integer.
Provide your answer below:
Answer:
144
Step-by-step explanation:
3x2x2
the sum is 12, and after that you do 12^2
the final answer is 144
The number of distinct ways to arrange 2 orange marbles, 2 clear marbles, and 3 yellow marbles in a row will be 144.
What is a permutation?A permutation is an act of arranging items or elements in the correct order.
There are 2 orange marbles, 2 clear marbles, and 3 yellow marbles.
Then the number of distinct ways to arrange 2 orange marbles, 2 clear marbles, and 3 yellow marbles in a row will be
⇒ (3 x 2 x 2)²
⇒ 12²
⇒ 144
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