The total number of winning hands are 276.
What is the probability?Probability is defined as the ratio of favorable outcomes to all other possible outcomes of an event. The symbol x can be used to express the quantity of successful outcomes for an experiment with 'n' outcomes. The probability of an event can be calculated using the following formula.
Probability of an event = Number of favourable outcomes/Total number of outcomes = x/n.
In the given question,
If the first card drawn is a 10, then there are
[tex]P_9^2=\frac{9!}{(9-2)!} =9*8=72 hands[/tex]
There are 9 possible numbers if the second card is a 10, and there are 8 possible numbers if the third card, giving us,
[tex]9*8= 72 hands[/tex]
If the third card is 10 then there are 9 possible numbers for the first card and 8 possible numbers for
second card, it gives us
[tex]9*8= 72 hands[/tex]
And there are 5 odd cards, and it gives us:
[tex]P_5^3=\frac{5!}{(5-3)!} =5*4*3=60 hands[/tex]
So, we have that in total we have
72+72+72+60=276 winning hands.
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David sold his house for $159,00 He got this amount knowing that he would have to pay a 6% commission to his agent. What amount did he have after the agent was paid?
The length of a rectangle is 8 feet longer than the width. If the perimeter is 88 feet, find the length and width of the rectangle.
Check the picture below.
[tex]\textit{perimeter of a rectangle}\\\\ P=2(L+w) ~~ \begin{cases} L=length\\ w=width\\[-0.5em] \hrulefill\\ P=88\\ L=w+8 \end{cases}\implies 88=2( ~~(w+8)+w ~~ ) \\\\\\ 88=2(2w+8)\implies 88=4(w+4)\implies \cfrac{88}{4}=w+4 \\\\\\ 44=w+4\implies \boxed{40=w}\hspace{5em}\stackrel{w+8}{\boxed{L=48}}[/tex]
NO LINKS!! URGENT HELP PLEASE!!!
1. What rectangle dimensions give the greatest possible area? Explain. (From the rectangle with a perimeter of 20 meters)
2. Suppose the dimensions were not restricted to whole numbers. Would this change your answer? Explain. (same as # 1)
Problem 1
L = length
W = width
P = perimeter of the rectangle
P = 2L+2W
P = 20
2L+2W = 20
L+W = 10 after dividing everything by 2.
L = 10-W
area = length*width
A = L*W
A = (10-W)*W
A = -W^2 + 10W
Let x replace W for a temporary basis.
If we graphed y = -x^2+10x, then we'd see the highest point occurs at (5, 25). This means a width of 5 meters leads to the largest area of 25 square meters.
The length would be L = 10-W = 10-5 = 5 meters as well.
It turns out that a 5 meter by 5 meter square is the best choice when trying to max out this rectangle's area.
====================================================
Problem 2
The results we got from the previous section was that a 5 by 5 square will max out the area.
If we allowed non-whole numbers into the mix, then it wouldn't change the previous answer. The best choice is still that 5 by 5 square.
The answer only would change if the result of the previous section was some non-integer value.
A test to determine whether a certain antibody is present is 99.5% effective. This means that the test will accurately come back negative if the antibody is not present (in the testsubject) 99.5% of the time. The probability of a test coming back positive when the antibody is not present (a false positive) is 0.005. Suppose the test is given to five randomly selected people who do not have the antibody.
(a) What is the probability that the test comes back negative for all five people?
(b) What is the probability that the test comes back positive for at least one of the five people?
The probability that the test is negative for all people is: P = 0.9655 and probability that the test comes back positive for at least one of the five people is P = 0.0344.
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. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.
The probability that the test is negative for all people is:
[tex]P = (0.995)^7[/tex]
P = 0.9655
b. The probability that the test comes back positive for at least one of the five people:
P = 1 - P (Negative for all 5)
P = 1 - 0.9655
P = 0.0344
Hence, the probability that the test is negative for all people is: P = 0.9655 and probability that the test comes back positive for at least one of the five people is P = 0.0344.
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Estimate : 0.93 x 2.6
After that:
Estimate: 93 x 0.26
After That :
Estimate: 9.3 x 26
After That
Estimate: 0.93 x 0.26
The value of the equations are
A = 0.93 x 2.6 = 2.418
B = 93 x 0.26 = 24.18
C = 9.3 x 26 = 241.8
D = 0.93 x 0.26 = 0.2418
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
a)
A = 0.93 x 2.6 be equation (1)
On simplifying the equation , we get
A = 2.418
b)
B = 93 x 0.26 be equation (2)
On simplifying the equation , we get
B = 24.18
c)
C = 9.3 x 26 be equation (3)
On simplifying the equation , we get
C = 241.8
d)
D = 0.93 x 0.26 be equation (4)
On simplifying the equation , we get
D = 0.2418
Hence , the equations are solved
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please help immediately what is the input if the output is 7
The side length of a square with area of 7 units squared is given as follows:
2.65 units.
How to obtain the area of a square?The area of a square of side length s is given by the side length squared, according to the equation given as follows:
A = s².
In this problem, we have that the output is of 7, that is, the area of the square is of seven, hence the side length of the square is given as follows:
s² = 7
s = sqrt(7)
s = 2.65 units.
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Composition fuction
I need to compute the following
#3 g(f(0))
#4 f(f(2))
Given that f(x)= 2x-1 g(x)=3x and h(x)=x^2+1
Pic is attached below
The values of the composite functions are g(f(0))= -3 and f(f(2)) = 5
How to evaluate the composite functionsFrom the question, we have the following parameters that can be used in our computation:
f(x)= 2x-1 g(x)=3x and h(x)=x^2+1
To calculate g(f(0)), we have
f(0)= 2(0)-1 = -1
This means that
g(f(0)) = g(-1)
So, we have
g(f(0)) = 3(-1) = 3
For f(f(2)), we have
f(2)= 2(2)-1 = 3
So, we have
f(f(2)) = 2(3) - 1 = 5
Hence, the composite functions are g(f(0))= -3 and f(f(2)) = 5
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when you have an exponent outside of parenthesis, do you do the parenthesis first?
Answer: Yes.
Step-by-step explanation: Follow PEMDAS.
P: PARENTHESIS
E: EXPONENTS
M: MULTIPLY
D: DIVIDE
A: ADDITION
S: SUBTRACT
we consider a triangle CDE such that : CD = 3,6cm ; CE = 4,2cm and DE = 5,5
Is the triangle CDE rectangular?
The given triangle CDE is not Rectangular.
What are types of triangles ?
Acute triangle . . . all three angles are less than 90°
Right triangle . . . one angle is 90°
Obtuse triangle . . . one angle is greater than 90°
Equilateral triangle . . . all three sides are the same length
Isosceles triangle . . . two sides are the same length
Scalene triangle . . . all three sides are different lengths
Given:
CD = 36cm ; CE = 42cm and DE = 55
Hence , the given triangle CDE is not Rectangular.
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Terrance buys 6 bottles of sports drink. He has coupons for $0.55 off the regular price of each bottle. After using the coupons, the total cost of the sports drinks is $4.44. Which equation can be used to find the regular price p of a bottle of sports drink?
Answer:
(4.44 + 0.55n) / n = p
(4.44 + 0.55 * 6) / 6 = p
(4.44 + 3.3) / 6 = p
(7.74) / 6 = p
1.29 = p
or
4.44 / 6 + 0.55 = p
Step-by-step explanation:
n = number of bottles
p = 1.29
A square placemat has an area of 169 in.² Sally decides to decorate the placemat by putting fringe around the edges how many inches of fringe will Sally need to buy how many feet is this
Answer:
4 feet and 4 inches of fringe
Step-by-step explanation:
The length and width of a square are equal to each other
Let x = length of a side of a square
Area of a square = Length × Width
= (x inches) × (x inches)
= [tex]x^{2}[/tex] [tex]in^{2}[/tex]
The area of the square placemat = 169 [tex]in^{2}[/tex]
∴ [tex]x^{2} in^{2}[/tex] = 169 [tex]in^{2}[/tex]
Taking the square root on both sides of the equation to get rid of the square:
x inches = [tex]\sqrt{169}[/tex] inches
x inches = [tex]\sqrt{169}[/tex] inches
([tex]\sqrt{169} =[/tex] ± 13. However, the negative value will be rejected since the length of a side CANNOT be negative)
So, x = 13 inches
This means the perimeter of the square = (13 + 13 + 13 + 13) inches
= 52 inches
∴ 52 inches of fringe will be needed by Sally
Unit conversion:
I foot = 12 inches
∴ y feet = 52 inches
Cross-multiplication is applied:
(y feet)(12 inches) = (52 inches)(1 foot)
Isolating y and making it the subject of the formula:
y feet = [tex]\frac{(52 inches)(1 foot)}{12 inches}[/tex]
Inches in the numerator and denominator will cancel each other out completely:
y feet = [tex]\frac{52}{12}[/tex] feet
Applying long division:
The highest quotient to be multiplied by 12 to give a number, which is closest to 52 but still less than 52. 12×4 = 48. Therefore, the quotient is 4 and the remainder is 4.
∴ 52 inches = 4 feet and 4 inches
Write an equation for the nth term of each arithmetic sequence. Then find the 12th term of the sequence.
as = -9, d = 2
Answer:
Step-by-step explanation:The equation for the nth term of an arithmetic sequence is given by:
an = a1 + (n-1)d
Where:
a1 is the first term of the sequence
d is the common difference
n is the number of the term we want to find
Using the given information, we have:
a1 = -9 and d = 2
Plugging these values into the formula, we get:
an = -9 + (n-1)2
To find the 12th term of the sequence:
n = 12
an = -9 + (12-1)2
an = -9 + 11 * 2
an = -9 + 22
an = 13
So the 12th term of the sequence is 13.
In AABC, the angle bisector of ZB also bisects AC. Classify AABC as
specifically
as possible.
Answer:
∆ABC is an isosceles triangle
Step-by-step explanation:
You have a triangle ABC such that the angle bisector of angle B also bisects side AC.
Angle bisectorAn angle bisector divides the sides of the triangle proportionally. This means the sides BA and BC will have the same ratio as the segments of AC on either side of the point of intersection with the angle bisector.
Since AC is bisected, that means those segments are congruent, hence sides BA and BC are congruent. The triangle is isosceles.
The movement of the progress bar may be uneven because questions.co be worth more or less (inc
Choose the fraction pair that is equivalent.
O and
4 and 20
and
and/
The fraction pairs that are equivalent to 4 and 20 is given as follows:
2 and 10 = 2/10.1 and 5 = 1/5.What are equivalent fractions?Equivalent fractions are fractions that have the same denominator.
The fraction for this problem is given as follows:
4/20.
Dividing both the numerator and the denominator by 2, an equivalent fraction is given as follows:
2/10.
Dividing again by two, we have that:
1/5.
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Elisa needs money to repair her home air conditioner, so she pawns her bicycle. The pawnbroker loans Elisa $270. Twenty four days later, Elisa gets her bicycle back by paying the pawnbroker $313.20. What annual simple interest rate did the pawnbroker charge Elisa? Assume 360 days in a year. Round simple interest rate to the nearest whole number as needed.
Elisa was charged a basic interest rate of 120% per year by the pawnbroker since she needed the money to fix her house air conditioner.
what is interest ?By dividing the initial by the interest income, the aging process, and other factors, simple interest is determined. Simple yield equals principal plus interest full days is the concept used in marketing. The easiest thing to compute interest is to employ this method. The most frequent method for calculating it is as a portion of the outstanding sum. For example, if he takes $100 from a buddy and undertakes to return the loan at 5% interest, he will only spend his share of the 100% interest. $100 (0.05) = $5. When you borrow money, you must make payments, and you must pay the interest whenever you lend it. Typically, interest is computed as an indicator of the overall of the loan total. The loan's interest is the name given to this percentage.
given
I = PRT/100
Simple interest (I) is calculated as follows: amount - principal ($279.90 - $270) = $9.90
P (principal) is the $270 loan made to Elisa.
R is the interest rate on a yearly basis.
The loan's amortisation period, or T (time), is 11 days, or 11/360 years.
9.9 = 270 × R × 11/360 × 1/100
R = (9.9×360×100)/(270×11) = 120%
120% is the annual simple interest rate.
Elisa was charged a basic interest rate of 120% per year by the pawnbroker since she needed the money to fix her house air conditioner.
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Given the equation 6.78w = 16.611, solve for w.
2.45
9.831
23.391
112.62
Select the correct answer.
Which inequality is equivalent to the given inequality?
-4(x + 7) < 3(z - 2)
OA. -7z<-34
OB. -7z > -34
OC. -7> 22
OD. -7z < 22
-22 < 7x is the inequality that is equivalent to the given inequality.
What is inequality?
An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations, including:
The symbol a < b indicates that an is smaller than b.
When a > b is used, it indicates that an is bigger than b.
Here, we have
Given: -4(x + 7) < 3(x - 2)
To find out which inequality is equivalent, you solve for x.
-4(x+7) < 3(x-2): distribute variables
-4x-28 < 3x-6: Add 6 to both sided
-4x-22 < 3x: add 4x to both sides
-22 < 7x
Hence, -22 < 7x is the inequality that is equivalent to the given inequality.
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Use the logical equivalences p → q ≡ ~p∨ q and p ↔ q ≡ (~p∨ q) ∧ (~ q∨ p) to rewrite the given statement forms without using the symbol → or ↔.
a) (p → r) ↔ (q → r)
The logical equivalence for the given statement is (p → r) ↔ (q → r)≡ (~p∨r)∧(~q∨r).
What is the logical equivalence?Logical equivalence is the condition of equality that exists between two statements or sentences in propositional logic or Boolean algebra.
Given that, p → q ≡ ~p∨q and p ↔ q ≡ (~p∨q)∧(~q∨ p)
a) (p → r) ↔ (q → r)
Now, (p → r)≡ ~p∨r
(q → r)= ~q∨r
So, (p → r) ↔ (q → r)≡ (~p∨r)∧(~q∨r)
Therefore, the logical equivalence for the given statement is (p → r) ↔ (q → r)≡ (~p∨r)∧(~q∨r).
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Someone to help me hereeeee
Answer: 485 is the answer.
Step-by-step explanation:
Solve for the value of w.
(4w-8)°
(3w+6)°
Answer: To find the value of w, we need to set the expressions equal to each other:
(4w-8) = (3w+6)
Subtracting 3w from both sides:
w - 8 = 6
Adding 8 to both sides:
w = 14
So the value of w is 14.
Step-by-step explanation:
3. Mr. Jackson could think about his experiment a little differently. How many times should he expect to roll a 4 if he rolls his number cube 30 times? This is called the mean, or expected value. You can find it if you know the number of trials and the probability of success for an individual trial. Use the formula μx = np to find the expected value.
The sample size based on the information is 30.
The probability is 0.1667.
How to calculate the valueFrom the information, Mr. Jackson could think about his experiment a little differently. How many times should he expect to roll a 4 if he rolls his number cube 30 times? This is called the mean, or expected value.
The Sample size , n = 30. The Probability of an event of interest, p = 0.1667
The Mean will be:
= np = 30 * 0.167
= 5.000
Standard deviation will be:
= √(np(1-p)) = √ 4.1667
= 2.04
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At a school play, there is a spotlight above the center of
the floor that covers a lighted area with a radius of 7 feet.
What is the area covered by the spotlight?
Area = 3.14*r²
According to the question we have ,The area covered by the spotlight is 153.86 square feet. The correct option is c.
What are diameter and radius?The diameter of a circle cuts through center whereas the radius extends from the center to the edges of the circle. A circle's diameter effectively splits the shape in half. The radius of a circle is the distance from the middle to any point on the edge. The diameter the radius are inversely proportional, or 2r=d2 r=d. A line connecting two points on either a circle is referred to as a chord.
We have the formula of Area of a circle: A = π[tex]r^2.[/tex]
According to the question we have ,there is a spotlight above the center of the ground that surrounds a 7-foot-radius lit area.
A = π[tex]r^2[/tex]. = π * [tex]7^2[/tex]
= 3.14 * 49 = 153.86 square feet.
So, the area covered by the spotlight is 153.86 square feet.
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2. The first and third term of a Gip are 5 and 80 respectively. What is the term
The fifth term of the geometric progression is given as 1280
The nth term of a geometric progressionThe formula for calculating the nth term of a geometric progression is expressed as:
Tn = ar^n-1
Given the following
First term = a = 5
Third term = ar^2 = 80
Determine the common ratio
5(r^2) = 80
r^2 = 16
r = 4
For the 5th term
T5 = ar^4
T5 = 5(4)^4
T5 = 1280
Hence the fifth term of the expression is 1280
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Complete question
The first and third term of a Gip are 5 and 80 respectively. What is the fifth term
6.6 Midpoints and Bisectors
(6.6.4 Apply the concept of midpoint to solve real-life problems)
55. SCAVENGER HUNT Pablo is going to ask
Bianca to prom by sending her on a scavenger hunt. At the end of the scavenger hunt, Pablo will be standing halfway between the gazebo and the ice cream shop in town. Where should
Pablo stand?
The coordinates of the position at which Pablo should stand are given as follows:
(6, 7.5).
What is the midpoint concept?The midpoint between two points is the halfway point between them, and is found using the mean of the coordinates.
Hence the x-coordinate of the position at which Pablo should stand is given as follows:
x = (2 + 10)/2
x = 6.
The y-coordinate of the position at which Pablo should stand is given as follows:
y = (3 + 12)/2
y = 7.5.
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Solve the following compound inequality for x
and express your answer in interval notation.
Assume x is an element of the real number system.
11 < 3x-2 ≤ 19
x is a component of the real number system 11 < 3x-2 ≤ 19, although as a compound inequality, it also belongs to 13/3 and 7.
what is inequality ?A interaction between two terms or concepts that is neither equal in mathematics is referred to as an inequality. Consequently, inequity results from imbalance. In algebra, an inequality establishes the connection between two non-equal numbers. Egality and inequalities are not the same. Use the not comparable symbol most usually when two components are really not equal (). Values of any size can be contrasted using a variety of inequalities. By changing the two aspects until only the variables are left, many straightforward inequalities can be solved. But, a variety of factors support inequality: Both sides' 0 are split or added. Exchange the left and the right.
given
11 < 3x-2 ≤ 19
11< 3x-2
3x-2 ≤ 19
11+ 2 < (3x-2)+ 2
(3x-2)+ 2 ≤ 19 + 2
x belongs to 13/3 and 7
x is a component of the real number system 11 < 3x-2 ≤ 19, although as a compound inequality, it also belongs to 13/3 and 7.
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Kelsey’s neighborhood has a straight road with stop signs at both ends and a fire hydrant at its midpoint. On a map, the fire hydrant is located at (12,7) and one of the stop signs is located at (3,11). Where on the map is the other stop sign located?
Answer: (21, 3)
Step-by-step explanation:
According to a recent survey, the probability that the driver in a fatal vehicle accident is female (event F) is 0.2058. The probability that the driver is 24 years old or less (event A) is 0.1887. The probability that the driver is female and is 24 years old or less is 0.0582. Answer parts (a) through (d) below.
Question content area bottom
(b) Find the probability of F′∪A.
The probability of F′∪A 0.9829
How to solve for the probability
The probability can be defined as the likelihood that an event is going to happen.
We are to find the probability F′∪A.
What is F'
This is gotten as 1 - probability of F
F' = 1 - 0.2058
F' = 0.7942
Then we are to get the probability of event A from the question
P(A) = 0.1887
Hence the probability of F′∪A.
= P(A) + P(F`)
= 0.1887 + 0.7942
= 0.9829
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If $300 is invested for 3 years with an interest rate of 6%
per annum, calculate the final balance, rounded to the
nearest cent, if:
Simple interest was used
The required final balance on interest rate of 6%per annul is $354.
What is interest?The fee you pay to borrow money or the fee you charge to lend money is called interest. The most common way to represent interest is as a yearly percentage of the loan amount. The interest rate on the loan is known as this percentage.
According to question:Simple interest is calculated as:
I = P * r * t
where I is the interest, P is the principal (initial investment), r is the annual interest rate as a decimal, and t is the number of years.
So, in this case:
I = 300 * 0.06 * 3
I = 300 * 0.06 * 3 = 54
The final balance would be the sum of the initial investment and the interest earned:
Final balance = P + I
Final balance = 300 + 54
Final balance = 300 + 54 = 354
Rounded to the nearest cent, the final balance is $354.
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The great pyramids of Giza are a set of ancient Egyptian structures large enough to be visible from space. Can you prove the front faces of the two pyramids are congruent triangles? Why or why not?
It cannot be proven that the front faces are congruent triangles.
Can you prove the front faces of the two pyramids are congruent triangles?No, I cannot prove that the front faces of the two pyramids of Giza are congruent triangles. The exact dimensions and shapes of the pyramids have been lost to history, and the information we have today is based on estimates and interpretations of archaeological evidence.
The exact shape of the pyramids is still the subject of some debate among experts, and there is no consensus on whether the front faces are congruent triangles.
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