Answers
Answer:
82.6%
Step-by-step explanation:
Conditional probability is defined as:
P(A|B) = P(A∩B) / P(B)
where P(A|B) is the probability of A on the condition of B, P(A∩B) is the probability of both A and B, and P(B) is the probability of B.
Here, we want P(P|K), so:
P(P|K) = P(P∩K) / P(K)
P(P|K) = 0.019 / 0.023
P(P|K) = 0.826
82.6% of the members in the key club are also enrolled in AP Physics.
Related Questions
Which expression equivalent to 9x^5 y^16 over 45x^5 y^4
Answers
the answer after simplify is:
[tex] \frac{ 9{x}^{5} {y}^{16} }{45 {x}^{5} {y}^{4} } = \frac{ {y}^{12} }{5} [/tex]
Answer:
[tex]\large\boxed{\dfrac{1}{5}y^{12}}[/tex]
Step-by-step explanation:
[tex]\text{Use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\\dfrac{9x^5y^{16}}{45x^5y^4}=\dfrac{9\!\!\!\!\diagup^1}{45\!\!\!\!\!\diagup_5}x^{5-5}y^{16-4}=\dfrac{1}{5}y^{12}[/tex]
If the graph of y= |x| is translated so that the point (1, 1) is moved to (4,1), what is the equation of the new graph?
Answers
Answer:
The new equation is y= (x-3)
Step-by-step explanation: we know that the point (1, 1) is moved to (4,1).
So, the rule of the translation is: [tex](x,y) -----> (x+3, y)[/tex]
that means the translation is 3 units to the right
Answer:
[tex]y=|x-3|[/tex]
Step-by-step explanation:
The parent absolute function is
[tex]y=|x|[/tex]
The graph of y= |x| is translated so that the point (1, 1) is moved to (4,1). It means the rule of translation is
[tex](x,y)\rightarrow (x+3,y)[/tex]
it means the graph of y=|x| translated 3 units right. So, the new vertex of the function is (3,0).
The vertex form of an absolute function is
[tex]y=|x-h|+k[/tex]
The new vertex of the function is (3,0). Substitute h=3 and k=0 in the above equation.
[tex]y=|x-3|+0[/tex]
[tex]y=|x-3|[/tex]
Therefore, the required equation is y=|x-3|.
Which statements are correct regarding mathematics in the Egyptian, Chinese, and Babylonian cultures? Check all the apply.
A.) Both the Egyptian and Chinese number systems use base 10.
B.)The Babylonian tablets have all the solution methods clearly shown.
C.)All three cultures had unique symbolism to represent their numbers.
D.)There are two primary sources for ancient Egyptian mathematics.
E.)Ancient Chinese mathematicians did not attempt to solve systems of linear equations.
Answers
Answer:
A,C,D
Step-by-step explanation:
Answer:
The following are the correct statements regarding mathematics in the Egyptian, Chinese, and Babylonian cultures:
A - Both Egyptian and Chinese number systems use base 10.
C - All three cultures had unique symbolism to represent their numbers(Earlier symbols were used to depict things)
D - There are two primary sources for ancient Egyptian mathematics(The primary sources are the Rhind Papyrus and the Moscow Papyrus)
Explain how to determine whether two known pairs of points are on the same line.
Answers
Answer:
Sample response: Use the slope formula three times: once for the first pair of points, then for the second pair of points, then for one point from each pair. If all three slopes are the same, then all the points lie on the same line.
Which did you include in your response:
Use the slope formula three times.If the slopes of both pairs are equal, then the lines may be parallel.If all three slopes are equal, including the slope using one point from each pair, then all the points coincide on the same line.The way in which a person can accurately determine whether two known pairs of points are on the same line is:
The use of the slope formula three different times.One of the ways through which a person can accurately determine whether two known points are on the same line when using a linear graph is to make use of the slope formula.
With this in mind, we can see that this slope formula is used to find the different pair of points on the graph to check if they all lie on the same line.
In conclusion, we can come to the determination that:
The lines are likely parallel if the slopes on the two pairs are equalIf the slopes are all equal, then all the points meet on the same line.Read more about slope formula here:
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Help!!!!! NEED HELP WITH INTRODUCTION TO INEQUALITIES
need help with Introduction to inequalities its says circle the numbers in the replacement set that make each inequality true. With questions 1,3,5,7
Answers
< less than ≤ less than or equal to (line underneath sign)
> greater than ≥ greater than or equal to (line underneath sign)
# is just the number they gave you in the inequality
x < # [you can put any number into "x", but it has to be less than #]
x > # [you can put any number into "x", but it has to be greater than #]
x ≤ # [number has to be less than or equal to #]
x ≥ # [number has to be greater than or equal to #]
1. t < 7 [t is a number less than 7]
So you circle: 4, 6, 8, 0, -6
3. a ≤ -4 [a is a number less than or equal to -4]
circle: -7, -4
5.
k + 5 < 9 You can simplify this by subtracting 5 on both sides
k < 4 [k is a number less than 4]
circle: -1, 3, -2, 3.5
7. u - 5 ≥ -1 Simplify
u ≥ 4 [u is a number greater than or equal to 4]
circle: 4, 5, 4.1
Write the number 7 ones 9 tens 9 hundreds
Answers
Answer:
997
From right to left, the place values are, ones, tens, hundreds, thousands, etc.
The number with '7 ones', '9 tens', and '9 hundreds' is written as 997 in numeral form, by combining the values of each digit based on their place value.
When writing the number that consists of '7 ones', '9 tens', and '9 hundreds', we are dealing with a three-digit number where each place value represents a power of 10. To construct the number, we consider the value each digit represents:
The '9 hundreds' means 9 × 100 (which is 900).
The '9 tens' means 9 × 10 (which is 90).
The '7 ones' means 7 × 1 (which is 7).
Adding these values together, we have 900 (hundreds) + 90 (tens) + 7 (ones), which equals 997. This is the decimal representation of the number expressed by the student.
Therefore, the number 7 ones 9 tens 9 hundreds written in numeral form is 997.
If f(x) = 1-x which value is equivalent to |f(I)|
Answers
Answer:given that
F (x)=1-x
Step-by-step explanation:
Answer:
The value of |f(i)| is √2.
Step-by-step explanation:
The given function is
[tex]f(x)=1-x[/tex]
We need to find the value of |f(i)|.
Substitute x=i in the given function.
[tex]f(i)=1-i[/tex]
Taking modulus on both the sides.
[tex]|f(i)|=|1-i|[/tex]
Using the formula for modulus of a complex number, we get
[tex]|f(i)|=\sqrt{(1)^2+(-1)^2}[/tex] [tex][\because |a+ib|=\sqrt{a^2+b^2}][/tex]
[tex]|f(i)|=\sqrt{1+1}[/tex]
[tex]|f(i)|=\sqrt{2}[/tex]
Therefore the value of |f(i)| is √2.
The school is t blocks from Jim's house. The library is twice as far as the school is from Jim's house. How far is the library?
Answers
Answer:
2t blocks
Step-by-step explanation:
We measure these distances from Jim's house.
The school is t blocks from Jim's house. Twice that is 2t blocks. Thus, the library is 2t blocks from Jim's house.
I have a circular piece of fabric I am going to make a tablecloth. The radius of the fabric is 2 meters. What is the area of the tablecloth I can make
Answers
Answer:
[tex]4\pi[/tex]
or
12.57
Step-by-step explanation:
I have a circular piece of fabric I am going to make a tablecloth. The radius of the fabric is 2 meters. What is the area of the tablecloth I can make
Essentially, you are attempting to find the area of a circle with a radius of 2 meters.
The formula for an area of a circle is [tex]\pi r^2[/tex], or pi times radius squared.
Plugging in 2 meters as your radius, that gets your answer to be [tex]4\pi[/tex], or 12.57 in decimal.
suppose that f(x) = x^2 and g(x) = 2/5 x^2 which statement best compares the graph of g(x) with the graph of f(x) A.the graph of g(x) is the graph of f(x) compressed vertically and flipped over the x-axis b.the graph of g(x) is the graph of f(x) compressed vertically c. the graph of g(x) is the graph of f(x) stretched vertically and flipped over the x-axis
Answers
Answer:
b.the graph of g(x) is the graph of f(x) compressed vertically
Step-by-step explanation:
The given functions are
[tex]f(x)=x^2[/tex]
and
[tex]g(x)=\frac{2}{5}x^2[/tex]
This is a transformation in the form
[tex]y=a*f(x)[/tex] where [tex]a=\frac{2}{5}[/tex]
Since 0<a<1, the graph of f(x) is compressed vertically by a factor of
[tex]\frac{2}{5}[/tex]
A function assigns the value of each element of one set to the other specific element of another set. The correct option is B.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
When the graph of the two function f(x) and g(x) is plotted, then it can be observed that the graph of g(x) is the graph of f(x) compressed vertically.
Hence, the correct option is B.
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Which equations have the same value of x as 5/6 x + 2/3 ? Check all that apply.
Answers
Answer:
B. [tex]6(\frac{5}{6} x+\dfrac{2}{3}) =-9(6)[/tex]
C. 5x + 4 = -54
F. 5x = -58
Step-by-step explanation:
Solving given equation step to step:
The given equation is a linear form and to solve for x.
[tex] \dfrac{5}{6} x+\dfrac{2}{3}=-9\\\Rightarrow6(\dfrac{5}{6} x+\dfrac{2}{3}) =-9(6)\ \ \ \ \ [\because \text{Multiplying both side by 6}]\\\Rightarrow 6(\dfrac{5x+4}{6}) =-9(6)\ \ \ \ \ [\because text{taking LCM of 6 and 3} ]\\\Rightarrow 5x+4=-9(6)\\\Rightarrow 5x+4 =-54\\\Rightarrow 5x =-54-4\\\Rightarrow 5x =-58 [/tex]
What is the direct variation equation iffy varies directly with x and y = 12 when x= 6
Answers
Answer:
y = 2x
Step-by-step explanation:
Given that y varies directly as x then the equation relating them is
y = kx ← k is the constant of variation
To find k use the condition y = 12 when x = 6
k = [tex]\frac{y}{x}[/tex] = [tex]\frac{12}{6}[/tex] = 2, hence
y = 2x ← equation of variation
The surface area of which composite figure is the sum of the areas of eight triangular faces?
Atwo rectangular pyramids joined at their congruent bases
Btwo rectangular pyramids joined at two congruent lateral faces
Ctwo triangular prisms joined at their congruent bases
Dtwo triangular prisms joined at two congruent lateral faces PLZ HELP ME ;C
Answers
The answer is B)Two rectangular pyramids joined at two congruent lateral faces
Answer:
Option B. is the answer.
Step-by-step explanation:
As you can see from the figure attached, Rectangular pyramid has five faces. Four triangular and one rectangular face.
In this question we have to find the a composite figure which has eight triangular faces.
Therefore, by adding two rectangular pyramids by common rectangular base we can get the composite figure with eight triangular faces.
Option B. will be the answer.
Find the value of this expression if x=-6 x^2-6/x-4
Answers
Answer:
x=−0.825789
Step-by-step explanation:
x=(−6x3−4x−6)/x
Step 1: Multiply both sides by x.
x2=−6x3−4x−6
x2−(−6x3−4x−6)=−6x3−4x−6−(−6x3−4x−6)(Subtract -6x^3-4x-6 from both sides)
6x3+x2+4x+6=0
(Use cubic formula)
x=−0.825789
Answer:
- 3
Step-by-step explanation:
Substitute x = - 6 into the expression
[tex]\frac{(-6)^2-6}{-6-4}[/tex]
= [tex]\frac{36-6}{-10}[/tex] = [tex]\frac{30}{-10}[/tex] = - 3
In the United States, birth weights of newborn babies are approximately normally distributed with a mean of μ = 3,500 g and a standard deviation of σ = 500 g.
What percent of babies born in the United States are classified as having a low birth weight (< 2,500 g)? Explain how you got your answer.
answer:The z-score for 2,500 g is –2.
According to the empirical rule, 95% of babies have a birth weight of between 2,500 g and 4,500 g.
5% of babies have a birth weight of less than 2,500 g or greater than 4,500 g.
Normal distributions are symmetric, so 2.5% of babies weigh less than 2,500g.
Answers
The z-score for 2,500 g is –2.According to the empirical rule, 95% of babies have a birth weight of between 2,500 g and 4,500 g.5% of babies have a birth weight of less than 2,500 g or greater than 4,500 g.Normal distributions are symmetric, so 2.5% of babies weigh less than 2,500g.
2.5% of babies weigh less than 2,500g.
Empirical ruleEmpirical rule states that for a normal distribution, 68% of the values are within 1 standard deviation from the mean, 95% of the values are within 2 standard deviation from the mean and 99.7% are within 3 standard deviation from the mean.
Given that mean (μ) = 3,500 g and a standard deviation of σ = 500 g.
95% of babies have a birth weight of between two standard deviation = 2,500 g and 4,500 gHence 2.5% of babies weigh less than 2,500g.
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The speed limit on a highway is 55 mph. A speed sensor showed that a car went 900 ft in 8 s. Is the car traveling over the speed limit? Explain.
Answers
Answer:
900 feet / 5,280 = 0.1704545... miles
8 seconds / 3,600 = 0.0022222222 hours
0.1704545 miles / 0.0022222222 hours = 76.704525767 miles per hour
The car is well over the speed limit
Step-by-step explanation:
A rectangle's length and width are in a ratio of 5:2. The area is 160 square centimeters. What are the length and width?
If you could solve this please do so asap
Answers
Answer: The length and width are 20 square centimeters and 8 square centimeters
Explain: 20:8 can be reduced to 5:2 as a ratio. 20 times 8 equals 160.
Answer:
length = 20 cm and width = 8 cmStep-by-step explanation:
l - length
w - width
length and width are in a ratio of 5:2
[tex]\dfrac{l}{w}=\dfrac{5}{2}[/tex] cross multiply
[tex]2l=5w[/tex] divide both sides by 2
[tex]l=\dfrac{5w}{2}[/tex]
the area is 160cm²
[tex]lw=160[/tex]
We have the system of equations:
[tex]\left\{\begin{array}{ccc}l=\dfrac{5w}{2}&(1)\\lw=160&(2)\end{array}\right[/tex]
Substitute (1) to (2):
[tex]\left(\dfrac{5w}{2}\right)(w)=160\\\\\dfrac{5w^2}{2}=160\qquad\text{multiply both sides by 2}\\\\5w^2=320\qquad\text{divide both sides by 5}\\\\w^2=64\to w=\sqrt{64}\\\\w=8[/tex]
Put the value of w to (1):
[tex]l=\dfrac{(5)(8)}{2}=\dfrac{40}{2}=20[/tex]
Kai is conducting a study about the percentage of students with jobs. His school has 2500 students. He asks everyone in his drama class to participate in a survey. He bases his findings on these results. Is this a valid study? Why or why not?
A) YES, he asked everyone in his class.
B) YES, since drama students tend to have after-school jobs.
C) NO, he should have taken a small sample from the drama class.
D) NO, the drama class does not represent all students in the school.
Answers
Answer: D
Step-by-step explanation:
That is a small sample out of the entire school
you have $47 to spend at the music store. Each cassette tape costs $5 and each CD cost $10. write a linear inequality that represent this situation. let x represent the number of tapes and y the number of CDs
Answers
Answer:
47 is greater than or equal to 5x+10y
Step-by-step explanation:
you can't spend more than $47 but you can spend less than or equal to that amount.
Answer:5x+10y=47
Step-by-step explanation:
Given
$47 money needed to spend
Each cassette tape cost $5
and each CD cost $10
Given no of cassette be x and no of CD be y
Thus cost of x cassette is 5x
cost of Y CD's 10y
Total cost=5x+10y
5x+10y=47
Find u•v when u= 12i+4j and v=15i-5j
Answers
Answer:
180i^2 - 20j^2
Step-by-step explanation:
u.v
(12i+4j) . (15i-5j)
12i(15i-5j) + 4j(15i-5j)
180i square -60ij + 60ij-20j square
180i^2 - 20j^2
The value of the dot product of the two vectors is u · v = -160.
What are vectors?The product of vectors can refer to several different operations, including the dot product, cross product, and scalar multiplication.
Dot Product:
The dot product of two vectors u and v is a scalar given by the formula:
u · v = ||u|| ||v|| cos θ
We have,
To find the dot product of two vectors, we need to multiply their corresponding components and add up the results:
u · v
= (12i + 4j) · (15i - 5j)
= 12i · 15i + 12i · (-5j) + 4j · 15i + 4j · (-5j)
= 180i^2 - 60ij + 60ij - 20j² [since i² = j² = -1]
= 180(-1) - 20(-1) [since ij = ji = 0]
= -160
Therefore,
The value of the dot product of the two vectors is u · v = -160.
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which of the following is true about the expression5*1/4
Answers
Answer:
C. It represents the product of two rational numbers and its equivalent to a rational number.
Step-by-step explanation:
5 is a natural number, a real number and a rational number.
[tex]\frac{1}{4}[/tex] is a real number and a rational number.
The product of 5 × [tex]\frac{1}{4}[/tex] = 1.25 which is also a rational number in addition to being a real number.
Answer:
The correct answer is option C.
Step-by-step explanation:
It s given that 5 * 1/4
To find the correct answer
The given expression is 5 * 1/4
Here 5 is a rational number and 1/4 is a rational number
5 * 1/4 = 5/4
The number 5/4 is a rational number.
5/4 represents the product of two rational numbers and is equivalent to a rational number.
Therefore the correct answer is option C
our product is 72. the difference between us is 1. what number are we?
Answers
Answer: 8 and 9
Step-by-step explanation:
8 times 9 equals 72
9 minus 8 equals 1.
find the quotient 3/4 ÷ 6/7.=
Answers
[tex]\bf \cfrac{3}{4}\div \cfrac{6}{7}\implies \cfrac{3}{4}\cdot \cfrac{7}{6}\implies \cfrac{7}{4}\cdot \cfrac{3}{6}\implies \cfrac{7}{4}\cdot\cfrac{1}{2}\implies \cfrac{7}{8}[/tex]
Suppose that the local sales tax rate is 7% and you purchase a car for 11,100 how much tax is paid?
Answers
Answer:
11877
Step-by-step explanation:
11100 * 7% = 777
11100 + 777 = 11877
When you multiply by 7%, you get the amount of additional tax. You add this to the original amount to get the answer.
I understand what they are asking, but I am wondering how you describe the verbal description and the algebraic representation?
Answers
Answer:
hmmm
Step-by-step explanation:
hmmm
i have 3 questions can you answer them?
what is 73 divided by 8967
what is 91 divided by 8743
and what is 37 divided by 86,322 ?????????????????
Answers
73 divided by 8967:
0.0081409613
91 divided by 8743:
0.01040832666
37 divided by 86322:
0.00042862769
The area of a square can be found using the equation A= s2, where A is the area and S is the measure of one side of the square. Match the equation for how to slice for the side length of a square to its description. A square has area of 99 in2
Answers
Answer:
the answer is the first option
The correct answer is [tex]\sqrt{99}[/tex] in.
What is a square?
A 2-dimensional figure bounded by 4 sides having 4 corners and hence 4 angles, in which all the sides are equal and opposite sides are parallel and all the angles are 90° is called a square. In a square the diagonals bisects each other at right angles.
How to find the area of a square?Area of square can be found by squaring the length of a side.How find length of each side of the square?In the question, the area of the square is given 99 in²
According to the problem,99 = S², S is the measure of one side of the square.
Length of each side will be [tex]\sqrt{99}[/tex] in.
Option a is correct.
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PLEASE HELP 14 POINTS
Answers
[tex] \frac{27}{30} \times 100\% \\ = 90\%[/tex]
Approximately 90 percent voted for her
Which statement best explains why the equation X +2=3x-14 can be used to slice for x ?
Answers
Answer:c
Diagonals bisect each other
Step-by-step explanation:
This cute the diagonal into two equal parts
Answer: Diagonals of a rhombus bisect each other
Step-by-step explanation:
i got that right
What is the distance between the points (1, 3) and (9, 9)?
a. 8 units
b. 10 units
c. 6 units
d. 12 units
Answers
the answer is 10 units
[tex]distance = \sqrt{(9 - 1) ^{2} + (9 - 3) {}^{2} } \\ = \sqrt{ {8}^{2} + {6}^{2} } \\ = 10[/tex]
The distance between points (1, 3) and (9, 9) will be 10 units so option (b) will be correct.
What are coordinates?A pair of numbers that employ the horizontal and vertical distinctions from the two reference axes to represent a point's placement on a coordinate plane. typically expressed by the x-value and y-value pairs (x,y).
For instance, in this case (5,3), 5 will represent the x and 3 the y.
(9,0) is another illustration, where 9 stands for x and 0 for y.
Coordinates are always written in the form of small brackets the first term will be x and the second term will be y.
The distance between two points (x₁,y₁) and (x₂,y₂) is given by
[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]
So,
Distance between (1, 3) and (9, 9)
[tex]d = \sqrt {\left( {1- 9 } \right)^2 + \left( {3 -9 } \right)^2 }[/tex]
d = √(64 + 36) = 10 units.
Hence, The distance between points (1, 3) and (9, 9) will be 10 units
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