The chances of winning the grand prize in this game are approximately 0.089, whereas the chances of winning the consolation prize are 0.01.
Explanation:The subject of this question is Probability, which is a branch of Mathematics. To calculate the probability, we'll need to determine the total number of outcomes and the count of the favorable outcomes.
a) To win the grand prize, all three balloons popped have to have 'Winner' slips. The probability of each dart hitting such a balloon will decrease as the total number of balloons decreases. First dart probability would be 5/8 (5 'Winner' balloons out of 8 total), the second one 4/7 (as one 'Winner' balloon is already popped), and 3/6 for the third. Multiply these probabilities together to get the overall probability: (5/8) * (4/7) * (3/6) = 0.089 (rounded to the third digit).
b) Similarly, for the consolation prize, we would have to hit all three balloons with blank slips. The process is equivalent, resulting in a probability of (3/8) * (2/7) * (1/6) = 0.01 (rounded to the third digit).
Learn more about Probability here:https://brainly.com/question/22962752
#SPJ3
A candy store makes a 10-lb mixture of gummy worms, candy corn, and sourballs. The cost of gummy worms is $1.00 per pound, candy corn cost $3.00 per pound, and sourballs cost $1.50 per pound. The mixture calls for three times as many gummy worms as candy corn. The total cost of the mixture is $15.00. How much of each ingredient did the store use?
Answer:
6 grams of gummy worms, 2 grams of candy corn and 2 grams of sourballs.
Step-by-step explanation:
Let the number of pounds of each ingredient be as follows:
Gummy Worms = x pounds
Candy Corn = y pounds
Sourballs = z pounds
The store makes a mixtures of 10 pounds. This means the sum of x, y and z would be 10. Setting up the equation:
[tex]x + y +z = 10[/tex] (Equation 1)
The mixture calls for 3 times as many gummy worms as candy corn. This means amount of gummy worm will be 3 times the candy corn. Setting up the Equation:
[tex]x=3y[/tex] (Equation 2)
Cost of gummy worms is $1.00 per pound, candy corn cost $3.00 per pound, and sourballs cost $1.50 per pound. So cost of x, y and z pounds would be:
1x , 3y and 1.5z, respectively. The total cost of mixture is $15. So we can set up the Equation as:
[tex]x+3y+1.5z=15[/tex] (Equation 3)
Using the value of x from Equation 2, in Equations 1 and 3 give us following two equations:
[tex]4y+z=10[/tex] By substitution in Equation 1. (Equation 4)[tex]6y+1.5z=15[/tex] By substitution in Equation 3. (Equation 5)
Multiplying the Equation 4 by 1.5 and subtracting from Equation 5 gives us:
[tex]6y +1.5z-1.5(4y+z)=15-1.5(10)\\\\ 6y+1.5z-6y-1.5z=15-15\\\\ 0=0[/tex]
When two sides of equations turn into something that is always positive, we conclude that there are infinite number of solutions. In such cases, we fix a variable and give different values to it, to find corresponding values of other variables. Lets re-write the solution in terms of z.
From Equation 4, we have:
[tex]y=\frac{10-z}{4}[/tex]
From Equation 2, we have:
[tex]x=3(\frac{10-z}{4} )[/tex]
Therefore, the solution set will be:
[tex](3(\frac{10-z}{4} ), \frac{10-z}{4} , z)[/tex]
Now in order to find any combination of ingredient, we give any value to z. Let, z is equal to 2 grams.
So,
x would be = 6 grams
y would be = 2 grams
So, one of the possible amount of ingredients that store can use is:
6 grams of gummy worms, 2 grams of candy corn and 2 grams of sourballs.
A paddock contains ducks and sheep. There are total of 42 heads and 96 feet in the paddock. How many ducks and how many sheep are in the paddock
Mrs.stevens has award winning rose bushes that grow at a rate of 3/4 foot per week. Her American home rose bush currently measures 5 feet tall, while her camp David Rose bush is 4 1/2 feet tall in two weeks how tall will mrs.stevens American home rose bush measure?
Answer:
The answer would be 6.5 feet.
Pre-Thinking:
Knowing that the rose bushes grow at a rate of 3/4 feet per week, we can turn that into 0.75, a decimal.
Because, we need to know the height of the rose bush in 2 weeks, multiply 0.75 by 2.
0.75 * 2 = 1.5
Working and Stuff:
Because we only need the length of the American Home Rose Bush, which is 5 feet tall, we can discard the other rose bush.
Lastly, add 1.5 to 5.
1.5 + 5 = 6.5 feet
Amazing MS-Paint drawing of a rose bush:
Sides KM and FH in the triangles below will be placed together to form a quadrilateral.
Which best describes the quadrilateral that will be formed?
parallelogram
rectangle
rhombus
trapezoid
Any polygon that has exactly 3 sides is called a triangle. Here you haven't provided any figure, so I'll assume that we have two triangles as indicated in the figure below. As you can see, we have two sides:
[tex]KM \ and \ FH[/tex]
When placing together we realize that those sides measures the same, so:
[tex]KM=FH[/tex]
So [tex]KM/FH[/tex] is the diagonal of the shape. From the figure we also know that opposite sides are equal and parallel, therefore, this shape represents a parallelogram. Remember that a parallelogram is a quadrilateral where both pairs of opposite sides are parallel.
So correct option is:
Parallelogram
Answer:
The correct answer is A. parallelogram
Step-by-step explanation:
Right on ED2021, goodluck!
Zack is taking inventory of loaves of bread at the grocery store where he works. There are 20 loaves in a full case, and Zack has 3 partially filled cases: 1 case is 12 full, 1 case is 14 full, and 1 case is 25 full. How many total
Answer:
51 loaves
Step-by-step explanation:
Given that one case contains 20 loaves.
-Sum the number of partially filled cases and divide to get complete cases:
[tex]T_{loaves}=12+14+25\\\\=51[/tex]
#He has a total of 51 loaves:
[tex]20 loaves = 1 case\\51 loaves=x\\\\x=\frac{51}{20}\\\\x=2 \ rem 11[/tex]
Hence, Zack has a total of 51 loaves (2 full cases, 1 partial of 11 loaves)
What are the domain and range of the function f(x) = 3x + 5?
A. domain: (negative infinity, infinity); range: (0, infinity)
B. domain: (negative infinity, infinity); range: (5, infinity)
C. domain:(0, infinity); range: (negative infinity, infinity)
D. domain: (5, infinity); range: (negative infinity, infinity)
Ella is checking roof frames to make sure that they are right triangles. Which of the following measures form right triangles? Select all that apply. 10, 24, 26 8, StartRoot 20 EndRoot, 25 8, StartRoot 161 EndRoot, 15 20, 21, 29 39, 80, 89
Answer:
A; C; D; E
Step-by-step explanation:
The answer is A, C, D, and E
A: 10, 24, 26
C: 8, StartRoot 161 EndRoot, 15
D: 20, 21, 29
E: 39, 80, 89
Answer:
A, C, D, E
Step-by-step explanation:
It's correct
can someone show me how to solve this? the lesson didnt show me how to do it.[tex]\frac{x^{2} }{2} -32 = 0[/tex]
Answer:
x=-8,8
Step-by-step explanation:
[tex]\frac{x^2}{2} -32=0\\multiply ~by~2\\x^2-64=0\\x^2-8^2=0\\(x+8)(x-8)=0\\ether~ x=-8\\or~x-8=0\\x=8\\x=-8,8x=-8[/tex]
missing either x+8=0
x=-8
-13m = 1 - 14m what is the answer
Answer:
m = 1
Step-by-step explanation:
Step 1: Add 14m to both sides
-13m + 14m = 1 - 14m + 14m
m = 1
Answer: m = 1
Johnny thinks that the slope of the line through (5,10) and (4,4) is -1/6. Is he correct? If he is explain why. If he’s not, provide the correct answer and explain what he did wrong.
Answer:
Johnny is incorrect because the slope is actually 6.
Step-by-step explanation:
To find the slope: m = [tex]\frac{y2 - y1}{x2 - x1}[/tex]
Step 1: Plug in the points
m = [tex]\frac{4 - 10}{4 - 5}[/tex]
m = [tex]\frac{-6}{-1}[/tex]
m = 6
Answer: Johnny is incorrect because the slope is actually 6.
Helpppppppppppppppppp
Option A:
[tex]\left(x^{4}\right)\left(3 x^{3}-2\right)\left(4 x^{2}+5 x\right)=12 x^{9} +15 x^{8} - 8 x^{6}-10 x^{5}[/tex]
Solution:
Given expression [tex]\left(x^{4}\right)\left(3 x^{3}-2\right)\left(4 x^{2}+5 x\right)[/tex].
To find the product of the above expression:
[tex]\left(x^{4}\right)\left(3 x^{3}-2\right)\left(4 x^{2}+5 x\right)[/tex]
First multiply first two factors with each term.
[tex]=(x^{4} \times 3 x^{3}- x^{4} \times 2 ) \left(4 x^{2}+5 x\right)[/tex]
Using exponent rule: [tex]a^m \cdot a^n=a^{m+n}[/tex]
[tex]=(3 x^{7}- 2x^{4} ) \left(4 x^{2}+5 x\right)[/tex]
Now multiply these two factors with each term.
[tex]=3 x^{7} (4 x^{2}+5 x)- 2x^{4} \left(4 x^{2}+5 x\right)[/tex]
[tex]=(4 x^{2} \times 3 x^{7} +5 x \times 3 x^{7} )- \left(4 x^{2} \times 2x^{4}+5 x \times 2x^{4}\right)[/tex]
Using exponent rule: [tex]a^m \cdot a^n=a^{m+n}[/tex]
[tex]=(12 x^{9} +15 x^{8} )- (8 x^{6}+10 x^{5})[/tex]
[tex]=12 x^{9} +15 x^{8} - 8 x^{6}-10 x^{5}[/tex]
[tex]\left(x^{4}\right)\left(3 x^{3}-2\right)\left(4 x^{2}+5 x\right)=12 x^{9} +15 x^{8} - 8 x^{6}-10 x^{5}[/tex]
Hence option A is the correct answer.
Company A is offering $6,000 for the first month's salary and will increase the amount each month by $5,000. Company B is offering $700 or the first month and will double the pay each month.
Use the given table to determine for which month Company B's payment will first exceed Company A's payment?
A) Month 4
B) Month 6
C) Month 7
D) Month 9
The month in which Company B's payment will first exceed Company A's payment is C) Month 7.
Step-by-step explanation:
Step 1:
Company A offers $6,000 for the first month and increases the salary each month by $5,000.
Company B offers $700 for the first month but doubles the payments each month.
We need to determine which month company B's payment is greater than company A's payment.
Step 2:
According to the table, at month 6 company A pays $31,000 while company B pays $22,400.
However after this month, in the seventh-month company A pays $36,000 while company B pays $44,800, which is higher than company A's salary.
So The month in which Company B's payment will first exceed Company A's payment is C) Month 7.
Question 2:
Describe the relationship between the following expressions:
3(25 x 25) and (25 x 25)
The relationship between the expressions 3(25 x 25) and (25 x 25) is that the first expression is 3 times greater than the second one.
Describe the relationship between the following expressions:
3 (25 x 25): This expression means 3 multiplied by the result of 25 multiplied by 25, which is 1875.
(25 x 25): This expression represents the result of multiplying 25 by 25, which is 625.
The relationship between these expressions is that the first expression is 3 times greater than the second expression.
Find the quotient
-54у^2 + 24/ 9y + 6
Answer:
56
Step-by-step explanation:
Paul needs to wrap yellow tape around the perimeter of a new patio in the shape of a semicircle. The diameter of the patio is 42 meters.
Use 3.14 for .
The minimum length of yellow tape Paul needs to wrap around the patio is meters.
Answer:
Step-by-step explanation:
We need to find the circumference
d= 42 m
r= 42/2 = 21 m
Circumference =2πr or πd
= 3.14*42
=131.88 m
length of yellow tape Paul needs to wrap around the patio = 131.88/2 + 42
= 65.94 + 42 = 107.94 m
4b-4=3b+4
solve for b
Answer:
4b-3b=4+4
b=8
Step-by-step explanation:
Hence, the value of b is 8
#hope it helps
Answer:
b=8
Step-by-step explanation:
4b-4=3b+4
You have to add 4 to both sides so that all the like terms are together
4b=3b+8
Then you subtract 3b from each side so that the like terms are all together
b=8
Which is the solution to the inequality? y + 15 less-than 3
A.) y less-than negative 12
B.) y greater-than negative 12
C.) y less-than 18
D>) y greater-than 18
Answer:
Option A.) y less-than negative 12
Step-by-step explanation:
we have
[tex]y+15<3[/tex]
solve for y
subtract 15 both sides
[tex]y+15-15<3-15[/tex]
[tex]y<3-15\\y<-12[/tex]
therefore
y less-than negative 12
Answer:
A
Step-by-step explanation:
What’s the next number in the sequence 72,81,90,99
they are increasing by 9 so next is 108
The value of a car is $30,000. It loses 6.5% of its value each year. What will the value of the car be after 5 years?
The value of a car that costs $30,000 and depreciates at 6.5% annually will be $22,530 after 5 years, calculated using exponential decay.
The value of a car is $30,000 and it loses 6.5% of its value each year. To calculate the value of the car after 5 years, we can apply the concept of exponential decay. The value after one year would be the initial value minus 6.5% of the initial value. Mathematically, we can express this as:
V1 = V0 (1 - 0.065),
where V1 is the value after one year and V0 is the initial value. To find the value after 5 years, we would apply this formula iteratively or use the formula for exponential decay:
Vn = V0 x (1 - 0.065)ⁿ,
where Vn is the value after n years. Therefore:
V5 = $30,000 x (1 - 0.065)⁵,
V5 = $30,000 x (0.935)⁵,
V5 = $30,000 x 0.7510,
V5 = $22,530.
After 5 years, the value of the car will be $22,530.
Find the value of x.
log x 8 = 0.5
O A. 4
OB. 16
C. 32
Answer:
c. 4 4÷2 =8 hope it helps
5) What is the solution to the system of equations?
y=-2x+1 and y=-4/7x +1
A) (0,1)
B) (1,0)
C) (-2,1)
D) (-2, -4/7)
Answer:
-2x + 1 = -4/7x + 1
-14/7x + 1 = -4/7x + 1
-10/7x = 0
x = 0
y = -2(0) + 1
y = 1
(0,1)
answer is a
Maureen has two hollow containers. One is a 5 cm cube and the other is a cylinder of radius 2 cm. She completely fills the cube with water and then pours it into the cylinder.
What is the depth of the water in the cylinder? Give your answer in cm correct to 3 significant figures.
You can assume that the cylinder is tall enough to hold all the water from the cube.
Answer:
it's 9.947
Step-by-step explanation:
for this we need an equation which contain height in it so we used volume in both so we get height
π2^2h=5*5*5
π4h=125
h=9.947
To find the depth of water in the cylinder, calculate the volume of the cube and then use that volume to find the height of the cylinder.
Explanation:To find the depth of water in the cylinder, we need to calculate the volume of the cube and then use that volume to find the height of the cylinder.
The volume of a cube is given by V = s^3, where s is the length of a side.
The volume of the cube is (5 cm)^3 = 125 cm^3.
Now, we can use the formula for the volume of a cylinder, V = πr^2h, where r is the radius and h is the height.
Using the volume of the cube as the volume of the water in the cylinder, we get 125 cm^3 = π(2 cm)^2h. Solving for h, we find h = 9.278 cm.
Therefore, the depth of the water in the cylinder is approximately 9.278 cm.
Which equation is equivalent to 2x + 6y = 12?
Answer:
Option C, y = -1/3x + 2
Step-by-step explanation:
2x + 6y = 12
Step 1: Solve for y
2x + 6y - 2x = 12 - 2x
6y / 6 = (12 - 2x) / 6
y = 2 - 1/3x
Answer: Option C, y = -1/3x + 2
Answer:
y = (1/3)x + 2
Step-by-step explanation:
2x + 6y = 12 can be reduced by dividing all three terms by 2; we get:
1x + 3y = 6.
We solve for y. First, subtract 1x from both sides, obtaining:
3y = -1x + 6.
Next, divide all three terms by 3. We get
y = (1/3)x + 2
A recipe calls for 2/5 of a pound of chicken for each person. If there are 8 people to be fed how many pounds of chicken are required?
Answer:
3 1/5
Step-by-step explanation:
The 2 pounds of chicken are required to feed 8 people.
To find out how many pounds of chicken are required to feed 8 people, we can multiply the amount of chicken required per person by the number of people:
2/5 pound of chicken per person * 8 people = 2 pounds of chicken
Therefore, 2 pounds of chicken are required to feed 8 people.
Another way to solve this problem is to use ratios. We know that we need to feed 8 people and that we have 2/5 of a pound of chicken per person. We can set up a ratio to find out how many pounds of chicken we need:
8 people / 2/5 pound of chicken per person = x pounds of chicken
To solve for x, we can multiply both sides of the equation by 2/5 pound of chicken per person:
8 people * 2/5 pound of chicken per person = x pounds of chicken
x = 2 pounds of chicken
Therefore, 2 pounds of chicken are required to feed 8 people.
For such more question on chicken
https://brainly.com/question/26801891
#SPJ2
Identify the slope and y-intercept of the line y=5x/3+1.
Answer:
slope: 5x/3 and y-intercept: 1
Answer:
5/3 is slope
(0, 1) or 1 is y-int
Step-by-step explanation:
y = mx + b
m is slope
b is y-int
y = 5 x/3 + 1
y = 5/3x + 1
5/3 is slope
(0, 1) or 1 is y-int
There are 4 students in a small class. To make a team, the names of 2 of them will be drawn from a hat. How many different teams of 2nstudents are possible?
Answer:
3
Step-by-step explanation:
List all the different teams:
A+B, C+D
A+C, B+D
A+D, B+C
There are 3.
Answer:
3
Step-by-step explanation:
2*2 - 1 = 3
The probability of getting a heads and an even number if you fill a die and flip a coin at the same time.
You need to buy enough sand to fill a sandbox to the top. The sandbox is modeled by the right rectangular prism in the diagram. How much sand do you need to buy?
A) 69 cubic feet
B) 70 cubic feet
C) 79 cubic feet
D) 80 cubic feet
Answer:80
Step-by-step explanation:
Mutiply all
Answer:
d
Step-by-step explanation:
What is the distance between -45 and -98 on a number line?
A) -67
B) 53
Eliminate
C) 67
D) 133
The distance between -45 and -98 on a number line is 53 units.
Explanation:The distance between -45 and -98 on a number line can be determined by subtracting the smaller number from the larger number:
-98 - (-45) = -98 + 45 = -53
The distance between -45 and -98 is 53 units.
Learn more about Distance on a number line here:https://brainly.com/question/16901376
#SPJ2
how many degreese are in 1/9
angle
Answer:
10 degrees
Step-by-step explanation:
1/9 of 90 = 1/9 x 90 = 90/9 = 10
The correct answer is (b) [tex]$40^\circ$[/tex].
To find out how many degrees are in [tex]$\frac{1}{9}$[/tex] of a circle, we first need to understand that a full circle has [tex]$360^\circ$[/tex].
To find [tex]$\frac{1}{9}$[/tex] of a circle, we need to divide [tex]$360^\circ$[/tex] by 9.
So, [tex]$\frac{360^\circ}{9} = 40^\circ$[/tex].
Therefore, [tex]$\frac{1}{9}$[/tex] of a circle is [tex]$40^\circ$[/tex].
Complete Question:
How many degrees are in [tex]$\frac{1}{9}$[/tex] of a circle?
a. [tex]$90^{\circ}$[/tex]
b. [tex]$40^{\circ}$[/tex]
c. [tex]$42^{\circ}$[/tex]
d. [tex]$65^{\circ}$[/tex]