Answer:
The exact probability that all three marbles drawn will be red is [tex]\frac{1}{56}[/tex]
Step-by-step explanation:
Number of red marbles = 5
Number of blue marbles = 4
Number of Green marbles = 7
Total Number of marbles = 5+4+7=16
We are given that three marbles are drawn out of the bag
Probability of getting 1 red marble on first draw=[tex]\frac{5}{16}[/tex]
Probability of getting 1 red marble on second draw= [tex]\frac{4}{15}[/tex]
Probability of getting 1 red marble on third draw=[tex]\frac{3}{14}[/tex]
So,the exact probability that all three marbles drawn will be red=[tex]\frac{5}{16} \times \frac{4}{15} \times \frac{3}{14}=\frac{1}{56}[/tex]
Hence The exact probability that all three marbles drawn will be red is [tex]\frac{1}{56}[/tex]
Final answer:
The exact probability of drawing three red marbles consecutively from a bag containing a mix of 16 marbles is 1 in 56, calculated by multiplying the probabilities of each draw without replacement.
Explanation:
The question asks for the exact probability that all three marbles drawn from a bag containing 5 red marbles, 4 blue marbles, and 7 green marbles will be red. To find this probability, we use the formula for conditional probability without replacement.
First, calculate the total number of marbles, which is 5 + 4 + 7 = 16 marbles. The probability of drawing a red marble first is 5 out of 16. Once a red marble is drawn, there are now 15 marbles left, and 4 of them are red. So, the probability of drawing a second red marble is 4 out of 15. Further, if a second red marble is drawn, there are now 14 marbles left, and 3 of them are red, making the probability of drawing a third red marble 3 out of 14.
The combined probability of all three events (drawing three red marbles in a row) happening is the product of their individual probabilities:
P(3 red marbles) = (5/16) * (4/15) * (3/14) = 60 / 3360 = 1/56
Therefore, the exact probability of drawing three red marbles in a row from the bag is 1 in 56.
PLEASE HELP ME FOR BRAINLIEST
Answer:
x = 3.873 units
or x = [tex]\sqrt{15}[/tex] units
Step-by-step explanation:
Hypotenuse = 4 , x = height of this isosceles triangle.
base is 2,
so Use Pythagorean Theorem.
x^2 + 1^2 = 4^2
x^2 = 4^2 - 1^2
x^2 = 16 - 1 = 15
x = root(15) =
Workout this equation
X(x+2)(x+4)
Answer:
x^3 <-- exponent, x to the power of three
Explanation:
x(x+2)(x+4)
=(x(x+2))(x+4)
=(x(x+2))(x)+(x(x+2))(4)
=x^3+2x^2+4x^2+8x
=x^3+6x^2+8x
Step-by-step explanation:
x(x+2)(x+4)
first get rid of the bracket
x square +2x+x+4
x^2 + 3x + 4
A package of 4 pairs of insulated gloves costs $28.76. What is the unit price of the pairs of gloves?
The unit price is $per pair of gloves.
Answer: $7.19
Step-by-step explanation:
28.76/4=7.19
Determine the volume of each right prism
A- area of base = 6cm2, height = 4cm
B- Area of base = 20cm, height =2cm
C- Height = 10cm, area of base = 15cm
Answer:
his page is about surface area of prism. ... Base is triangular so either use 1) Area = ½ x base x height or if the height is ... 1) The base of a triangular prism is ΔABC, where AB = 3 cm, BC = 4 cm and ∠B = 90. If the height of the prism is 10 cm. ... by Pythagorean theorem in ΔABC, C 2 = a 2 + b 2 = 3 2 + 4 2 = 9 + 16. C 2 = 25
Step-by-step explanation:
Jordan is using centimeter cubes to build a model. She makes a rectangular prism that is 25 cubes long, 6 cubes tall, and 16 cubes wide. What is the volume of Jordan's model?
Answer:
2,400 cm3
Step-by-step explanation:
If the dimensions of the rectangular prism are 25 cubes, 6 cubes and 16 cubes, and each cube has 1 centimeters, the dimensions in centimeters are:
25 cm, 6 cm and 16 cm.
Then, to find the volume of the rectangular prism, we just need to multiply all three dimensions:
Volume = 25 * 6 * 16 = 2,400 cm3.
Sharon hits a golf ball off the ground. The function h represents the height of the golf ball, in feet, t seconds after it is hit. h(t) = -16(t − 3)2 + 144 Which of the following statements describes this situation correctly?
The statement which best describes the situation correctly is that the golf ball is on the ground at 0 and 6 seconds.
Given that:
Sharon hits a golf ball off the ground.
The function h represents the height of the golf ball, in feet, t seconds after it is hit.
h(t) = -16(t - 3)² + 144, which is a quadratic function.
Since the options contain the time when the ball hits the ground, it is required to find the time when the ball hits the ground.
When the ball is on the ground, the height is 0.
So, h(t) = 0
-16(t - 3)² + 144 = 0
-16(t - 3)² = -144
Divide both sides by -16.
(t - 3)² = 9
Take the square root on both sides.
t - 3 = ±√9
t - 3 = ±3
So, t = 3 + 3 and t = -3 + 3
So, t = 6 and t = 0
Hence, the ball hits the ground when t = 0 and t = 6, which is option B.
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The complete question is given below.
Find the solution to the system of equations.
You can use the interactive graph below to find the solution.
y=−4x−3
y=−2x+1
Answer:
X = -2
Y = 5
Step-by-step explanation:
Look at attachment:
Hope this helps! :)
3. Kathy is planning a party. She decides to serve pizza to her guests and estimates that she
will need 12 pizzas with 8 slices each. If each person eats & pieces, how many people can she serve?
Answer:
96
Step-by-step explanation:
12x8=96
Answer:
15 people
Step-by-step explanation:
if each person eats 8 pieces of pizza, 12 people can be served because 8 slices are in 1 pizza and he ordered 12 pizzas.
Write a formula for r in terms of θ based on the image below.
The angle in the figure is a central angle in radians.
Answer:
7pi/theta
Step-by-step explanation:
Arc length = r × theta
7pi = r × theta
r = 7pi/theta
Answer:
7pi/theta
Step-by-step explanation:
hope it helps <3
What’s 0 divided by 0
Answer:
YOU CANNOT DIVIDE BY 0
Step-by-step explanation:
Answer:
Undefined. You cannot divide zero by zero.
Evaluate. 5(-6) = _______
Answer:
-30
Step-by-step explanation:
-6*5=-30
The value of the x is -30 or the value of the number expression is -30 after performing the arithmetic operation the answer is -30.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
It is given that;
The number expression is:
= 5(-6)
Let x be the value of the expression;
x = 5(-6)
After performing the arithmetic operation:
x = -30
Thus, the value of the x is -30 or the value of the number expression is -30 after performing the arithmetic operation the answer is -30.
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The length of a rectangle is 7 inches longer than it is wide. If the area is 20 square inches, what are the dimensions of the rectangle?
Area of a rectangle is length x width.
Let the width = x
The length would be x +7. ( 7 inches longer than the width)
Area = 20
Set up the formula:
20 = x * x+7
Simplify the right side:
20 = x^2 + 7x
Subtract 29 from both sides:
X^2 + 7x -20 = 0
Solve using the quadratic equation
X = -b + sqrt(b^2 -4ac) / 2a
X = -7 + sqrt(7^2-4(1)(-20) / 2(1) (exact answer)
X = 2.178908 ( as a decimal)
The width is 2.178907 inches (round as needed)
The length would be 9.178907 inches ( round as needed.)
Depending on how you round, when you multiply them together you get approximately 20 square inches.
Step-by-step explanation:
Step 1: Find the dimensions
l = 7 + w
Area = 20
Find width
[tex]A = l * w[/tex]
[tex]20 = (7 + w)(w)[/tex]
[tex]20 - 20 = 7w + w^2 - 20[/tex]
[tex]w^2 + 7w - 20 = 0[/tex]
[tex]w=\frac{-(7)\pm\sqrt{(7)^2-5(1)(-20)}}{2(1)}[/tex]
[tex]w = 2.17890...[/tex]
Find length
[tex]l = 7 + w[/tex]
[tex]l = 7 + 2.17890...[/tex]
[tex]l = 9.17890...[/tex]
Answer: [tex]Width = 2.17890..., Length = 9.17890...[/tex]
The sum of two numbers is 90. The larger
number is 14 more than 3 times the smaller
number. Find the numbers.
First complete the equations below, where x stands for
the larger number and y stands for the smaller number
x + y = [?]; x = [ ] + [ ]y
Answer:
x= 71, y= 19.
Step-by-step explanation:
To solve this, we will need to set up an algebraic equation. Since y is the smaller number, we can think of x in terms of y:
x= 3y+14
We can substitute this in the equation to get:
90= y+3y+14.
Simplifying this will give us:
76= 4y.
When solved, we get the value of y (the smaller number) to be 19.
To solve for x, we must plug this into the equation giving us:
x= 3(19)+14
x= 71.
Answer: x+y=90;x=14+3y
71, 19
Step-by-step explanation:
A box is partially filled with books. If 24 cubic inches of the box are already filled and there are 12 cubic inches of space left, what is the total volume of the box (in cubic inches)?
Answer:
The box has a total volume of 36 cubic inches.
Step-by-step explanation:
The total volume of the box is given by the volume that is filled with books plus the volume that doesn't have any books in it. Therefore, in order to solve this problem we must sum the two volumes. We have:
total volume = volume with books + volume without books
total volume = 24 + 12
total volume = 36 cubic inches
The box has a total volume of 36 cubic inches.
Add or subtract.
7z2 − 2z4 − 2z2 − 5z4
To solve the given polynomial addition and subtraction question, combine like terms. The z4 terms combined are -7z4 and the z2 terms are 5z2, resulting in the simplified expression 5z2 - 7z4.
Explanation:To add or subtract the polynomials 7z2 − 2z4 − 2z2 − 5z4, you'll want to combine like terms. Like terms are terms that have the same variables raised to the same power.
Here, z2 and z4 are like terms, so you can combine them separately.
Starting with the z4 terms:
-2z4 and -5z4 combine to give you -7z4. They both have the same variable z raised to the fourth power, so you just add the coefficients, keeping the exponent the same.
Then, combine the z2 terms:
7z2 and -2z2 combine to give you 5z2.
Similarly, these terms have the same variable z raised to the second power.
Now, putting it all together, you get:
5z2 − 7z4
This is the simplified version of the polynomial after combining like terms.
Can you help me work out the circumference of this circle? If so, give your answer in terms of Pi
The circumference of a circle can be calculated using the formula C = 2πr, where C is the circumference and r is the radius.
Explanation:The circumference of a circle can be found using the formula C = 2πr, where C represents the circumference and r is the radius of the circle.
For example, if the radius of the circle is 5cm, the circumference would be C = 2π(5) = 10π cm. It is important to note that the circumference is always given in terms of π, which represents the mathematical constant.
Therefore, the circumference of a circle can be calculated by multiplying the radius by 2π.
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Convert
102.48
°
to radian measure.
Round your answer to the nearest hundredth.
Answer:
1.79 radians to the nearest hundredth.
Step-by-step explanation:
To covert, we multiply degrees by π/180
so radians = 102.48 * π/180
= 1.7886 radians.
A wave has a frequency of 900Hz and a wavelength of 200m at what speed is this wave traveling
Answer:
180000 m/s
Step-by-step explanation:
The frequency of the wave is 900 Hz.
The wavelength of the wave is 200 m.
The speed of a wave is given as the product of wavelength and frequency. That is:
v = λf
where λ = wavelength
f = frequency
The speed of the wave is therefore:
v = 200 * 900 = 180000 m/s
The speed of the wave is 180000 m/s.
A sphere has a diameter of 0.926 inch what is the volume of the sphere use 3.14 for Pie
Answer:
The volume of the sphere is [tex]0.415\ \text{inch}^3[/tex].
Step-by-step explanation:
The diameter of a sphere is 0.926 inch. It is required to find the volume of the sphere. The formula used to find the volume of sphere is given by :
[tex]V=\dfrac{4}{3}\pi r^3[/tex]
Since, r is radius, r = d/2 = 0.463 inch
So,
[tex]V=\dfrac{4}{3}\times 3.14\times (0.463)^3\\\\V=0.415\ \text{inch}^3[/tex]
So, the volume of the sphere is [tex]0.415\ \text{inch}^3[/tex].
What is the y-intercept when f(0) = 5^1?
Answer:
(0,5)
Step-by-step explanation:
5^1=5, meaning that the y coordinate y-intercept is 5. Therefore, the y intercept is (0,5). Hope this helps!
11x+14y=13
11x+10y=25
Given the figure. Find AC.
(10) COS(40°) = AC
10/cos(40°) = AC
10/sin(40°) = AC
(10) sin(40%) =
Image is missing, so i have attached it.
Answer:
AC = 10sin 40°
Step-by-step explanation:
From the diagram attached, using terms in trigonometric ratio, AC is the opposite side, BC is the adjacent side and AB is the hypotenuse.
Thus, since we want to find AC;
We know that in trigonometric ratios; opposite/hypotenuse = sin θ
In the diagram, θ = 40° and AB = 10
Thus,
AC/10 = sin 40°
Multiply both sides by 10 to get;
AC = 10sin 40°
please help me!!!!!!!!
Answer:
C
Step-by-step explanation:
Using the sine ratio in the right triangle
sin17° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{25}[/tex]
Multiply both sides by 25
25 × sin17° = x, thus
x ≈ 7.3 → C
Find the area of the figure?
Answer:
14 m
Step-by-step explanation:
For the triangle, you use the formula A=1/2bh. So in this case it's 3×4×1/2. 3×4 is 12, times 1/2 is 6 m. Now for the rectangle it's just 2×4 which is 8. 8+6 is 14. Hope this helps! If you are still confused please comment!
Fido’s domain is limited by a 10-foot long leash that is tethered to the corner of his expansive 7 by 5-foot dog mansion. How much outdoor territory can Fido mark?
9514 1404 393
Answer:
83.5π ft² ≈ 262.3 square feet
Step-by-step explanation:
Fido's area is 3/4 of a 10' radius circle plus 1/4 each of a 3' radius and 5' radius circle.
A = (3/4)(π(10 ft)²) +(1/4)(π)((3 ft)² +(5 ft)²)
= (75π +34/4π) ft² = 83.5π ft² ≈ 262.3 square feet
Answer:
approximately 262.3 square feet
Step-by-step explanation:
What is the simplified form of
Answer:
Step-by-step explanation:
[tex]\sqrt{64x^{16}} =\sqrt{8^{2}*x^{8*2}}\\\\ =\sqrt{8^{2}*(x^{8})^{*2}}\\\\=8x^{8}[/tex]
Jessica records the number of winners at the Dunk-a-Teacher booth at the town fair as shown in the table. If there are 750 contestants on Monday, how many should Jessica expect to dunk a teacher?
Answer:
do you need help
Step-by-step explanation:
Answer:
Between 75 and 98.
Step-by-step explanation:
Let's first have a look at the previous data available:
Friday, 27 dunk teachers out of 215 participants (12.5%)
Saturday: 54 dunk teachers out of 417 participants (12.9%)
Sunday: 39 dunk teachers out of 368 participants (10.6%)
So, based on the previous 3 days, she can expect between 10% and 13% will dunk a teacher.
If she has 750 contestants on Monday, the number of winners should then be in the range of 75 (10% of 750) and 98 (13% of 750).
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Step-by-step explanation:
FP!!!!!!!!!!!!!!!!!!!!
(10 x 6 ) + 20
Answer:
80
Step-by-step explanation:
Following the order of operations (PEMDAS), you would first multiply 10 by 6 to get 60. You would then add 20 to the product to get your answer.
(10 · 6) + 20
60 + 20 = 80
look at the attached picture
hope it will help you
5. Caroline and Grant are building sandcastles in
the annual Coney Island Sand Sculpting Contest
The diagram below represents their final products
a. Which sandcastle has the greatest volume?
Answer:
The sandcastle B has the greatest volume
Step-by-step explanation:
The volume of a pyramid is given by the following formula:
V = (1/3) * A * h
Where A is the base area and h is the height.
Now we can calculate the volume of both pyramids:
V1 = (1/3) * 30 * 6 = 60 in3
V2 = (1/3) * 24 * 8 = 64 in3
So the volume of the pyramid B is bigger than the volume of the pyramid A.
Angela paints a wall that has an area of 42 2/3 square yards.
She uses 1 1/3 gallons of paint.
Part A
What is Angela’s rate of paint coverage in square yards per gallon?
________ square yards per gallon.
Part B
The label on the paint container states that its average coverage rate is 275 square feet per gallon.
What is the difference in square feet per gallon between Angela’s rate of paint coverage and the average rate indicated on the label on the container?
(Note: 1 square yard = 9 square feet )
______________square feet per gallon difference.
Answer:
Part A: 32 square yards per gallon
Part B: 13 square feet per gallon difference
Step-by-step explanation:
Part A:
To find how many square yards each gallon covers, you have to divide 42 2/3 by 1 1/3, which equals 32. That means each gallon of paint covers 32 square yards.
Part B:
First, you have to convert how much Angela covered in square yards to square feet. Since one square yard is equal to 9 square feet, we have to multiply 32 by 9, which equals 288. To find the difference, you have to subtract 288 - 275, which equals 13.
Final answer:
Angela's rate of paint coverage in square yards per gallon is 32, and the difference in square feet per gallon between Angela’s rate and the average rate on the paint label is 13 square feet per gallon.
Explanation:
Part A: Calculating Paint Coverage
To find Angela’s rate of paint coverage in square yards per gallon, we would divide the total area painted by the amount of paint used. We have 42 2/3 square yards painted using 1 1/3 gallons of paint. First, it's easier to work with improper fractions, so we convert 42 2/3 to (126/3 + 2/3) = 128/3 square yards, and 1 1/3 to (3/3 + 1/3) = 4/3 gallons. Now, we calculate the rate by dividing the square yards by the gallons:
Rate = (128/3) / (4/3) = (128/3) × (3/4) = 128/4 = 32 square yards per gallon.
Part B: Difference in Square Feet per Gallon
To find the difference in square feet per gallon, we need to compare Angela's rate to the average rate given on the label. Angela's rate is 32 square yards per gallon, and there are 9 square feet in a square yard. So, Angela's rate in square feet would be 32 × 9 = 288 square feet per gallon. The label states an average coverage rate of 275 square feet per gallon. Thus, the difference is:
Difference = Angela’s rate - Label’s rate = 288 - 275 = 13 square feet per gallon difference.