0.3 or 30%. The probability that Ace pick a banana from a basket that content others fruits is 0.3.
The key to solve this problem is using the equation of probability [tex]P(A)=\frac{n(A)}{n}[/tex] where n(A) the numbers of favorables outcomes and n the numbers of possible outcomes.
There are in the basket 10 fruits in total (3 bananas + 4 apples + 3 oranges = 10fruits). Then, extract a fruit can occur in 10 ways, this is n. There is only 3 bananas in the basket, so the fruit that ACE will pick be a banana can occur in 3 ways out of 10, so 3 is n(A).
Solving the equation:
[tex]P(A)=\frac{3}{10}=0.3[/tex]
The probability that Ace will pick a banana from the basket is 3/10, as there are 3 bananas out of a total of 10 pieces of fruit.
The question asks for the probability that Ace will pick a banana from a basket containing 3 bananas, 4 apples, and 3 oranges. To calculate this, you sum up the total number of pieces of fruit, which is 3 bananas + 4 apples + 3 oranges = 10 pieces of fruit. The probability is then the number of desired outcomes (bananas) over the total number of possible outcomes (all pieces of fruit), which is 3 bananas / 10 pieces of fruit = 3/10 or 30%.
Each player rolls two six sided die once each and the sum of the highest roll wins. The first player rolls a 3 and 4 so that his sum is 7, what is the probability that the secon player will win
Answer:
5/12 or 41.66%
Step-by-step explanation:
When throwing two six-sided dice, you have 36 possible outcomes:
{1,1} {1,2} {1,3} {1,4} {1,5} {1,6} {2,1} {2,2} {2,3} {2,4} {2,5} {2,6} {3,1} {3,2} {3,3} {3,4} {3,5} {3,6} {4,1} {4,2} {4,3} {4,4} {4,5} {4,6} {5,1} {5,2} {5,3} {5,4} {5,5} {5,6} {6,1} {6,2} {6,3} {6,4} {6,5} {6,6}
To find what is the probability the second player will win, we need to see how many of those 36 possibilities have a combined total of 8 or more (to beat the 7 of the first player):
These 15 combinations have a total of 8 or more:
{2,6} {3,5} {3,6} {4,4} {4,5} {4,6} {5,3} {5,4} {5,5} {5,6} {6,2} {6,3} {6,4} {6,5} {6,6}
So, the probability the second player gets 8 or more and wins is:
15/36 or 5/12 or 41.66%
Find the area of the shaded regions:
The area of shaded regions can be found using geometric principles or methods of integration depending on the actual shape and context. In most cases, area is proportional to the square of the distances. Integration techniques would be used if the shaded region is under a curve on a graph.
Explanation:To find the area of the shaded regions, depending upon the shape and complexity of the region, you'd typically use geometric principles and calculations, potentially including those related to rectangles, triangles, circles, and/or other shapes. In some cases, these calculations might include figuring out the area of a larger shape and then subtracting the area of a smaller, non-shaded shape. For example, the area of a disc could be found by using the equation А = лr², and placing limits of integration from r = 0 to r = R in case the shaded area is comprised of thin rings of different radii. In other cases, you might be using principles of integration if the shaded region is under a curve on a graph, integrating the function f(x) from a certain lower limit x₁ to upper limit x₂. Also, keep in mind that the area is usually proportional to the square of the distances in a certain set-up.
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find 2(cos 240+isin 240) ^4 (answer choices below)
1. C. -512√3+512i
2. B. 16(cos240°+i sin240°)
3. D. 3√2+3√6i, -3√2-3√6i
4. A. cos60°+i sin60°, cos180°+i sin180°, cos300°+i sin300°
5. D. 2√3(cos π/6+i sin π/6), 2√3(cos 7π/6+i sin 7π/6)
We will see that the equivalent expression is:
[tex]8*(cos(240\°) + i*sin(240\°))[/tex]
So the correct option is the first one.
How to rewrite the given expression?
We have the expression:
[2*(cos(240°) + i*sin(240°))]^4
Remember that Euler's formula says that:
[tex]e^{ix} = cos(x) + i*sin(x)[/tex]
Then we can rewrite our expression as:
[tex][2*(cos(240\°) + i*sin(240\°)]^4 = [2*e^{i*240\°}]^4[/tex]
Now we distribute the exponent:
[tex]2^4*e^{4*i*240\°} = 8*e^{i*960\°}[/tex]
Now, we need to find an angle equivalent to 960°.
Remember that the period of the trigonometric functions is 360°, then we can rewrite:
960° - 2*360° = 240°
This means that 960° is equivalent to 240°. Then we can write:
[tex]8*e^{i*960\°} = 8*e^{i*240\°} = 8*(cos(240\°) + i*sin(240\°))[/tex]
So the correct option is the first one.
If you want to learn more about complex numbers, you can read:
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need help with this one
Answer:
68
Step-by-step explanation:
∠DPG and ∠EPF are vertical angles, so they are equal.
7x = 4x + 48
3x = 48
x = 16
So ∠DPG is:
∠DPG = 7x
∠DPG = 112
∠DPE and ∠DPG are supplementary, so they add up to 180:
∠DPE + ∠DPG = 180
∠DPE + 112 = 180
∠DPE = 68
Find the solution set for the equation, given the replacement set.
y = –5x + 8; {(6, –11), (4, –12), (5, –9), (3, –14)}
a.
{(6, –11)}
c.
{(4, –12)}
b.
{(3, –14)}
d.
{(5, –9)}
Answer:
c. {(4, -12)}
Step-by-step explanation:
It is convenient to rearrange the equation to standard form:
5x +y = 8
Then check the offered points.
(6, -11): 5·6 -11 = 19 ≠ 8
(4, -12): 5·4 -12 = 8 . . . . . . this is in the solution set
(5, -9): 5·5 -9 = 16 ≠ 8
(3, -14): 5·3 -14 = 1 ≠ 8
To find the solution set, substitute the x and y values into the equation and check if it is true.
Explanation:To find the solution set for the equation, we need to check which coordinates from the replacement set satisfy the equation y = -5x + 8.
For (6, -11): Substituting x = 6 and y = -11 into the equation, we get -11 = -5(6) + 8, which simplifies to -11 = -30 + 8. This is not true, so (6, -11) is not a solution.For (4, -12): Substituting x = 4 and y = -12 into the equation, we get -12 = -5(4) + 8, which simplifies to -12 = -20 + 8. This is not true, so (4, -12) is not a solution.For (5, -9): Substituting x = 5 and y = -9 into the equation, we get -9 = -5(5) + 8, which simplifies to -9 = -25 + 8. This is not true, so (5, -9) is not a solution.For (3, -14): Substituting x = 3 and y = -14 into the equation, we get -14 = -5(3) + 8, which simplifies to -14 = -15 + 8. This is true, so (3, -14) is a solution.The solution set for the equation, given the replacement set, is {(3, -14)}.
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Which statement describes what these four powers have in common?
Answer:
b
Step-by-step explanation:
Please help last question
Find the total of male students:
4 + 6 + 2 + 2 = 14 total males.
There are 2 male juniors.
The probability of a male being a junior is 2/14 = 1/7 = 0.143 = 14.3 = 14%
Find the total of male students:
4 + 6 + 2 + 2 = 14 total males.
There are 2 male juniors.
The probability of a male being a junior is 2/14 = 1/7 = 0.143 = 14.3 = 14%
What transformation has changed the parent function f(x) = log2x to its new appearance shown in the graph below?
logarithmic graph passing through point 2, 4.
f(x + 3)
f(x − 3)
f(x) + 3
f(x) − 3
Answer: Third Option
[tex]f(x) +3[/tex]
Step-by-step explanation:
The function [tex]y=log_2(x)[/tex] passes through point (2, 1) because the exponential function [tex]2 ^ x = 2[/tex] when [tex]x = 1[/tex].
Then, if the transformed function passes through point (2, 4) then this means that the graph of [tex]y=log_2(x)[/tex] was moved vertically 3 units up.
The transformation that vertically displaces the graph of a function k units upwards is:
[tex]y = f (x) + k[/tex]
Where k is a positive number. In this case [tex]k = 3[/tex]
Then the transformation is:
[tex]f(x) +3[/tex]
and the transformed function is:
[tex]y = log_2 (x) +3[/tex]
Which is a solution to (x – 3)(x + 9) = –27?
x = –9
x = –3
x = 0
x = 6
Answer:
x = 0
Step-by-step explanation:
Since the product is not equal zero, we need to multiply both parenthesis first:
[tex](x-3)(x+9) =-27[/tex]
[tex]x*x+x*9+(-3)*x+(-3)*9=27[/tex]
[tex]x^2+9x-3x-27=27[/tex]
[tex]x^2+6x-27=27[/tex]
Add 27 from both sides:
[tex]x^2+6x-27+27=-27+27[/tex]
[tex]x^2-6x=0[/tex]
Factor [tex]x[/tex] out:
[tex]x(x+6)=0[/tex]
Apply the zero product:
[tex]x=0,x+6=0[/tex]
[tex]x=0,x=-6[/tex]
The solutions of the equation are [tex]x=0[/tex] and [tex]x=-6[/tex].
We can conclude that the correct answer is x = 0.
Answer:
C: x = 0
There is no solution.
Consider the functions f(x) = 3x2, g(x)=1/3x , and h(x) = 3x. Which statements accurately compare the domain and range of the functions? Select two options.
1All of the functions have a unique range.
2The range of all three functions is all real numbers.
3 The domain of all three functions is all real numbers.
4The range of f(x) and h(x) is all real numbers, but the range of g(x) is all real numbers except 0.
5 The domain of f(x) and h(x) is all real numbers, but the domain of g(x) is all real numbers except 0.
The domain of all three functions is all real numbers. The range of f(x) and h(x) is all real numbers, but the range of g(x) is all real numbers except 0.
Explanation:The statements that accurately compare the domain and range of the functions are:
The domain of all three functions is all real numbers.The range of f(x) and h(x) is all real numbers, but the range of g(x) is all real numbers except 0.For the functions f(x) = 3x^2, g(x) = 1/3x, and h(x) = 3x:
The domain of all three functions is all real numbers because x can take any real value.The range of f(x) and h(x) is all real numbers because the function values can be positive or negative for any real value of x.The range of g(x) is all real numbers except 0 because division by 0 is undefined.Learn more about Functions here:https://brainly.com/question/21145944
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Answer:c and d
Step-by-step explanation:
i got it right
Please help me out guys. The photo will show you what to do. 50 points cause I need it done fast
Answer:
a) starting height: 5.5 ft
b) hang time: 5.562 seconds
c) maximum height: 126.5 ft
d) time to maximum height: 2.75 seconds
Step-by-step explanation:
a) The starting height is the height at t=0.
h(0) = -16·0 +88·0 +5.5
h(0) = 5.5
The starting height is 5.5 feet.
__
b) The ball is in the air between t=0 and the non-zero time when h(t) = 0. We can find the latter by solving ...
-16t^2 + 8t +5.5 = 0
t^2 -(11/2)t = 5.5/16 . . . . . subtract 5.5, then divide by -16
t^2 -(11/2)t +(11/4)^2 = (5.5/16) +(11/4)^2 . . . . complete the square
(t -11/4)^2 = 126.5/16 . . . . . . . . . . . . . . . . . . . . call this [eq1] for later use
t -11/4 = √7.90625
t = 2.75 +√7.90625 ≈ 5.562
The ball will be in the air about 5.562 seconds.
__
c) If we multiply [eq1] above by -16 and add the constant on the right, we get the vertex form of the height equation:
h(t) = -16(t -11/4) +126.5
The vertex at (2.75, 126.5) tells us ...
The maximum height of the ball is 126.5 feet.
__
d) That same vertex point tells us ...
The maximum height will be reached at t = 2.75 seconds.
_____
If you really need answers fast, a graphing calculator can give them to you in very short order (less than a minute).
A diner has collected data about customer coffee-drinking habits. They have calculated that P(cream) = 0.5, P(sugar) = 0.6, and P(cream or sugar) = 0.7. Determine the P(cream and sugar). (2 points)
Answer:
P(cream and sugar) = 0.4
Step-by-step explanation:
* Lets study the meaning of or , and on probability
- The use of the word or means that you are calculating the probability
that either event A or event B happened
- Both events do not have to happen
- The use the word and, means that both event A and B have to happen
* The addition rules are:
# P(A or B) = P(A) + P(B) ⇒ mutually exclusive (events cannot happen
at the same time)
# P(A or B) = P(A) + P(B) - P(A and B) ⇒ non-mutually exclusive (if they
have at least one outcome in common)
- The union is written as A∪B or “A or B”.
- The intersection is written as A∩B or “A and B”
* Lets solve the question
∵ P(cream) = 0.5
∵ P(sugar) = 0.6
∵ P(cream or sugar) = 0.7
- To find P(cream and sugar) lets use the rule of non-mutually exclusive
∵ P(A or B) = P(A) + P(B) - P(A and B)
∴ P(cream or sugar) = P(cream) + P(sugar) - P(cream and sugar)
- Lets substitute the values of P(cream) , P(sugar) , P(cream or sugar)
in the rule
∵ 0.7 = 0.5 + 0.6 - P(cream and sugar) ⇒ add the like terms
∴ 0.7 = 1.1 - P(cream and sugar) ⇒ subtract 1.1 from both sides
∴ 0.7 - 1.1 = - P(cream and sugar)
∴ - 0.4 = - P(cream and sugar) ⇒ multiply both sides by -1
∴ 0.4 = P(cream and sugar)
* P(cream and sugar) = 0.4
Answer:
0.4
Step-by-step explanation:
Prove that for all whole values of n the value of the expression:
n(n–1)–(n+3)(n+2) is divisible by 6.
Expand:
[tex]n(n-1)-(n+3)(n+2)=(n^2-n)-(n^2+5n+6)=-6n-6[/tex]
Then we can write
[tex]n(n-1)-(n+3)(n+2)=6\boxed{(-n-1)}[/tex]
which means [tex]6\mid n(n-1)-(n+3)(n+2)[/tex] as required.
What transformation has changed the parent function f(x) = (.5)x to its new appearance shown in the graph below?
exponential graph passing through point negative 1, negative 2 and point 0, negative 1.
f(x) − 2
2 • f(x)
f(x) + 1
−1 • f(x)
Answer:
Last option
−1 • f(x)
Step-by-step explanation:
The function [tex]f(x) = (0.5) ^ x[/tex] passes through point (-1, 2) because:
[tex]f(-1) = (0.5) ^ {-1}= \frac{1}{(0.5)} = 2[/tex]
and also goes through the point (0, 1)
Because:
[tex]f(0) = (0.5)^0 = 1[/tex]
Then, if the transformed function passes through the point (0, -1) and passes through the point (-1, -2) then this means that the graph of [tex]f(x) = (0.5) ^ x[/tex] reflected on the axis x. This means that if the point [tex](x_0, y_0)[/tex] belongs to f(x), then the point [tex](x_0, -y_0)[/tex] belongs to the transformed function
The transformation that reflects the graph of a function on the x-axis is.
[tex]y = cf(x)[/tex]
Where c is a negative number. In this case [tex]c = -1[/tex]
Then the transformation is:
[tex]y = -1*f(x)[/tex]
and the transformed function is:
[tex]f (x) = - (0.5) ^ x[/tex]
Observe the attached image.Answer:
f(x) -2 is the correct answer.
Step-by-step explanation:
Just took the test!
For the following system, use the second equation to make a substitution for x in the first equation. x + 2y = 7 x + 5 = 3y What is the resulting equation? 3y - 5 - 2y = 7 3y + 5 + 2y = 7 3y - 5 + 2y = 7
Answer:
3y - 5 + 2y = 7
Step-by-step explanation:
Subtracting 5 from the second equation gives ...
x = 3y -5
Using the expression on the right for x in the first equation gives ...
x + 2y = 7 . . . . . . . . first equation
(3y -5) +2y = 7 . . . . with expression substituted for x
3y - 5 + 2y = 7 . . . . with parentheses removed
If Sally can make 10 free throws in one minute or 3 three-point baskets in one minute, while Jesse can make 8 free throws in one minute or 1 three-point basket in one minute, ___ has an absolute advantage in free throws and ___ has a comparative advantage in free throws. Sally; Sally Sally; Jesse Jesse; Sally Jesse; Jesse
Answer:
Sally; Sally
Step-by-step explanation:
For the free throws... let's see the stats:
Sally: 10 free throws
Jesse: 8 free throws.
Advantage?: Sally
For the three-points baskets:
Sally: 3
Jesse: 1
Advantage: Sally
Sally dominates in both categories, sorry Jesse.
Answer:
sally sally
Step-by-step explanation:
the numbers are just greater for both stats for her
Find an equation of the tangent to the curve x =5+lnt, y=t2+5 at the point (5,6) by both eliminating the parameter and without eliminating the parameter.
ANSWER
[tex]y = 2x -4[/tex]
EXPLANATION
Part a)
Eliminating the parameter:
The parametric equation is
[tex]x = 5 + ln(t) [/tex]
[tex]y = {t}^{2} + 5[/tex]
From the first equation we make t the subject to get;
[tex]x - 5 = ln(t) [/tex]
[tex]t = {e}^{x - 5} [/tex]
We put it into the second equation.
[tex]y = { ({e}^{x - 5}) }^{2} + 5[/tex]
[tex]y = { ({e}^{2(x - 5)}) } + 5[/tex]
We differentiate to get;
[tex] \frac{dy}{dx} = 2 {e}^{2(x - 5)} [/tex]
At x=5,
[tex] \frac{dy}{dx} = 2 {e}^{2(5 - 5)} [/tex]
[tex]\frac{dy}{dx} = 2 {e}^{0} = 2[/tex]
The slope of the tangent is 2.
The equation of the tangent through
(5,6) is given by
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y - 6 = 2(x - 5)[/tex]
[tex]y = 2x - 10 + 6[/tex]
[tex]y = 2x -4[/tex]
Without eliminating the parameter,
[tex] \frac{dy}{dx} = \frac{ \frac{dy}{dt} }{ \frac{dx}{dt} } [/tex]
[tex]\frac{dy}{dx} = \frac{ 2t}{ \frac{1}{t} } [/tex]
[tex]\frac{dy}{dx} = 2 {t}^{2} [/tex]
At x=5,
[tex]5 = 5 + ln(t) [/tex]
[tex] ln(t) = 0[/tex]
[tex]t = {e}^{0} = 1[/tex]
This implies that,
[tex]\frac{dy}{dx} = 2 {(1)}^{2} = 2[/tex]
The slope of the tangent is 2.
The equation of the tangent through
(5,6) is given by
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y - 6 = 2(x - 5) =[/tex]
[tex]y = 2x -4[/tex]
The equation of the tangent to the curve at the point (5,6) is [tex]\(y = 2x - 4\)[/tex].
To find the equation of the tangent to the curve given by the parametric equations [tex]\(x = 5 + \ln(t)\)[/tex] and [tex]\(y = t^2 + 5\)[/tex] at the point (5,6), we can approach this problem in two ways: by eliminating the parameter \(t\) and without eliminating the parameter.
Method 1: Eliminating the Parameter
Step 1: Express (t) in terms of (x)
[tex]\[ x = 5 + \ln(t) \implies \ln(t) = x - 5 \implies t = e^{x-5} \][/tex]
Step 2: Substitute (t) into (y)
[tex]\[ y = t^2 + 5 \implies y = (e^{x-5})^2 + 5 \implies y = e^{2(x-5)} + 5 \][/tex]
Step 3: Find [tex]\(\frac{dy}{dx}\)[/tex]
[tex]\[ y = e^{2(x-5)} + 5 \][/tex]
[tex]\[ \frac{dy}{dx} = 2e^{2(x-5)} \][/tex]
Step 4: Evaluate [tex]\(\frac{dy}{dx}\)[/tex] at (x = 5)
[tex]\[ \frac{dy}{dx}\bigg|_{x=5} = 2e^{2(5-5)} = 2e^0 = 2 \][/tex]
Step 5: Equation of the tangent line
The slope (m = 2). The tangent line at (5,6) is:
[tex]\[ y - 6 = 2(x - 5) \][/tex]
[tex]\[ y = 2x - 10 + 6 \][/tex]
[tex]\[ y = 2x - 4 \][/tex]
Method 2: Without Eliminating the Parameter
Step 1: Find [tex]\(\frac{dx}{dt}\)[/tex] and [tex]\(\frac{dy}{dt}\)[/tex]
[tex]\[ x = 5 + \ln(t) \implies \frac{dx}{dt} = \frac{1}{t} \][/tex]
[tex]\[ y = t^2 + 5 \implies \frac{dy}{dt} = 2t \][/tex]
Step 2: Find [tex]\(\frac{dy}{dx}\)[/tex]
[tex]\[ \frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}} = \frac{2t}{\frac{1}{t}} = 2t^2 \][/tex]
Step 3: Find (t) at the point (5,6)
From [tex]\(x = 5 + \ln(t)\)[/tex]:
[tex]\[ 5 = 5 + \ln(t) \implies \ln(t) = 0 \implies t = e^0 = 1 \][/tex]
Step 4: Evaluate [tex]\(\frac{dy}{dx}\)[/tex] at (t = 1)
[tex]\[ \frac{dy}{dx}\bigg|_{t=1} = 2(1)^2 = 2 \][/tex]
Step 5: Equation of the tangent line
The slope (m = 2). The tangent line at (5,6) is:
[tex]\[ y - 6 = 2(x - 5) \][/tex]
[tex]\[ y = 2x - 10 + 6 \][/tex]
[tex]\[ y = 2x - 4 \][/tex]
Thus, using both methods, the equation of the tangent to the curve at the point (5,6) is [tex]\(y = 2x - 4\)[/tex].
The area of a rectangle is 144 square centimeters. The width is 9 centimeters. Which of the following statements is true? Select all that apply. A. The length is 3 times the width. B. The length is 63 centimeters. C. The length is less than 2 times the width. D. The perimeter is 50 centimeters. E. The rectangle is a square since its length and width are equal.
Answer:
Option C and D are correct.
Step-by-step explanation:
Area of rectangle = 144 cm^2
Width of rectangle = 9 cm
Length of rectangle = ?
We know,
Area of rectangle = Length * Width
144 = Length * 9
144/9 = Length
=> length = 16 cm
Option A is incorrect as 3 times width = 3* 9 = 27 but our length = 16 cm
Option B is incorrect as length = 16 cm and not 63 cm
Option C is correct as Length < 2(Width)
=> 16 < 2(9) => 16 < 18 which is true.
Option D is correct.
Perimeter = 2(Length + Width)
Perimeter = 2(16+9)
Perimeter = 50 cm
Option E is incorrect as Length ≠ Width
Answer:
C. The length is less than 2 times the width.
D. The perimeter is 50 centimeters.
Step-by-step explanation:
The area of the rectangle is given as 144 square centimeters and its width is 9 centimeters. The formula for the area of a rectangle is given as;
Area = length*width
144 = length*9
length = 144/9
length = 16 centimeters
A. The length is 3 times the width.
3 times the width; 3*9 = 27 cm which is not equal to 16. Hence this statement is false.
B.The length is 63 centimeters.
This statement is also false since the length is 16 cm
C.The length is less than 2 times the width.
Doreen Schmidt is a chemist. She needs to prepare 24 ounces of a 9% hydrochloric acid solution. Find the amount of 12% solution and the amount of 6% solution she should mix to get this solution.
PLEASE HELP ME
Answer:
Step-by-step explanation:
So we need to balance two things here. The overall volume, and the amount of hydrochloric acid.
Let's say x is the volume of the 12% solution and y is the volume of the 6% solution.
The sum of the volumes equals the total volume:
x + y = 24
And the sum of the amounts is the total amount:
0.12 x + 0.06 y = 0.09 (24)
We now have two equations and two variables. We can solve this system of equations with either substitution or elimination. Using substitution:
x = 24 - y
0.12 (24 - y) + 0.06 y = 0.09 (24)
2.88 - 0.12 y + 0.06 y = 2.16
0.72 = 0.06 y
y = 12
x = 24 - 12 = 12
So she needs to mix 12 ounces of 12% solution with 12 ounces of 6% solution to get 24 ounces of 9% solution.
The amount of 12% solution and the amount of 6% solution Doreen Schmidt should mix to obtain 9% hydrochloric acid solution is 12 ounces each.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Let the amount of 12% solution needed to be mixed be represented by x, while the amount of 6% solution needed to be mixed be represented by y.
Now, since the total amount of solution needed to be made is 24 ounces, therefore, an equation can be formed as,
x+y=24
Solve the equation of x,
x=24 - y
Also, the total concentration of the combined should be 9%, therefore, we can write,
(12% of x) + (6% of y) = 9% of 24
0.12x + 0.06y = (0.09×24)
Substitute the value of x,
0.12(24-y) + 0.06y = 2.16
2.88 - 0.12y + 0.06y = 2.16
y = 12 ounces
substitute the value of y in the equation of x,
x = 24 - y
x = 24 - 12
x = 12
Hence, the amount of 12% solution and the amount of 6% solution Doreen Schmidt should mix to obtain 9% hydrochloric acid solution is 12 ounces each.
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please help me asap 12 PTS
Answer:
D.
Step-by-step explanation:
I also haven't learned this yet but i could tell that in the second image if A.F = 1/2AC and DE = A.F, therefore DE = 1/2AC. The problem is that i don't know if it is B or D.
Sorry .-.
A cone with volume 5000 m^3 is dilated by a scale factor of 1/5
ANSWER
The volume of the dilated cone is
[tex]40 {m}^{3}[/tex]
EXPLANATION
The volume of the given cone is
[tex]5000 {m}^{3} [/tex]
When this cone is dilated with a scale factor of 1/5, the volume of the dilated cone becomes,
[tex] ({ \frac{1}{5} })^{3} \times 5000 {m}^{3} [/tex]
We simplify to obtain:
[tex] { \frac{1}{125} }\times 5000 {m}^{3} [/tex]
This gives us:
[tex]40 {m}^{3} [/tex]
Final answer:
When a cone is scaled down by a factor of 1/5, its new volume is 40 m³, calculated by cubing the scale factor and multiplying it by the original volume.
Explanation:
When a cone is dilated by a scale factor, its volume changes according to the cube of that scale factor.
Since the original volume of the cone is 5000 m³ and the scale factor is 1/5, we use the proportionality principle which states that the volume of a shape is proportional to the cube of its linear dimensions (V ∝ L3).
Therefore, if we dilate the cone by a scale factor of 1/5, the new volume (V1) would be:
V1 = V-original × (scale factor)³
= 5000 m³ × (1/5)³
= 5000 m³ × 1/125
= 40 m³
This calculation shows that, as a result of applying the scale factor, the volume of the cone has been reduced significantly.
A physician prescribes alprazolam for a patient on an as needed basis. The patient can take up to 2.25mg per day in divided does. If alprazolam comes in .25 mg tablets, how many tablets can the patient take throughout the day?
Answer:
9
Step-by-step explanation:
If n is the number of tablets, the maximum value it can have is given by ...
0.25n = 2.25
Dividing by the coefficient of n gives ...
n = 2.25/0.25 = 9
The patient can take a total of 9 tablets through the day.
Answer:
The answer is 2:9
Step-by-step explanation:
On plato
Plz help ASAP!! Explain your answer! I will mark at brainliest!!! And don’t copy anybody else’s answer
Answer:
No. Anna is incorrect.
Step-by-step explanation:
In order to find if the answer is right, just find the diagonals using the pythogorean theorem.
a² + b² = c²
For the rectangle, the base is 14 and the height is 7. We will have to find the hypotenuse.
14² + 7² = c²
196 + 49 = c²
245 = c²
c = √245
c = √49 × √5
c = 7√5
For the square, the base is 7 and the height is 7. We will have to find the hypotenuse.
7² + 7² = c²
49 + 49 = c²
98 = c²
c = √98
c = √49 × √2
c = 7√2
Now compare :
7√5 and 7√2
Clearly, 7√5 is not the double of 7√2
The lengths of two sides of a parallelogram are 24 cm and 15 cm. One angle measures 120°. Find the length of the longer diagonal.
A) 13.3 cm
B) 34.1 cm
C) 177.5 cm
D) 1161 cm
Answer:
B) 34.1 cm
Step-by-step explanation:
The longer diagonal is longer than either side, but shorter than their sum. The only answer choice in the range of 24–39 cm is choice B.
_____
You are given sufficient information to use the Law of Cosines to find the diagonal length. If we call it "c", then the angle opposite that diagonal is the larger of the angles in the parallelogram: 120°. The law of cosines tells you ...
c^2 = a^2 +b^2 -2ab·cos(C)
Here, we have a=24, b=15, C=120°, so ...
c^2 = 24^2 +15^2 -2·24·15·cos(120°) = 576 +225 +360 = 1161
c = √1161 ≈ 34.073 . . . . cm
Rounded to tenths, the diagonal length is 34.1 cm.
....Help Please.......
Answer:
y = 2x+3
Step-by-step explanation:
The slope is "what happens to the graph when you move one unit to the right in x-direction". As you can check, if you move 1 to the right, the y value increases by 2. Therefore the slope is 2.
The intercept is the graph's y value when x=0, ie., when it passes the y axis. This is at y=3.
Now we have our two ingredients, so y = slope * x + intercept, so 2x+3
The National Football League (NFL) polls fans to develop a rating for each football game (NFL website, October 24, 2012). Each game is rated on a scale from 0 (forgettable) to 100 (memorable). The fan ratings for a random sample of 12 games follow. 57 61 86 74 72 73 20 57 80 79 83 74 a. Develop a point estimate of mean fan rating for the population of NFL games. b. Develop a point estimate of the standard deviation for the population of NFL games.
The point estimates for the mean and standard deviation of the given data set is respectively; 68 and 17.6.
What is a point Estimate?
A) In order to find the point estimate of the mean, we will add up the data and divide it by the number of values.
Here,
∑x = 57 + 61 + 86 + 74 + 72 + 73 + 20 + 57 + 80 + 79 + 83 + 74
= 816
n = 12 numbers
Thus;
Mean = ∑x/n
= 816/12
Mean = 68
B) In order to find the estimate of the standard deviation, we have the formula;
s = √[(n*(∑x²) - (∑x)²)/n(n - 1)]
∑x² = 57² + 61² + 86² + ... + 74²
= 59,010
s = √[ (12*(59,010) - (816)²)/(12)(11)]
s = 17.6
Hence, The point estimates for the mean and standard deviation of the given data set is respectively; 68 and 17.6.
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Find the value of x in the figure below. Show all your work.
Answer:
x = 52/9
Step-by-step explanation:
The exterior angle is half the difference of the intercepted arcs, so we have ...
9x -5 = (158 -64)/2
9x = 52 . . . . . . . . . . . add 5
x = 52/9 = 5 7/9
Nickola swam at a rate of 2 km/hr and ran at a rate of 15 km/hr for a total distance traveled of 90.5 km. If he completed the race in 9.5 hours, how long did he take to
complete each part of the race?
The time Nickola spent swimming is______? hours, and the time he spent running is_____? hours.
I NEED HELP PLEASE
Answer:
Nickola swam for 4 hours and ran for 5.5 hours
Step-by-step explanation:
To solve this, we can use a system of equations.
First we can set up a system of equations like this
[tex]2s+15r=90.5[/tex] and
[tex]s+r=9.5[/tex]
Next we will use substitution to solve for one of the values. We can solve the second equation such that
[tex]s=9.5-r[/tex]
Now we can substitute this into the first equation for s
[tex]2(9.5-r)+15r=90.5[/tex]
Now we can solve for r
[tex]19-2r+15r=90.5[/tex]
[tex]19+13r=90.5[/tex]
[tex]13r=71.5[/tex]
[tex]r=5.5[/tex]
Now we can plug this value into the second equation to get the value for s
[tex]s+5.5=9.5[/tex]
[tex]s=4[/tex]
Now we can plug these values into the first equation to make sure we have the right values
[tex]2(4)+15(5.5)=90.5[/tex]
[tex]90.5=90.5[/tex]
14/30÷14.00 show all work
1 Simplify \frac{14}{30}
30
14
to \frac{7}{15}
15
7
.
\frac{7}{15}\div 14.00
15
7
÷14.00
2 Use this rule: a\div \frac{b}{c}=a\times \frac{c}{b}a÷
c
b
=a×
b
c
.
\frac{7}{15}\times \frac{1}{14.00}
15
7
×
14.00
1
3 Use this rule: \frac{a}{b}\times \frac{c}{d}=\frac{ac}{bd}
b
a
×
d
c
=
bd
ac
.
\frac{7\times 1}{15\times 14.00}
15×14.00
7×1
4 Simplify 7\times 17×1 to 77.
\frac{7}{15\times 14.00}
15×14.00
7
5 Simplify 15\times 14.0015×14.00 to 210210.
\frac{7}{210}
210
7
6 Simplify.
1/30
The last answer choice is 15/2, 10
Helppp
Find the points of Midtown and Downtown then use the midpoint formula.
Midtown = (6,12)
Downtown = (12,4)
Midpoint = X2+X1 /2 , Y2+Y1 /2
Midpoint = 12+6 /2 , 4+12 /2
Midpoint = 18/2 , 16,2
Midpoint = (9,8)