Answer:
Once the number of possible heads and tail in 12 tosses is [tex]2^{12} =4096[/tex]
[tex]\frac{12!}{\left(7!\right)\left(5!\right)}\\\\\frac{12\cdot \:11\cdot \:10\cdot \:9\cdot \:8}{5!}\\\\\frac{95040}{120}\\\\792[/tex]
So the probability of getting exactly 8 heads in 12 coin tosses is: [tex]\frac{792}{4096}[/tex]
The Royal Fruit Company produces two types of fruit drinks. The first type is 45% pure fruit juice, and the second type is 70% pure fruit juice. The company is attempting to produce a fruit drink that contains 65% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 80 pints of a mixture that is 65% pure fruit juice?
Answer:
64 70% and 16 45%
Step-by-step explanation:
it's 4 70% and 1 45% to make 5 pints of 65% so 64 70% and 16 45%
Solve the following system of equations
-5x+2y=6
10x-2y=-16
X=
Y=
Answer:
5x = - 10
5. 5
x = 2
y = -10
its easyyy
A sphere has a radius of 6 meters. A second sphere has a radius of 3 meters. What is the difference of the volumes of the spheres? The volume of the larger sphere is π cubic meters greater than the volume of the smaller sphere.
Answer:
Step-by-step explanation:
volume of sphere = (4/3)πr³
Difference= [(4/3)*π*6³]-[(4/3)*π*3³]
[tex]=\pi*[(\frac{4}{3}*6*6*6) - (\frac{4}{3}*3*3*3)]\\\\=\pi*[(4*2*6*6)-(4*3*3)]\\\\=\pi *[288-36]\\\\=252\pi[/tex]
Melissa rolls two number cubes, each with sides that are labeled 1 to 6. What is the probability that both number cubes show a 1?
A 1/2
B 1/6
C 1/24
D 1/36
Answer:
1/36
Step-by-step explanation:
(1/6 * 1/6) = 1/36
Answer:
D 1/36
Step-by-step explanation:
6*6= 36 but if you do (1/6*1/6)= 1/36
H represents hours and p represents pay in dollars. CHOOSE THE CORRECT STATEMENT.
Answer:
The value of p is always 15 times the value of h
Step-by-step explanation:
5 * 15 = 75
10 * 15 = 150
15 * 15 = 225
20 * 15 = 300
Answer:
The value of p is always 15 times the value of h
Step-by-step explanation:
H p
5 x 15 = 75
10 x 15 = 150
HELP PLZ WORTH EXTRA POINTS
Answer:
The answer to your question is 42°
Step-by-step explanation:
Data
m∠BOC = 6x - 6
m∠AOB = 5x + 8
m∠BOC = ?
Process
We know that the segments OA ⊥ OC so they are complementary angles.
1.- The sum of complementary angles equals 90°
m∠BOC + m∠AOB = 90°
2.- Substitution
6x - 6 + 5x + 8 = 90°
3.- Solve for x
6x + 5x = 90 + 6 - 8
4.- Simplify
11x = 88
5.- Result
x = 88/11
x = 8
6.- Calculate m∠BOC
m∠BOC = 6(8) - 6
= 48 - 6
= 42°
Josie found a small bird bath at a garage sale. The bird bath has a circular opening with a radius of 10 cm, as shown in the diagram below. Using 3.14 for pi, Josie calculates that the water in the small bird bath has 314 cm2 of surface area. Josie lives in a wooded area with lots of birds, so she plans to use the bird bath she found as a scale model to build a much larger bird bath. If she doubles the dimensions of the scale model, how many square centimeters of surface area will the larger bird bath have for bathing?
Answer: 1256cm
Step-by-step explanation:
Final answer:
When Josie doubles the radius of the bird bath to build a larger one, the new surface area will be 1256 cm², as surface area quadruples when doubling the radius of a circle.
Explanation:
Josie calculated that the surface area of her small bird bath with a radius of 10 cm is 314 cm^2. If she doubles the dimensions for a larger bird bath, the new radius will be 20 cm. To find the surface area of the larger bird bath, we use the formula for the area of a circle, A = πr².
Plugging in the new radius:
A = 3.14 × (20 cm)^2
A = 3.14 × 400 cm^2
A = 1256 cm2
This means the surface area for the larger bird bath Josie plans to build will have 1256 cm^2 for bird bathing. This calculation demonstrates how the surface area of a circle quadruples when the radius is doubled, which is consistent with the principle that surface area scales with the square of the dimension changes.
Which of the following statements that Jasmine made about the string lengths are true? Select all that apply.
A.
The difference between the longest length and shortest length is 14 inches.
B.
I have twice as many 12-inch strings as I do 8-inch strings.
C.
The total length of string that I have is 84 inches.
D.
I cannot determine what the shortest string is by looking at my line plot.
E.
Since I need 100 total inches of string for my project, I have enough string.
helppp
A.P.S!
Answer:E and D i think
i had this on before and the answer is b and c
An Apple producer sells their product in bags that each contain 16 apples. These apples have a mean weight of 80 grams and a standard deviation of 5 grams. Suppose that each bag represents an SRS of apples, and we calculate the sample mean weight of the apples in each bag. What is the mean and standard deviation of the sampling distribution?
Mean: 80 grams
Standard Deviation: 1.25 grams
The mean stays the same.
How to find standard deviation in this case would be:
SD divided by the squareroot of the sample.
So, 5/[tex]\sqrt{16}[/tex] = 1.25
I hope this helps!
For the following exercises, use the table of values that represent points on the graph of a quadratic function. By determining the vertex and axis of symmetry, find the general form of the equation of the quadratic function.
Answer:
y = x² + 2x + 1
Step-by-step explanation:
Same y value at x = -2 & x = 0
So line of symmetry is at:
x = (-2+0)/2
x = -1
Vertex: (-1,0)
y = a(x - -1)² + 0
y = a(x + 1)²
At x = 1, y = 4
4 = a(1 + 1)²
4 = 4a
a = 1
y = (x + 1)²
y = x² + 2x + 1
The general form of the equation of the quadratic function is x² + 2x + 1
The formula expressing the equation of the quadratic function will be expressed as:
y = a(x -h)² + k
From the table shown, we can see that the y-values are the same at where x = -2 and 0
Get the line of symmetry:
[tex]x =\frac{-2+0}{2}\\x=\frac{-2}{2} \\x=-1[/tex]
We can see that when x = -1, y = 0. Hence the vertex will be at (-1, 0)
h = -1
k = 0
Substitute into the formula y = a(x -h)² + k
y = a(x -(-1))² + 0
y = a(x+1)²
From the table at where x = 1, y = 4. On substituting to get "a" we have:
4 = a(1+1)²
4 = 4a
a = 1
Get the required quadratic function by substituting the parameters into the general formula as shown:
y = a(x -h)² + k
y = 1(x +1)² + 0
y = (x+1)²
y = (x+1) (x+1)
y = x² + x +x + 1
y = x² + 2x + 1
Hence the general form of the equation of the quadratic function is x² + 2x + 1
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Triangle ABC is a right triangle where B is the right angle, AB = x, and BC = x. What could be the first step of a proof BD of the triangle
divides the hypotenuse into two segments of equal length?
Answer:
x=20
Step-by-step explanation:
Right angle triangle ABC
ac^2=ab^2+bc^2
or (x+9)^2=x^2+(x+1)^2
or x^2+81+18x=x^2+x^2+1+2x
or 80= X^2-16x
or x^2-16x-80=0
x^2-20x+4x-80=0
x(x-20)+4(x-20)=0
(x+4)(x-20)=0
either x=-4 or x=20
since x is a length it can not be negative
why did the bay of pigs invasion happen?
Answer:
The Bay of Pigs invasion begins when a CIA-financed and -trained group of Cuban refugees lands in Cuba and attempts to topple the communist government of Fidel Castro. The attack was an utter failure. Fidel Castro had been a concern to U.S. policymakers since he seized power in Cuba with a revolution in January 1959.
The cruising speed of the bullet train will be at least 170 miles per hour. Use s to represent the train's cruising speed (in miles per hour). Write an inequality to represent the situation
Answer:
s ≥ 170
Step-by-step explanation:
The problem raises the following statement: "The cruising speed of the bullet train will be at least 170 miles per hour"
Which means that the train has a speed of 170 miles for now or higher, knowing this we can pose the inequality.
Knowing that "s" is the train's cruising speed (in miles per hour), we have to:
s ≥ 170
This would be the inequality that the statement represents.
The inequality representing the bullet train's cruising speed being at least 170 miles per hour is s ≥ 170.
The situation described involves finding an inequality for the train's cruising speed. To represent the train's cruising speed in miles per hour, we use the variable s.
Given that the cruising speed of the bullet train will be at least 170 miles per hour, we need an inequality that expresses this condition.
The inequality is:
s ≥ 170
This means that the cruising speed s can be 170 miles per hour or higher.
What is its length?
Enter the correct answer.
The perimeter of a rectangle is twice the
sum of its length and its width. The
perimeter is 34 meters and its length is 2
meters more than twice its width
What is the length?
Step-by-step explanation:
The answer is 15
Find the reference angle for 517°
a.23°
c.113°
b.157°
d.67°
the anwser is 23 dregrees
A regular convex polygon has 14 sides. What is the sum of the measures of the interior angles?
Answer:
he measure of each interior angle of a regular polygon with 14 sides is about 154.3.
Step-by-step explanation:
Create a Y and X table using the expression Y= -2x +5
solve for x: X + 3 = 15
Answer:
x=12
Step-by-step explanation:
x+3=15
move constant to the right
x=15-3
subtract 15 to 3
x=12
Answer:
X =12
Step-by-step explanation:
X+3 =15
subtract 3 from each side
X+3-3 =15-3
X = 12
a. f(x) = 4x3 – 10x + 7 one to one
Answer:
I think is it.
Step-by-step explanation:
An odd function is a function f such that, for all x in the domain of f, -f(x) = f(-x). A one-to-one function is a function f such that f(a) = f(b) implies a = b.
Jay just graduated from college and he has decided to open a retirement account that pays 1.75% interest compounded monthly. If he has direct deposits of $100 per month taken out of his paycheck, how much will he have in the account after 42 years?
Answer:
$51,282
Step-by-step explanation:
100*1.75%=1.75*504 months (42 years)=882
100*504 months (42 years)=50,400
50,400+882=$51,282
Hope this is correct, and helps you out :)
He will have $74,356.50 in his account.
what is interest?Interest is the price you pay to borrow money or the cost you charge to lend money.
Initial investment (PV)= $100
Number of periods (n)=42 years
Interest rate (i)= 1.75%
So, FV= P(1+r/100)^(nt) -1)) / (r/n)
FV= 100(1+0.0175/100)^(12*42) -1)) / (0.0175/12)
FV= $74,356.50
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Which is the better buy, 12 ounces for $7.50 or 1 pound for $9.00? Explain your reasoning.
To determine the better buy, compare the cost per ounce for each option. The second option of 1 pound for $9.00 is the better buy with a lower cost per ounce.
Explanation:To determine which option is the better buy, we need to compare the cost per ounce for each option.
The first option is 12 ounces for $7.50. To find the cost per ounce, we divide the total cost ($7.50) by the number of ounces (12), giving us a cost of $0.625 per ounce.The second option is 1 pound for $9.00, which is equivalent to 16 ounces. To find the cost per ounce, we divide the total cost ($9.00) by the number of ounces (16), giving us a cost of $0.5625 per ounce.Therefore, the second option of 1 pound for $9.00 is the better buy as it has a lower cost per ounce.
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How do the temperature compare? Fro
Answer:
Step-by-step explanation:
-43.6F/-37.4F/-17/37.3/51.9/52
Addison is making caramel apples. She has 2 1/2 bags of apples. One full bag has 8 apples, and each apple weighs 5 ounces. Write an expression that could be used to find the total number of ounces of apples Addison has. Then find the total number of ounces. USE A NUMERICAL EXPRESSION. WILL MARK BRAINLIEST.
Answer:
20 × 5 = 100 ounces. 100 is the total number of ounces
Is the slope Positive, Negative, Zero or Undefined?
Find the slope
What does m=
Answer:
0 slope
Step-by-step explanation:
Because if were to be any answer that is greater or less than 0 it would show as going diagonally down or up and that shows as 0 so it goes as a horizontal line.
Answer:
The slope is zero
and m=0
last Saturday two of the houses were having a party each family invited 9 guests to their house how many guests were in total
Answer:
18
Step-by-step explanation:
because there where two houses each invited 9 guests and 9 + 9 = 18
A 4-column table with 3 rows. Column 1 has entries run, do not run, total. Column 2 is labeled lift weights with entries 40, blank, 65. Column 3 is labeled do not lift weights with entries blank, x, blank. Column 4 is labeled total with entries 75, blank, 120. Can you determine what number x represents from the information given? Explain how you got your answer.
The required value of a number of people is 20 who don't do either.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.
here, we have,
Column 1 has the entries run, do not run, and total. Column 2 is called lift weights, and it has the values 40, blank, and 65. Column 3 is captioned "do not lift weights" and has entries blank, x, and blank. Column 4 is called total and has the entries 75, blank, and 120.
As per the given information, the required solution would be as:
The number of people who do not run or lift weights by first determining that 55 individuals do not lift weights and 35 people run but do not lift weights. When you subtract 35 from 55, you get 20 people who don't do either.
Thus, the required value of a number of people is 20 who don't do either.
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The number x represents the number of people who do not run and do not lift weights. To calculate x, subtract the number of people who lift weights from the total number, then subtract the number of people who run and lift weights.
Explanation:To find the number that x represents, we can use the information given in a table with a row and column structure. From the total number of people (120) and the number of people that lift weights (65), we deduct the number that run and lift weights (40), leaving us with the number of people who either do not run or do not lift weights.
The total number of people that run is given as 75. Therefore, the number who do not run is 120 - 75 = 45. We know that 65 people lift weights, so by subtraction, 120 - 65 gives us the total number of people who do not lift weights.
Now, using the total number of people who do not lift weights, we can calculate the value of x, which represents the number of people who do not run and also do not lift weights. Subtracting the number of people who run but do not lift weights from the total number who do not lift weights gives us:
Number of people who do not lift weights = Total number of people - Number of people who lift weights
Number of people who do not lift weights = 120 - 65 = 55
Therefore, x equals 55 - 40, since 40 is the number of people who run and lift weights.
x = 55 - 40 = 15
Which of the following represents the least percent of change? *
a. A coat that was originally priced at $90 is now $72
b. A puppy who weighed 6 ounces at birth now weighs 96 ounces
c. A child grew from 54 inches to 60 inches in 1 year
d. A savings account increased from $500 to $550 in 6 months
Answer:
Step-by-step explanation:
B. It didn’t grow at all
Use the following function rule to find f(2).
f(x) = (9)* + 7
F(2) =
The value of f(2) for the given function is 25.
Given that, the function rule is f(x)=9x+7.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
To find f(2), substitute x=2 in the given function, we get
f(2)=9(2)+7
= 18+7
= 25
Hence, the value of f(2) for the given function is 25.
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To find f(2) for the function f(x) = 9x + 7, you substitute x with 2, resulting in the calculation 9(2) + 7, which equals 25.
Explanation:To find f(2) for the function f(x) = 9x + 7, we simply substitute x with 2 and calculate the value of the function at that point. Here is the step-by-step calculation:
Substitute x with 2 into the function: f(2) = 9(2) + 7.Multiply 9 by 2: 9 * 2 = 18.Add 7 to the result of step 2: 18 + 7 = 25.Therefore, the value of f(2) is 25.
If point Q is translated 4 units to the right and 2 units up, what are the coordinates of Q'?
Answer:
-4,2
Step-by-step explanation:
Answer
Q=(4,2)
Step-by-step explanation:
In X axis, count 4 units to the right
In Y axis, count 2 units up
Graph would look like this.
What minus 3/8 equals 3/4
your answer is 3/8
pls mark me brainliest
Answer:
9/8 or 1 1/8
Step-by-step explanation:
You need to find out __ - 3/8 = 3/4, so you first add 3/4 plus 3/8. This gets you 9/8, or 1 and 1/8. This is your answer. To double check, you need to subtract 1 1/8 from 3/8 to get you 3/4.