so, they are not equally likely. Thus, P(spade) = 13/52 or 1/4, and P(heart) = 13/52 or 1/4, but P(spade) ≠ P(heart).
What is Probability?Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain to occur. The probability of an event is calculated by dividing the number of ways an event can occur by the total number of possible outcomes.
The true statements are:
P(ace) = 4/52 or 1/13
P(jack) = 4/13
P(ace) > P(king)
The false statements are:
P (numbered card) > P (face card) - this is not true since there are 12 face cards (4 jacks, 4 queens, 4 kings) and 40 numbered cards (2-10), so P(face card) = 12/52 or 3/13, and P (numbered card) = 40/52 or 10/13, which means that P (numbered card) > P (face card).
P(spade) = P(heart) - this is not true either, since there are 13 cards of each suit, but the spades and hearts are different suits, so they are not equally likely. Thus, P(spade) = 13/52 or 1/4, and P(heart) = 13/52 or 1/4, but P(spade) ≠ P(heart).
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a number m, rounded to 1 dp is 48.2
another number, n, rounded to 1 dp is 6.7
what are the lower and upper bound of m-n???
Answer:
I just had to say those numbers because of so I can send it like I'm about
To find the lower bound and upper bound of the difference m-n, we need to first find the possible range of values for m and n.
• For m rounded to 1 decimal place, the actual value could be anywhere between 48.15 and 48.25 (since the digit in the second decimal place could be anything from 0 to 9, and we round to the nearest 0.1).
• For n rounded to 1 decimal place, the actual value could be anywhere between 6.65 and 6.75.
Now, we can calculate the lower bound and upper bound of m-n:
Lower bound of m-n = (48.15 - 6.75) = 41.4
Upper bound of m-n = (48.25 - 6.65) = 41.6
Therefore, the lower and upper bounds of m-n are 41.4 and 41.6, respectively.
Write the polynomial in standard form. Then name the polynomial based on its degree and number of terms. x²+6-9x
Answer:
x² - 9x + 6
Step-by-step explanation:
The polynomial in standard form is:
x² - 9x + 6
This is a quadratic polynomial because it has a degree of 2, and it has three terms.
(1 point) in how many ways can 5 different novels, 3 different mathematics books, and 1 biology book be arranged on a bookshelf if (a) the books can be arranged in any order? answer: 362880 (b) the mathematics books must be together and the novels must be together?
(a) The number of ways the books can be arranged in any order is 362880,
(b) The number of ways the mathematics books must be together and the novels must be together is 4320.
Part(a) :
The number of mathematics-book is = 3,
The number of novels is = 5,
The number of biology books is = 1,
So, there are total of (5+3+1) = 9 books
These 9 books can be arranged in 9! = 362880 ways.
Part(b) :
If the mathematics book are together we can consider the mathematics books as 1 book and
if the novels are together then these 5 novels can be considered as one.
So, there are total 3 books which can be arranged in 3! Ways.
And these 5 novels can be arranged in themselves in 5! Ways and
these 3 mathematics books can be arranged in themselves in 3! ways.
So, total number of ways = 3!×3!×5! =6×6×120 = 4320 ways.
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numbers that are both positive and less then -3
Real number that is greater than or equal to zero. The only number that is both positive and negative is the number 0.
Please answer this question asap!!!!Find the surface area of a sphere with a volume of 33.51 cubic inches
Answer: 59.02 square inches
Step-by-step explanation:
We can use the formulas for the volume and surface area of a sphere to solve this problem.
The formula for the volume of a sphere is:
V = (4/3)πr^3
Where V is the volume, r is the radius, and π is pi (approximately equal to 3.14159).
We know that the volume of the sphere is 33.51 cubic inches, so we can plug that in and solve for the radius:
33.51 = (4/3)πr^3
r^3 = (3/4) * (33.51/π)
r^3 = 10.56
r ≈ 2.17
Now that we know the radius is approximately 2.17 inches, we can use the formula for the surface area of a sphere to find the surface area:
A = 4πr^2
A = 4π(2.17)^2
A ≈ 59.02 square inches
Therefore, the surface area of the sphere is approximately 59.02 square inches.
Factor the following polynomial completely 6x^2+12x+6 the correct answer is 6(x+1)^2 explain in full detail how this answer is achieved you must show every step to receive full credit
please
Answer: 6(x+1)^2
Step-by-step explanation:
1. Find the GCF. Because you know the equation is 6x^2+12x+6, you can see that the coefficients, 6 and 12, are all factors of 6. To make factoring easier, factor out 6 from all the coefficients, which leaves you with 6(x^2+2x+1)
2. Factor the equation in the parentheses. If you have learned your perfect squares, then you know that x^2+2x+1 is (x+1)^2 because x^2+2x+1 = (x+1)(x+1) (you can foil that out if you want to check). Once finished with this, it leaves you with 6(x+1)^2
An airplane traveling from Chicago to Los Angeles travels 15 miles every 2 minutes. On the return trip, the plane travels 25 miles every 3 minutes. Graph each ratio relationship in the coordinate plane.
Answer:
(6,45)
Step-by-step explanation:
To graph each ratio relationship in the coordinate plane, we can plot the ordered pairs (time, distance) for each leg of the trip. For the first leg from Chicago to Los Angeles, the plane travels 15 miles every 2 minutes. So we can plot the following points:
(0, 0) - starting point
(2, 15) - after 2 minutes, the plane has traveled 15 miles
(4, 30) - after 4 minutes, the plane has traveled 30 miles
(6, 45) - after 6 minutes, the plane has traveled 45 miles
(8, 60) - after 8 minutes, the plane has traveled 60 miles
We can plot these points on a coordinate plane, with time on the x-axis and distance on the y-axis. The resulting graph would show a straight line with a slope of 7.5 (rise of 15/2 and run of 1).
For the second leg from Los Angeles to Chicago, the plane travels 25 miles every 3 minutes. So we can plot the following points:
(0, 0) - starting point
(3, 25) - after 3 minutes, the plane has traveled 25 miles
(6, 50) - after 6 minutes, the plane has traveled 50 miles
(9, 75) - after 9 minutes, the plane has traveled 75 miles
(12, 100) - after 12 minutes, the plane has traveled 100 miles
We can plot these points on the same coordinate plane as the first leg. The resulting graph would also show a straight line with a slope of 8.33 (rise of 25/3 and run of 1).
The two graphs would intersect at the point (6, 45), which represents the halfway point of the round trip.
Triangle proofs level 2 please help!!!
HELP ITS URGENT PLEASE
The total area of the given composite geometric figure is: 27 cm²
How to find the area of the composite figure?The formula for the area of a parallelogram is:
Area = base * height
The formula for the area of a square is:
Area = ¹/₂ * base * height
The area of the square is:
Area = 3 * 3
= 9 cm²
Area of parallelogram = 3 * 6
Area of parallelogram = 18 cm²
Total area of composite figure = 18 + 9
= 27 cm²
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What is the equation in vertex form of a parabola with a vertex of (–3, 4) that passes through the point (1, –4)
Answer:
y = - [tex]\frac{1}{2}[/tex] (x + 3)² + 4
Step-by-step explanation:
the equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
here (h, k ) = (- 3, 4 ) , then
y = a(x - (- 3) )² + 4 , that is
y = a(x + 3)² + 4
to ind a substitute the point (1, - 4 ) into the equation
- 4 = a(1 + 3)² + 4
- 4 = a(4)² + 4 ( subtract 4 from both sides )
- 8 = 16a ( divide both sides by 16 )
- [tex]\frac{8}{16}[/tex] = a , that is
a = - [tex]\frac{1}{2}[/tex]
y = - [tex]\frac{1}{2}[/tex] (x + 3)² + 4 ← equation of parabola
in which of the following ways are binomial distributions and hypergeometric distributions similar? multiple select question. they are both discrete distributions. they both have two possible outcomes: success or failure. the probability of success is constant in each trial. they both assume each trial is independent of each other.
Binomial distributions and hypergeometric distributions are similar in that they both have two possible outcomes (success or failure) and the probability of success is constant in each trial. They also both assume that each trial is independent of each other.
Both binomial distributions and hypergeometric distributions are similar in the following ways: they are both discrete distributions, they both have two possible outcomes (success or failure), the probability of success is constant in each trial, and they both assume that each trial is independent of each other.
A binomial distribution is a probability distribution that models the number of successes in a given number of independent trials with the same probability of success for each trial. In a binomial distribution, the random variable X is the number of successes in the given number of trials.
The probability of a success for each trial remains constant. The mean and variance of the binomial distribution are given by the formula: μ = np and σ2 = npq, respectively.
A hypergeometric distribution is a probability distribution that models the probability of selecting a certain number of successes in a given number of draws from a finite population without replacement. In a hypergeometric distribution, the random variable X is the number of successes in the given number of draws.
The probability of a success for each draw remains constant.
The mean and variance of the hypergeometric distribution are given by the formula: μ = nx/N and σ2 = nx(N-n)(N-x)/N2(N-1), respectively.
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You and two friends go to a restaurant and order a sandwich. The menu has 10 types of sandwiches and each of you is equally likely to order any type. What is the probability that each of you orders a different type?
The probability that each of you orders a different type of sandwich is 72%.
To find the probability that each of you orders a different type of sandwich, we can use the counting principle.
Step 1: Determine the total number of ways you and your friends can order sandwiches.
Since there are 10 types and each of you can choose any type, there are 10 * 10 * 10 = 1000 possible ways to order.
Step 2: Calculate the number of ways you can order different types of sandwiches.
For the first person, there are 10 choices.
For the second person, there are 9 remaining choices (since their sandwich must be different from the first person's). For the third person, there are 8 remaining choices (different from both the first and second person's choices). So there are 10 * 9 * 8 = 720 ways to order different types of sandwiches.
Step 3: Calculate the probability of ordering different types of sandwiches.
Divide the number of ways to order different sandwiches by the total number of ways to order:
Probability = (Number of ways to order different sandwiches) / (Total number of ways to order)
Probability = 720 / 1000 = 0.72 or 72%.
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Expand this equation 5(y+3)
5y+15
I think this is correct. Hope this helps:)
Answer: 5y + 15
Step-by-step explanation: 5(y+3)
= 5(y) + 5(3)
= 5y + 15
I need help!
Given the points Q(-8, -8) and R(2, 7), find the coordinates of the point P on directed line segment QR that partitions segment QR in the ratio 2:3.
Answer:
(-2/5, 11/5)
Step-by-step explanation:
We can use the formula for finding a point that divides a line segment into a given ratio. Let P be the point on the line segment QR that partitions it in the ratio 2:3. Then we have:
P = ( (3x2 + 2x1)/(3+2), (3y2 + 2y1)/(3+2) )
where (x1, y1) = (-8, -8) is the coordinates of Q and (x2, y2) = (2, 7) is the coordinates of R.
Substituting the values, we get:
P = ( (32 + 2(-8))/(3+2), (37 + 2(-8))/(3+2) )
P = ( (-2/5), (11/5) )
Therefore, the coordinates of the point P on the directed line segment QR that partitions it in the ratio 2:3 are (-2/5, 11/5).
Data were recorded for the temperature of a cup of coffee over a 30 minute period. It is known that the temperature of
hot coffee will cool to room temperature following an exponential model.
Which of the following would linearize the data for temperature and minutes?
Minutes, Temperature
O Minutes, In(Temperature)
O In(Minutes), Temperature
In(Minutes), In(Temperature)
As it is known that the temperature of hot coffee will cool to room temperature following an exponential mode, the option which would linearize the data for temperature and minutes is "Minutes, ln(Temperature)". The Option B is correct.
What will linearize the data for temperature and minutes?Using logarithmic transformation, we can convert the exponential relationship between temperature and time into a linear relationship. By taking the natural logarithm of the temperature, we can rewrite the exponential model as:
ln(Temperature) = -kt + ln(T0)
In this model, ln(Temperature) is the natural logarithm of the temperature, k is a constant representing the rate of cooling, t is the time elapsed, and T0 is the initial temperature of the coffee.
This equation is in the form of a linear equation, y = mx + b, where ln(Temperature) is the y variable, -k is the slope, t is the x variable, and ln(T0) is the y-intercept. Therefore, plotting Minutes versus In(Temperature) will give a linear relationship.
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Describe the range of the relationship shown here
Help asap first answer will get brainliest
Answer:
C. 13,200 mm²
Step-by-step explanation:
Split the irregular shape.2 triangles and a rectangleFind the areas of each shape.Triangle = A = 1/2 bhWe figured that, 60 is the height of a rectangle and 90 is the length that is connected to the triangles. Which is 90 - 60 = 30. And then the width is 200 that was not disrupted by the irregular shape. The we found that 120 + 2x = 200 because there are 2 triangles that are disrupting the straight line of the width of a rectangle. As a result, it is x = 40 so 40 are the base of the triangle.We plug it in, A = 1/2 40(30), 1/2 (1200), and A = 600.We multiply this by 2 because we have 2 triangles so 600 x 2 = 1200.Rectangle = A = bhWe found the A = bh so we have base which is 200 and we have height which is 60.We multiply 60 and 200. A = 60 x 200 = 12000Overall, we have area of a rectangle which is 12000 and the area of the two triangles are 1200.
We both add them to get the area of the irregular shape.
12000 + 1200 = 13,200 mm²
50 points! Find the value of < Z O X:
< Z O X =
Answer:
64°
Step-by-step explanation:
You want the measure of angle ZOX, the smaller of a linear pair marked (3x -2)° and (5x +6)°.
Linear pairThe angles of a linear pair are supplementary—they total 180°.
(5x +6) +(3x -2) = 180
8x +4 = 180 . . . . . simplify
8x = 176 . . . . . . subtract 4
x = 22 . . . . . . divide by 8
The measure of angle ZOX is ...
∠ZOX = (3x -2)° = (3·22 -2)°
∠ZOX = 64°
__
Additional comment
Angle ZOY is ...
∠ZOY = (5·22 +6)° = 116°, the supplement of 64°.
The total cost of a vacation rental depends on when it is being rented: during the week, on the weekend, or over a holiday. The total cost for three different groups to stay at the rental is shown in the table.
The correct statement regarding the solution of the system of equations is given as follows:
A. The solution to the system is viable.
How to model the situation?The situation is modeled by a system of equations, for which the variables are given as follows:
Variable x: cost of a weeknight.Variable y: cost of a weekend night.Variable z: cost of a holiday.From each row of the table, the equations are given as follows:
4x + 2y = 614.3x + y + z = 555.5x + y + z = 733.Subtracting the third equation by the second, the value of x is given as follows:
2x = 178
x = 178/2
x = 89.
From the first equation, the value of y is given as follows:
y = [614 - 4 x 89]/2
y = 129.
From the second equation, the value of z is given as follows:
z = 555 - 3 x 89 - 129
z = 159.
Hence the system has a viable solution.
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Gary bought n notebooks for $3 each. he spent a total of $15. How many notebooks did he buy?
Answer:
Gary bought 5 notebooks
Step-by-step explanation:
the equation used for this would be 3n = 15
meaning you divide both sides by 3 which gets you n = 5
>Y. Write exponential functions: word problems LZW
Dr. Powell is a veterinarian. He gave Ruby, one of the cats he is treating, 40 micrograms of
medication. Based on Ruby's size, Dr. Powell expects there will be about 32 micrograms of
medication remaining in her body after one hour. Dr. Powell knows that the amount of
medication remaining in Ruby's body will continue decreasing each hour.
Write an exponential equation in the form y = a(b)* that can model the amount of medication
in Ruby's body, y, x hours after it was administered.
Use whole numbers, decimals, or simplified fractions for the values of a and b.
y
DO
(0)
To the nearest whole number, how many micrograms of medication can Dr. Powell expect to
be remaining in Ruby's body after 4 hours?
micrograms
Rounding to the nearest whole number, Dr. Powell can expect about 16 micrograms of medication to be remaining in Ruby's body after 4 hours.
What is equation?In mathematics, an equation is a statement that two expressions are equal. It typically consists of two sides, a left-hand side and a right-hand side, separated by an equal sign (=). Equations are used to represent relationships between variables or to solve for unknown values. They are an important tool in algebra, calculus, and other areas of mathematics and science.
Here,
The exponential equation in the form y = a(b)^x that can model the amount of medication in Ruby's body, y, x hours after it was administered is:
y = 40(0.8)ˣ
where:
a = 40, the initial amount of medication given to Ruby
b = 0.8, the factor by which the medication decreases each hour
To find the amount of medication remaining in Ruby's body after 4 hours, we can substitute x = 4 into the equation and evaluate:
y = 40(0.8)⁴
y = 40(0.4096)
y = 16.384
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Whats the answer to this question?
The triangles are necessarily congruent by the ASA congruence rule.
What is the ASA congruence rule?The ASA, which is an acronym for Angle-Side-Angle, congruence rule states that if two angles and an included side of one triangle are congruent to two angles and an included side of another triangle, then the two triangles are congruent.
The angle markings on the triangles ΔJLK and ΔZXY indicates;
∠J ≅ ∠Z, ∠K ≅ ∠Y
The side markings on the triangles indicates
Side JK in triangle ΔJLK is congruent to side ZY in triangle ΔZXY
Therefore, two angles and an included side in triangle ΔJLK are congruent to two angles and an included side in triangle ΔZXY, therefore, triangle ΔJLK is congruent to triangle ΔZXY by Angle-Side-Angle, ASA congruence rule.
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What is 16 + 2x = 2 + 4x
Answer:
x=7
Step-by-step explanation:
Check the attachment below:
Select the expression that makes the equation true.
one half x (3 x 5 + 1) – 2 = ___
4 x (2 + 3)
(4 x 3) ÷ 2
6 ÷ 3 + 2
6 + 8 ÷ 4
The expression that makes the equation true is: (4 x 3) ÷ 2.
option 1 is the correct answer.
What is expression ?In mathematics, an expression is a combination of symbols and/or values that represents a quantity or a relationship between quantities. It can include variables, constants, mathematical operations, and functions.
According to the given information:first, let's simplify the expression within the parentheses:
3 x 5 + 1 = 15 + 1 = 16
Now, we can simplify the entire expression:
1/2 x (3 x 5 + 1) - 2 = 1/2 x 16 - 2 = 8 - 2 = 6
So, we need to select the expression that equals 6:
6 ÷ 3 + 2 = 4
6 + 8 ÷ 4 = 8
(4 x 3) ÷ 2 = 6
Therefore, the expression that makes the equation true is: (4 x 3) ÷ 2.
option 1 is the correct answer.
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Answer:
.
(4x3)---- 2
.
B
Step-by-step explanation:
hope this help!
express x squared minus 5x + 8 in the form (x-a) squared + b
Answer:
(x-2.5)^2 + 1.75
Step-by-step explanation:
To write that as an equation, we get x^2 - 5x + 8.
now, we need to complete the square:
x^2 - 5x + 6.25 + 1.75 =
(x-2.5)^2 + 1.75.
Equivalent Expressions & the Distributive Property-Instruction-Levi
The bedroom and the bathroom in a tiny house share a wall. The area of the bedroom is
70 square feet. The area of the bathroom is 35 square feet. The expression 70 +35
represents the total area in square feet.
Which expressions also represent the
total area of the two rooms?
Choose ALL that apply.
10(7+5)
7.10+7.5
10-7+10.5
7(10+5)
70 ft
A=70+35
35 ft
Answer:
Step-by-step explanation:
The distributive property of multiplication over addition can be used when you multiply a number by a sum. For example, suppose you want to multiply 3 by the sum of 10 + 2. 3(10 + 2) = ? According to this property, you can add the numbers and then multiply by 3.
It would be very much appreciated if you helped me with this one problem...
Answer:Exact Form:
g=10/3
Decimal Form:
g=3. ¯3
Mixed Number Form:
g=3 1/3
Step-by-step explanation:
how many teaspoons of minced garlic equals one clove
in a survey of employees on a island, we find that as their primary vehicle to commute to work, 10% use a boat, 35% use a sedan, 50% use a suv, 5% use a bicycle. if an employee is selected at random, what is the probability that you will select a person who uses a suv or sedan?
If an employee is selected at random, the probability that you will select a person who uses a suv or sedan is 85%.
Given data: Primary vehicles to commute to work :
Percentage of employees who use a boat = 10%
Percentage of employees who use a Sedan = 35%
Percentage of employees who use a SUV = 50%
Percentage of employees who use a Bicycle = 5%
Probability of selecting a person who uses a SUV or Sedan can be calculated as follows:
Probability of selecting a person who uses a SUV or Sedan= Probability of selecting a person who uses a SUV + Probability of selecting a person who uses a Sedan
Probability of selecting a person who uses a SUV or Sedan= 50% + 35%= 85%
Hence, the probability of selecting a person who uses a SUV or Sedan is 85%.
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The diameter,D , of a sphere is 19 mm. Calculate the sphere's volume , V.
I NEED THE ANSWER QUICKKKK
I remember doing this but I don’t seem to remember sorry