Answer:
P(A)= 21/36
P(B)=1/2
Step-by-step explanation:
Given:
An ordinary Fair die is a cube with the numbers 1 through 6 on the sides represented by painted spots imagine that such a die is rolled twice
So the sample space of rolling two dices is:
(1,1) (2,1) (3,1) (4,1) (5,1) (6,1)
(1,2) (2,2) (3,2) (4,2) (5,2) (6,2)
(1,3) (2,3) (3,3) (4,3) (5,3) (6,3)
(1,4) (2,4) (3,4) (4,4) (5,4) (6,4)
(1,5) (2,5) (3,5) (4,5) (5,5) (6,5)
(1,6) (2,6) (3,6) (4,6) (5,6) (6,6)
Total number of sets=36
1)Now Finding probability of
Event A: The sum is greater than 6
From the above sample space sets that have the sum >6 are
(6,1)
(5,2) (6,2)
(4,3) (5,3) (6,3)
(3,4) (4,4) (5,4) (6,4)
(2,5) (3,5) (4,5) (5,5) (6,5)
(1,6) (2,6) (3,6) (4,6) (5,6) (6,6)
there are 21 sets
hence probability of Event A= 21/36
P(A)= 21/36
2) Now Finding probability of
Event B: The sum is an odd number
From the above sample space sets that have the sum an odd number are
(2,1)(4,1) (6,1)
(1,2)(3,2) (5,2)
(2,3) (4,3)(6,3)
(1,4) (3,4) (5,4)
(2,5) (4,5) (6,5)
(1,6) (3,6) (5,6)
there are 18 sets
hence the probability of Event B = 18/36
P(B)= 1/2 !
what is the answer to: 2/3(n-6)=5n-43
Answer:
n = 9Step-by-step explanation:
[tex]\dfrac{2}{3}(n-6)=5n-43\qquad\text{multiply both sides by 3}\\\\2(n-6)=15n-129\qquad\text{use the distributive property}\\\\2n-12=15n-129\qquad\text{add 12 to both sides}\\\\2n=15n-117\qquad\text{subtract}\ 15n\ \text{from both sides}\\\\-13n=-117\qquad\text{divide both sides by (-13)}\\\\n=9[/tex]
The equation 2/3(n-6) = 5n - 43 is solved by distributing, combining like terms, and isolating the variable n to find that n = 9.
To solve the equation 2/3(n-6) = 5n - 43, first distribute the 2/3 across the parentheses: 2/3n - 2/3 6 = 5n - 43. This simplifies to 2/3n - 4 = 5n - 43. Next, add 4 to both sides to get 2/3n = 5n - 39. Multiply everything by 3 to clear the fraction: 2n = 15n - 117. Now, we will subtract 15n from both sides to get -13n = -117. Finally, divide by -13 to find n: n = 9. This is the value of n that solves the original equation.
A painting includes a frame of a fixed width around the painting. The total area of the painting is represented by the expression (4+2x)(9+2x) . What does the (9+2x) represent?
the length of the painting, including the frame
the area of the painting only
the length of the frame
the length of the painting
Answer:
The length of the painting, including the frame.
Step-by-step explanation:
We are given that a painting includes a frame of a fixed width around the painting and the total area of the painting is represented by the expression:
[tex](4+2x)(9+2x)[/tex]
We are to determine what does [tex](9+2x)[/tex] represent.
(9+2x) represents the length of the painting, including the frame because [tex](4+2x)(9+2x)[/tex] is the area of the painting including the frame. The longer side [tex](9+2x)[/tex] represents the length.
Find the quotient. Which expression is the result of dividing?
Answer:
its B
Step-by-step explanation:
A dealership purchased a four-door sedan for $19,000 and then sold it at 15%
markup. The dealership paid the buyer $5000 for a trade-in, which was sold
the following week at 25% markup. What was the dealership's profit on these
two vehicles?
Answer:
$4,100
Step-by-step explanation:
Final answer:
The dealership's profit from selling the two vehicles, after considering a 15% markup on the four-door sedan and a 25% markup on the trade-in vehicle, was $4,100.
Explanation:
To calculate the dealership's profit on the two vehicles, we need to consider the markup on each transaction.
Profit from the Four-Door Sedan
The dealership purchased the sedan for $19,000 and sold it at a 15% markup. The markup is calculated as 15% of the purchase price:
Markup on sedan = 0.15 times $19,000 = $2,850
The selling price of the sedan would thus be:
Sell price of sedan = Purchase price + Markup = $19,000 + $2,850 = $21,850
Profit from the Trade-In Vehicle
After trading in the first car and effectively reducing its cost by $5,000, the dealership then sells the trade-in at a 25% markup. First, we calculate the trade-in's sale price:
Trade-in value = $5,000
Markup on trade-in = 0.25 times $5,000 = $1,250
Sell price of trade-in = Trade-in value + Markup = $5,000 + $1,250 = $6,250
Total Profit
The total profit is the sum of profits from both vehicles:
Total profit = Markup on sedan + Markup on trade-in = $2,850 + $1,250 = $4,100
Therefore, the dealership's profit on these two vehicles was $4,100.
Need Help Fast Please!!! :)
Answer:
a: C = $4.70d, (d ≤ 5, C = $4.70d - $1 ?: d ≥ 5, C = $4.70d)
b.(1) dvd returned after 4 days = ($4.70 × 4) - $1 ⇒ $18.8 -$1 ⇒ $17.8
(2) dvd returned after 7 days = $4.70 × 7 ⇒ $32.9
Which equation represents a circle at (-3,-5) and radius of 6 units
Answer:
The equation of the circle is (x + 3)² + (y + 5)² = 36
Step-by-step explanation:
* Lets revise the standard form of the equation of the circle
- The center-radius form of the circle equation is in the format
(x – h)² + (y – k)² = r², where the center is the point (h, k) and
the radius is r.
- This form of the equation is helpful, because you can easily find
the center and the radius.
* Now lets solve the problem
∵ The center of the circle is (-3 , -5)
∵ The center of the circle in the equation is (h , k)
∴ h = -3
∴ k = -5
∴ The equation of the circle is (x - -3)² + (y - -5)² = r²
∴ The equation is (x + 3)² + (y + 5)² = r²
* Now lets find the value of r²
∵ The length of the radius of the circle is 6 units
∴ r = 6
∴ r² = (6)² = 36
∴ The equation of the circle is (x + 3)² + (y + 5)² = 36
4. Find area of irregular shape
5. Find area of BLUE portion of shape
Answer:
4. Option 3: 65.1 cm^2
5. Option 3: 3.4 inches^2
Step-by-step explanation:
Question 4 :
We can see that there is a rectangle and a half circle in the picture.
So we will find the area of both separately
For the area of rectangle
Area=length*width
=8*5
=40 cm^2
We know that the line which is representing the diameter has length 8 cm
To find the radius
r=d/2
=8/2
=4 cm
As we cannot find the area of half circle, we will find the area of full circle and will divide it in half.
So,
area= πr^2
=3.14*(4)
=3.14*16
=50.24 cm^2
Area of half circle=(Area of full circle)/2
=50.24/2
=25.12 cm^2
So the area of shape will be
Area of rectangle+area of half circle
=40 cm^2+25.12 cm^2
=65.12 cm^2
Rounding off to nearest 10 will give 65.1 cm^2
So, option 3 is the correct answer ..
Question 5 :
To find the area of shaded region we have to find the area of circle and area of square in which it is inscribed
So,
area of circle= πr^2
=3.14*(2)^2
=3.14*4
=12.56 inches^2
And to find the area of square we need one of its side, we can clearly see that the diameter of circle will be equal to the side of square
So,
Side of square=s=r*2
=2*2
=4 inches
Area of square=s^2
=4^2
=16 inches^2
To find the area of shaded region we have to subtract the area of circle from the area of square
So,
Area of Shaded Region=Area of Square-Area of Circle
=16-12.56
=3.44 inches^2
Rounding off to the nearest 10 will give 3.4 inches^2 ..
So, option 3 is the correct answer ..
Please help me with this question thanks
Answer:
x = 40.375Step-by-step explanation:
ΔYVH and ΔYBA are similar. Therefore the corresponding sides are in proportion:
[tex]\dfrac{YH}{YA}=\dfrac{YV}{YB}[/tex]
We have
[tex]YH=x,\ YA=17,\ YV=16+22=38,\ YB=16[/tex]
Substitute:
[tex]\dfrac{x}{17}=\dfrac{38}{16}[/tex] cross multiply
[tex]16x=(17)(38)[/tex] divdie both sides by 16
[tex]x=\dfrac{(17)(38)}{16}\\\\x=40.375[/tex]
Which employee's path is the critical path on this activity graph? Explain how you know that this employee's path is the critical path.
Answer:
Jim's path is the critical path on this activity graph.
Step-by-step explanation:
Critical Path:
Critical path is the the longest path in the project task paths. It shows the least amount of time in which project can be completed. It can be find by looking at the longest path in the network diagram of the project; not in term of nodes or activities instead in term of days.
In given case:
Path 1 Bill task's total duration= 6 days
Path 2 Jim's task's total duration= 17 days
Path 3 Betty task's total duration= 7 days
Path 4 Cynthia task's total duration= 14 days
Hence the longest path i.e. critical path is of Jim's activity path !
What is the slope of the line through the points (–3, 5) and (4, 5)?
The slope here is 0.
Answer:
slope = 0
Step-by-step explanation:
Calculate the slope m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 3, 5) and (x₂, y₂ ) = (4, 5)
m = [tex]\frac{5-5}{4+3}[/tex] = [tex]\frac{0}{7}[/tex] = 0
identify any outliers in the table. and describe the association between the altitude and the temperature using the table above.
Answer:
-68 could be a potential outlier, but other than that, the data seems pretty steady.
The association between the altitude and the temperature is the higher up in the atmosphere you are, the colder it gets.
What is the solution to the equation 3x + 2(x − 9) = 8x + x − 14?
−8
−1
1
8
Answer:
Step-by-step explanation:
3x+2(x-9)=8x+x-14
3x+2-9x=8x+x-14
add3xand-9x
-6x+2=8X+x-14
8X +X=9X
-6X+2=9X-14
+6X to both sides
2=3x-14
subtract 2 on both sides
3x/-12
the answer is -8
Answer:
The actual answer is 1!
Step-by-step explanation
A 2-pound bag of broccoli costs $2.88. What is the price per ounce
Answer:
$0.09
Step-by-step explanation:
1 pound = 16 ounces
So 2 pounds = 32 ounces
Write a proportion:
$2.88 / 32 oz = x / 1 oz
Solve:
x = $0.09
The price per ounce is $0.09.
Final answer:
To find the price per ounce of a 2-pound broccoli bag costing $2.88, divide the total price by the number of ounces (32), resulting in a price per ounce of $0.09.
Explanation:
To calculate the price per ounce of a 2-pound bag of broccoli that costs $2.88, you first need to know the total number of ounces in the bag. Since there are 16 ounces in 1 pound, a 2-pound bag contains 32 ounces (16 ounces/pound x 2 pounds). To find the price per ounce, you divide the total price of the bag by the total number of ounces.
Price per ounce calculation:
Total price of the bag = $2.88
Total ounces in the bag = 32 ounces
Price per ounce = Total price of the bag / Total ounces in the bag
Price per ounce = $2.88 / 32 ounces
Therefore, the price per ounce is $0.09.
Write the following as a complex number in the form a + bi square root -245
Answer:
Step-by-step explanation:
√(-245)=√(49×5×i^2)=7√5 i=0+7√5 i
Answer:
[tex]\sqrt{-245}[/tex] in the form a + bi is [tex]0+7\sqrt{5}i[/tex]
Step-by-step explanation:
We know that
[tex]i=\sqrt{-1}[/tex]
We need to find [tex]\sqrt{-245}[/tex]
[tex]\sqrt{-245}=\sqrt{-1}\times \sqrt{245}=i\sqrt{245}=i\sqrt{49\times 5}=i\times 7\sqrt{5}[/tex]
[tex]\sqrt{-245}[/tex] in the form a + bi is [tex]0+7\sqrt{5}i[/tex]
Jennifer has $26 less than triple the savings of Matthew. Matthew has saved $81. How much has Jennifer Saved?
To find out how much Jennifer has saved, you start by tripling the amount Matthew has saved, which is $81. Then you subtract $26 from the result to get $217. Therefore, Jennifer has saved $217.
Explanation:From the problems statement, we can model Jennifer's savings using the mathematical model, where Jennifer's savings is equal to triple Matthew's savings minus $26. Given that Matthew’s savings amount to $81, we can multiply Matthew's savings by three, which equals $243. Then, to find Jennifer's savings, we subtract $26 from $243 resulting in $217. Therefore, Jennifer has $217 saved.
Learn more about Algebraic problemhttps://brainly.com/question/33031196
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Finish this simile. Use your imagination to complete the description.
She is as mean as . . .
She is as mean as my cat.
This is a simile that makes sense because the ferocity of “she” is compared to the ferocity of my cat, which is unmatched.
What is the equation of a circle with center (-3,-5) and radius 4?
A. (x+3)2 + (y + 5)2 = 4
B. (x-3)2 + (y- 5)2 = 4
C. (x-3)2 + (y-5)2 = 16
D. (x+3)2 + (y + 5)2 = 16
Answer:
D ans
Step-by-step explanation:
equation of circle=(x-h)^2+(y-k)^2=r^2
Answer:
(x+3)2 + (y + 5)2 = 16
Step-by-step explanation:
A savings account pays an annual rate of 2% simple interest. How much would you need to deposit to earn $100 interest by the end of the 2nd year?
Answer:
You would need to deposit $2500
Step-by-step explanation:
The simple Interest formula is given as;
[tex]I=\frac{P*R*T}{100}[/tex]
Where I is the interest earned, P the principal amount deposited, R the simple interest rate and T the time.
The question requires us to determine the Principal given that;
I = 100
R = 2
T = 2
We make the Principal the subject of the formula;
[tex]P=\frac{100*I}{R*T}\\\\P=\frac{100*100}{2*2}=2500[/tex]
How to change proper fractions to improper fraction
Step-by-step explanation:
You already know that proper fractions have numerators smaller than the denominators, such as 1/2, 2/10 or 3/4, making them equal less than 1. The improper fraction has a numerator larger than the denominator. And mixed numbers have a whole number sitting next to a proper fraction -- for example, 4 3/6 or 1 1/2. As you work on converting improper fractions, you’ll find yourself using your knowledge of division.
Write down the improper fraction -- for example, 27/6. The fraction bar means you need to divide 27 by 6.
Divide 27 by 6. The answer is 4, with a remainder of 3. Use the answer as the whole number part of the mixed number, and place the remainder over the original denominator: 4 3/6.
Reduce the fraction, if necessary. For example, 3/6 equals 1/2 (the lowest common denominator of 3 and 6 is 3, so divide both the numerator and the denominator by 3 to reduce the fraction to 1/2).
If it is a mixed number fraction: 1 1/2
1. multiple the whole number and the denominator 2 x 1 = 2
2. Add that to the numerator 2+1= 3
*Denominator stays the same
3. example answer is... 3/2
******* only mixed numbers can be converted into improper fractions
Write the equation in slope-intercept form (y=mx+b) that contains the following point with the given slope. Slope = 2 ; (-3, 1) Hint: Use point-slope form first. Then, solve that equation for y.
Answer:
y = 2x + 7
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = 2, so
y = 2x + c ← is the partial equation
To find c substitute (- 3, 1) into the partial equation
1 = - 6 + c ⇒ c = 1 + 6 = 7
y = 2x + 7 ← equation in slope- intercept form
here,
given point is (-3,2) and slope(m) is 2
so y=mx + b
or 2=2×(-3) +b
or b=8
the equation is
y=mx+b
or y=2x+8
or2x-y+8=0
can someone help with this
Answer:
∠6 = 80°
Step-by-step explanation:
∠5 and ∠6 form a straight angle and are supplementary, hence
∠5 + ∠6 = 180 ← ∠5 = 100° ( given ), hence
100 + ∠6 = 180 ( subtract 100 from both sides )
∠6 = 80°
Consider the functions f(x)=3x2 and g(x)=-2x-5. What is the value of f[g(-4)]?
Answer: C: 27 just took the test..
Step-by-step explanation:
What is the best estimate of the mass of a butterfly
"Dr. Paul Opler states, "I have some information on butterfly weights but not exact weights for the largest and smallest butterflies. However, I can make pretty good guesses. I have weights ranging from 0.3 gram for a large swallowtail to 0.04 gram for a small butterfly called the elf."
from the intern3t
Answer:
It would most likely 0.02 - 0.03 because if u think about it there wings don't weight more than about 0.1 and if the wings can hold up the body of the butterfly then i would assume that it would weight between 0.02 - 0.03.
Step-by-step explanation:
Factories these 2 plz!!
Answer:
a) 3x(x+4y-3y^2)
b) 3x(3x -y + 5y^3)
Step-by-step explanation:
a) 3x^2+12xy-9xy^2
We need to factorize the above equation.
We can take 3x common from the above equation.
3x(x+4y-3y^2)
It cannot be further factorized. So the factors are:
3x(x+4y-3y^2)
b) 9x^2 - 3xy +15xy^3
We need to factorize this equation.
Since 3x is common in all terms, taking 3x common
3x(3x -y + 5y^3)
It cannot be further factorized. So the factors are:
3x(3x -y + 5y^3)
Help me pleaseeeeeee
The area of the complete circle is PI x 11^2 = 379.94 cm^2
The shaded part is 30 degrees out of 360 degrees
The shaded area = 379.94 x 30/360 = 31.66 = 31.7 cm^2.
The answer is B.
How to find compound interest rate
Answer:
Step-by-step explanation
I don't know if you are asking for a formula but Compound interest is calculated by multiplying the initial principal amount by one plus the annual interest rate raised to the number of compound periods minus one. The total initial amount of the loan is then subtracted from the resulting value.
What are the center and radius of the circle with equation (x-7)^2 + (y+5)^2 = 36?
Answer:
Center (7, -5) and radius=6
Step-by-step explanation:
The question is on center and radius of a circle
The general circle equation is given as (x-h)² + (y-k)²= r² where the center is (h,k) and radius is r
Given (x-7)^2 + (y+5)^2 = 36?
(x-7)² + (y+5)²= 6²
h=7 and y=-5 and r=6
ANSWER
Center:(7,-5)
Radius:r=6
EXPLANATION
The given circle has equation;
[tex] {(x - 7)}^{2} + {(y + 5)}^{2} = 36[/tex]
We can rewrite this as:
[tex]{(x - 7)}^{2} + {(y - - 5)}^{2} = {6}^{2} [/tex]
Comparing this to the standard equation of the circle:
[tex]{(x - h)}^{2} + {(y - k)}^{2} = {r}^{2} [/tex]
we have h=7,k=-5, and r=6.
Therefore the center (h,k)=(7,-5) and the radius is r=6.
The Width Of A Rectangle is The Sum Of The length and 3. The Area Of The Rectangle Is A 54 units. What is the length, in units of the rectangle?
The length of the rectangle is 6 units.
4. Find the lateral area and surface area of the given prism.
11.Find the volume of the square pyramid.
Answer:
Q4. S.A. = 752.28 m²Q11. V = 384 ft³Step-by-step explanation:
[tex]\bold{Q4}\\\text{We have}\\\text{two right triangles with legs a = 4m and b = 7m}\\\text{three rectangles}\ 7m\ \times 38m,\ 8.06m\ \times\ 38m\ \text{and}\ 4m\ \times\ 38m\\\\\text{The formula of an area of a right triangle:}\\\\A=\dfrac{ab}{2}\\\\\text{substitute:}\\\\A_1=\dfrac{(4)(7)}{2}=\dfrac{28}{2}=14\ m^2\\\\\text{The formula of an area of a rectangle}\ l\ \times w:\\\\A=lw\\\\\text{substitute:}\\\\A_2=(7)(38)=266\ m^2\\A_3=(8.06)(38)=306.28\ m^2\\A_4=(4)(38)=152\ m^2\\\\\text{The Surface Area:}[/tex]
[tex]S.A.=2A_1+A_2+A_3+A_4\\\\S.A.=2(14)+266+306.28+152=752.28\ m^2[/tex]
[tex]\bold{Q11}\\(look\ at\ the\ picture)\\\\\text{The formula of a volume of a pyramid:}\\\\V=\dfrac{1}{3}BH\\\\B-\text{area of a base}\\H-\text{height}\\\\\text{In the base we have the square. The formula of an area of a square with side a:}\\\\A=a^2\\\\\text{We have}\ a=12ft.\ \text{Substitute:}\\\\B=12^2=144\ ft^2\\\\\text{For}\ H\ \text{we need use the Pythagorean theorem:}\\\\H^2+6^2=10^2\\\\H^2+36=100\qquad\text{subtract 36 from both sides}\\\\H^2=64\to H=\sqrt{64}\\\\H=8\ m[/tex]
[tex]\text{Substitute:}\\\\V=\dfrac{1}{3}(144)(8)=(48)(8)=384\ ft^3[/tex]
Ricardo has one quiz each week in math class. The table gives the probability of having a quiz on each day of the week. What is the probability that Ricardo will have a quiz Tuesday, Thursday, or Friday? Express your answer as a percent.
Final answer:
To find the probability that Ricardo will have a quiz on Tuesday, Thursday, or Friday, we add the individual probabilities for each of those days, resulting in a total probability of 60%.
Explanation:
Probability is a measure of the likelihood of an event occurring. To find the probability that Ricardo will have a quiz on Tuesday, Thursday, or Friday, we add the individual probabilities for each of those days.
Probability of having a quiz on Tuesday = 0.2
Probability of having a quiz on Thursday = 0.1
Probability of having a quiz on Friday = 0.3
Total probability = Probability on Tuesday + Probability on Thursday + Probability on Friday = 0.2 + 0.1 + 0.3 = 0.6. Expressing this as a percentage, we get 60%.