Answer:
A. x=2 y=7
Step-by-step explanation:
-12x -3 = 3y
6x + 3y = 33
sooo you add them up...
so its
-6x = -12
x=2
and then you plug in the x value into one of the equations
6x + 3y = 33
6(2) + 3y = 33
12 + 3y = 33
3y = 33 - 12
3y = 21
21/3=7
y=7
In an examination every student took history or geography or both of 500 candidates 60% took history whiles 72% took geography. How many students took both subjects
Answer:
80 students
Step-by-step explanation:
Answer:
80
Step-by-step explanation:
60% of 500 = 300
72% of 500 = 360
40% of 500 = 200
28% of 500 = 140
300+360 = 660
660 - 2x = 500
660 - 500 = 2x
160 = 2x
2x = 160
x = 80
A statistician calculates that 7% of Americans are vegetarians. If the statistician is correct, what is the probability that the proportion of vegetarians in a sample of 403 Americans would differ from the population proportion by more than 3%
Answer:
0.0182 = 1.82% probability that the proportion of vegetarians in a sample of 403 Americans would differ from the population proportion by more than 3%.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
A statistician calculates that 7% of Americans are vegetarians.
This means that [tex]p = 0.07[/tex]
Sample of 403 Americans
This means that [tex]n = 403[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.07[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.07*0.93}{403}} = 0.0127[/tex]
What is the probability that the proportion of vegetarians in a sample of 403 Americans would differ from the population proportion by more than 3%?
Proportion below 7 - 3 = 4% or above 7 + 3 = 10%. Since the normal distribution is symmetric, these probabilities are equal, which means that we find one of them, and multiply by 2.
Probability the proportion is below 4%
p-value of Z when X = 0.04.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.04 - 0.07}{0.0127}[/tex]
[tex]Z = -2.36[/tex]
[tex]Z = -2.36[/tex] has a p-value of 0.0091
2*0.0091 = 0.0182
0.0182 = 1.82% probability that the proportion of vegetarians in a sample of 403 Americans would differ from the population proportion by more than 3%.
You are dealt one card from a 52-card deck.
a) Find the odds in favor of getting a red king.
b) Find the odds against getting a red king.
Answer:
(a)So, there are 2 kings in red- one of hearts and the other of diamonds. Therefore, the probability of selecting a red king from a deck of cards= 2/52 or 1/26.
(b) There are 6 red face cards in a 52-card deck (so 46 other cards). PROBABILITIES compare the number of favorable outcomes to the total number of possible outcomes: The PROBABILITY of getting a red face card is 6/52 = 3/26.
The odds in favor of getting a red king will be 1/26. And the odds against getting a red king will be 25/26.
What is probability?Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.
You are dealt one card from a 52-card deck.
Total events = 52
The odds in favor of getting a red king will be
Favorable events = 2
Then the probability will be
P = 2/52
P = 1/26
The odds against getting a red king will be
q = 1 – P
q = 1 – 1/26
q = 25/26
More about the probability link is given below.
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Warren drives his car 330 miles and has an average of a certain speed. If the average speed had been 3 mph more. he could have traveled 352 miles in the same length
of time. What was his average speed?
Keypad
Answer:
45 miles per hour
Step-by-step explanation:
d=distance in miles
r=rate miles/hr
t = time in hours
t = 352/(r+3)
330/r = 352/(r+3)
352r = 330r + 990
22r = 990
r = 45
The radius of a sphere is increasing at a rate of 2 mm/s. How fast is the volume increasing (in mm3/s) when the diameter is 60 mm?
Answer:
22608 mm³/s
Step-by-step explanation:
Applying chain rule,
dV/dt = (dV/dr)(dr/dt)............... Equation 1
Where dV/dr = rate at which the volume is increasing
But,
V = 4πr³/3
Therefore,
dV/dr = 4πr²............... Equation 2
Substitute equation 2 into equation 1
dV/dt = 4πr²(dr/dt).............. Equation 3
From the question,
Given: dr/dt = 2 mm/s, r = 60/2 = 30 mm
Consatant: π = 3.14
Substitute these values into equation 3
dV/dt = 4×3.14×30²×2
dV/dt = 22608 mm³/s
if 18 : 6 = x : 3 then what is 5 + 3x
Answer:
32
Step-by-step explanation:
18 : 6 = 3
therefore, x : 3 has to equal 3.
X : 3 = 3
X = 3 × 3
X = 9
To verify:
18 : 6 = 9 : 3
3 = 3
It's true that X = 9, so now just replace the X with 9 in the next equation
5 + 3(9) = 32
Answer:
32
Step-by-step explanation:
18 : 6 = x : 3
Product of means = Product of extremes
6 * x = 3*18
x = [tex]\frac{3*18}{6}[/tex]
x = 3*3
x = 9
Now plugin x = 9 in the expression
5 + 3x = 5 + 3*9
= 5 + 27
= 32
what is a value between 1/4 and 1/3 is
9514 1404 393
Answer:
2/7
Step-by-step explanation:
Any unit fraction with a denominator between 3 and 4 will be between 1/3 and 1/4. For example, ...
1/3.5 = 2/7 . . . . is between 1/3 and 1/4
__
You can also go at this considering decimal equivalents.
1/4 = 0.25
1/3 = 0.333... (repeating)
So, decimal numbers like 0.26, 0.295, 0.3330 are all values that are between 1/4 and 1/3.
The figure shows trapezoid ABCD on a coordinate plane.
Which of the following represents the area of this figure, rounded to the nearest square unit?
99
121
198
231
Answer:
121 unit^2.
Step-by-step explanation:
The area = height/2 * ( sum of the opposite parallel lines)
= h/2(BC + AD
h = BF = 14 - 3 = 11 units.
BC = 13 - 5 = 8 units.
AD = 16 - 2 = 14 units.
Area = (11/2)(8 + 14)
= 5.5 * 22
= 121 unit^2.
Answer:
121
Step-by-step explanation:
evaluate the expression when b= -6 and c=3
-4c+b
Answer:
-18
Step-by-step explanation:
b = -6
c = 3
-4c + b = ?
Plug in the value of each variable into the equation
-4c + b = ?
= -4(3) + (-6)
= -12 - 6
= -18
I am a 2 digit number ,my two digit and the sum of my digit are in sequence .what number I am?
Answer:
I don't understand the meaning of question
The sum of an a.p is 340. the first term is 7 and the common difference is 6. Cal the number of terms in the sequence.
anyone?
Common difference: 6
First term: 7
Second term: 13
Third term: 19
Fourth term: 25
Fifth term: 31
I hope this is correct and helps!
Answer to the following question is as follows;
Number of term in AP (N) = 10
Step-by-step explanation:
Given:
Sum of arithmetic progression (Sn) = 340
First term of AP (a) = 7
Common difference of AP (d) = 6
Find;
Number of term in AP (N)
Computation:
Sn = [n/2][2a + (n-1)d]
340 = [n/2][2(7) + (n-1)6]
340 = [n/2][14 + 6n - 6]
680 = n[6n + 8]
6n² + 8n - 680
Using Quadratic Formula
n = 10
Number of term in AP (N) = 10
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Use the parametric equations of an ellipse, x=acosθ, y=bsinθ, 0≤θ≤2π , to find the area that it encloses.
Answer:
Area of ellipse=[tex]\pi ab[/tex]
Step-by-step explanation:
We are given that
[tex]x=acos\theta[/tex]
[tex]y=bsin\theta[/tex]
[tex]0\leq\theta\leq 2\pi[/tex]
We have to find the area enclose by it.
[tex]x/a=cos\theta, y/b=sin\theta[/tex]
[tex]sin^2\theta+cos^2\theta=x^2/a^2+y^2/b^2[/tex]
Using the formula
[tex]sin^2x+cos^2x=1[/tex]
[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]
This is the equation of ellipse.
Area of ellipse
=[tex]4\int_{0}^{a}\frac{b}{a}\sqrt{a^2-x^2}dx[/tex]
When x=0,[tex]\theta=\pi/2[/tex]
When x=a, [tex]\theta=0[/tex]
Using the formula
Area of ellipse
=[tex]\frac{4b}{a}\int_{\pi/2}^{0}\sqrt{a^2-a^2cos^2\theta}(-asin\theta)d\theta[/tex]
Area of ellipse=[tex]-4ba\int_{\pi/2}^{0}\sqrt{1-cos^2\theta}(sin\theta)d\theta[/tex]
Area of ellipse=[tex]-4ba\int_{\pi/2}^{0} sin^2\theta d\theta[/tex]
Area of ellipse=[tex]-2ba\int_{\pi/2}^{0}(2sin^2\theta)d\theta[/tex]
Area of ellipse=[tex]-2ba\int_{\pi/2}^{0}(1-cos2\theta)d\theta[/tex]
Using the formula
[tex]1-cos2\theta=2sin^2\theta[/tex]
Area of ellipse=[tex]-2ba[\theta-1/2sin(2\theta)]^{0}_{\pi/2}[/tex]
Area of ellipse[tex]=-2ba(-\pi/2-0)[/tex]
Area of ellipse=[tex]\pi ab[/tex]
Simplify. v80
A. 16v5
B. 5v4
C. 4v5
D. 20v4
Hi!
√80 = √(16 • 5) = √(4² • 5) = 4√5
B
13 ft.
5 ft.
A
C
12 ft.
Find the value of Cos (B) =
Answer: the answer is 12/13
HELP ASAP! I don’t know how to solve this problem nor where to start. Can someone please help me out here?
===============================================
Explanation:
It might help to draw out the picture as shown below. The pool itself (just the water only) is the inner rectangle. The outer rectangle is the pool plus the border of those 1 by 1 tiles.
The pool is a rectangle 90 feet by 80 feet. If we add on the tiles, then we get a larger rectangle that is 90+2 = 92 feet by 80+2 = 82 feet.
We add on 2 since we're adding two copies of "1" on either side of each dimension.
The larger rectangle's area is 92*82 = 7544 square feet
The smaller rectangle's area is 90*80 = 7200 square feet
The difference in areas is 7544-7200 = 344 square feet.
Each 1 by 1 tile is of area 1*1 = 1 sq foot, meaning that 344 tiles will get us the 344 square foot border around the pool.
Which of the following numbers is rational? Assume that the decimal patterns continue.
Answer:
[tex]\sqrt{49}[/tex]
Step-by-step explanation:
Define a rational number by a number able to expressed a fraction where the denominator is not 0 or 1.
Non-terminating (never-ending) decimals cannot be expressed as a fraction and therefore are irrational. However, recall that [tex]\sqrt{49}=7[/tex], which can be expressed as a fraction (e.g. [tex]\frac{14}{2}[/tex], etc). Thus, the answer is [tex]\boxed{\sqrt{49}}[/tex].
If ∆ABC is an isosceles triangle and ∆DBE is an equilateral triangle, find each missing
measure.
Answer:
Step-by-step explanation:
The measure for each angle is shown below.
What is Equilateral Triangle?A triangle is said to be equilateral if each of its three sides is the same length. In the well-known Euclidean geometry, an equilateral triangle is also equiangular, meaning that each of its three internal angles is 60 degrees and congruent with the others.
Given:
As, ∆ABC and ∆DBE is an equilateral triangle.
In Equilateral Triangle all the angles are Equal.
So, 4x+ 3= 9x- 7
5x = 50
x= 10
and, <1 = <9 = 4x+ 3= 43
and, <4 = <5 = <6 = 180/ 3= 60
ans, <3 = <8 = 180-60= 120
Also, <2 = < 7 = 180- <1- <3= 17
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what type of number cannot be written as a fraction p/q, where p and q are intergers and q is not equal to zero
Answer:
irrational numbers
Step-by-step explanation:
An irrational number is a number that cannot be expressed as a fraction p/q for any integers p and q.
Hi there!
»»————- ★ ————-««
I believe your answer is:
Irrational Number
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
The definition that is given in the question was the definition of a irrational number.A number that cannot be written as a fraction with two integers is called a irrational number. Some examples of irrational numbers are non-terminating decimals that do not repeat and non-perfect squares. A number that CAN be written as a fraction with two integers is called a rational number.⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
In which quadrant do the points have negative x-coordinates and negative y-coordinates?
Hi there!
»»————- ★ ————-««
I believe your answer is:
Quadrant III
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
The plane is split into four quadrants. Quadrant III houses all the points with negative signs for both X and Y values.⸻⸻⸻⸻
See the attached picture for reference.
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
How to find the surface area of a cuboid
Answer:
To find the surface area of a cuboid we can also label the length, width and the height of the prism and use the formula SA=2LW+2LH+2HW to find the area of a cuboid
Answer:
202 cm²
Step-by-step explanation:
The opposite faces of a cuboid are congruent , then
SA = top/bottom + front/ back + sides , that is
SA = 2(9 × 4) + 2(9 × 5) + 2(4 × 5)
= 2(36) + 2(45) + 2(20)
= 72 + 90 + 40
= 202 cm²
Find the volume of the cone. Round to the nearest hundredth.
Answer:
Step-by-step explanation:
volume of cone=1/3 πr²h
=1/3×π×5²×11
=275/3 ×3.14
≈287.33 in³
What is the lcd for 3/6 and 2/9
9514 1404 393
Answer:
LCD = 18
Step-by-step explanation:
6 and 9 have a common factor of 3, so the LCD is ...
(6×9)/3 = 18
Then the fractions can be written as ...
3/6 = 9/18
2/9 = 4/18
Give an example of a function with both a removable and a non-removable discontinuity.
Answer:
(x+5)(x-3) / (x+5)(x+1)
Step-by-step explanation:
A removeable discontinuity is always found in the denominator of a rational function and is one that can be reduced away with an identical term in the numerator. It is still, however, a problem because it causes the denominator to equal 0 if filled in with the necessary value of x. In my function above, the terms (x + 5) in the numerator and denominator can cancel each other out, leaving a hole in your graph at -5 since x doesn't exist at -5, but the x + 1 doesn't have anything to cancel out with, so this will present as a vertical asymptote in your graph at x = -1, a nonremoveable discontinuity.
im stuck on this question!!!!
Answer:
reflected across the y axis: (5,2)
reflected across the x axis: (-2,5)
Answer:
Answer: (5,2) when reflected off the y-axis. (-5,-2) when reflected off the x-axis
Put the equation y = x^2- 14x + 48 into the form y = (x-h)^2+k
please help me!
Answer:
Step-by-step explanation:
Answer:
[tex]y=(x-7)^2-1[/tex]
Step-by-step explanation:
We want to convert the equation:
[tex]\displaystyle y=x^2-14x+48[/tex]
Into vertex form, given by:
[tex]\displaystyle y=a(x-h)^2+k[/tex]
Where a is the leading coefficient and (h, k) is the vertex.
There are two methods of doing this. We can either: (1) use the vertex formulas or (2) complete the square.
Method 1) Vertex Formulas
Let's use the vertex formulas. First, note that the leading coefficient a of our equation is 1.
Recall that the vertex is given by:
[tex]\displaystyle \text{Vertex}=\left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)[/tex]
In this case, a = 1, b = -14, and c = 48. Find the x-coordinate of the vertex:
[tex]\displaystyle x=-\frac{(-14)}{2(1)}=7[/tex]
To find the y-coordinate, substitute this value back into the equation. Hence:
[tex]y=(7)^2-14(7)+48=-1[/tex]
Therefore, our vertex (h, k) is (7, -1), where h = 7 and k = -1.
And since we already determined a = 1, our equation in vertex form is:
[tex]\displaystyle y=(x-7)^2-1[/tex]
Method 2) Completing the Square
We can also complete the square to acquire the vertex form. We have:
[tex]y=x^2-14x+48[/tex]
Factor out the leading coefficient from the first two terms. Since the leading coefficient is one in this case, we do not need to do anything significant:
[tex]y=(x^2-14x)+48[/tex]
Now, we half b and square it. The value of b in this case is -14. Half of -14 is -7 and its square is 49.
We will add this value inside the parentheses. Since we added 49 inside the parentheses, we will also subtract 49 outside to retain the equality of the equation. Hence:
[tex]y=(x^2-14x+49)+48-49[/tex]
Factor using the perfect square trinomial and simplify:
[tex]y=(x-7)^2-1[/tex]
We acquire the same solution as before, with the vertex being (7, -1).
What type of line is PQ⎯⎯⎯⎯⎯⎯⎯⎯?
Answer:
median
Step-by-step explanation:
Q is at the midpoint of RS and so PQ is a median
A median is a segment from a vertex to the midpoint of the opposite side.
We want to define what type of line is PQ (the line that passes through points P and Q) by looking at the given image, one can easily see that the line PQ is a median, now let's explain why.
First, let's analyze the image:
In the image, we can see that P is one vertex of the triangle, and Q is the midpoint of the segment RS (you can see that RQ = 4 and QS = 4) , where R and S are the other two vertexes of the triangle.
Particularly, we can define a median of a triangle as the line that passes through the midpoint of one side of the triangle and by the vertex that does not belong to that side.
With that definition, we can see that PQ is a median because Q is the midpoint of one side of the triangle and P is the vertex that does not belong to that side.
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1 Find the value of C to that the function probability density function defined as follow, also calculate the man and variance /4
X -1 0 1
f(x) 3c 3c 6c
Answer:
[tex]c = \frac{1}{12}[/tex]
The mean of the distribution is 0.25.
The variance of the distribution is of 0.6875.
Step-by-step explanation:
Probability density function:
For it to be a probability function, the sum of the probabilities must be 1. The probabilities are 3c, 3c and 6c, so:
[tex]3c + 3c + 6c = 1[/tex]
[tex]12c = 1[/tex]
[tex]c = \frac{1}{12}[/tex]
So the probability distribution is:
[tex]P(X = -1) = 3c = 3\frac{1}{12} = \frac{1}{4} = 0.25[/tex]
[tex]P(X = 0) = 3c = 3\frac{1}{12} = \frac{1}{4} = 0.25[/tex]
[tex]P(X = 1) = 6c = 6\frac{1}{12} = \frac{1}{2} = 0.5[/tex]
Mean:
Sum of each outcome multiplied by its probability. So
[tex]E(X) = -1(0.25) + 0(0.25) + 1(0.5) = -0.25 + 0.5 = 0.25[/tex]
The mean of the distribution is 0.25.
Variance:
Sum of the difference squared between each value and the mean, multiplied by its probability. So
[tex]V^2(X) = 0.25(-1-0.25)^2 + 0.25(0 - 0.25)^2 + 0.5(1 - 0.25)^2 = 0.6875[/tex]
The variance of the distribution is of 0.6875.
please help me i begging.
Answer:
The two equivalent expressions are 6(x − y) and 6x − 6y.
Step-by-step explanation:
What is the sum of 4th squared number and the 2nd cube number
Answer:
mark me as brinalist if answers are correct
whether the distribution of the mean of a large number of independent, identically distributed variables. true or false
Answer:
The statement is false
Step-by-step explanation:
Given
See comment for complete statement
Required
Is the statement true or false
From central limit theorem, we understand that a distribution is approximately normal if the distribution takes a sample considered to be large enough from the population.
Also, the mean and the standard deviation are known.
However, the given statement implies that the distribution will be normal depending on an underlying distribution; this is false.
