In a town. the population of registered voters is 46% democrat, 42% republican and 12% independent polling data shows 57% of democrats support the increase , 38% of republicans support the increase, and 76% of independents support the increase.
Required:
a. Find the probability that a randomly selected voter in the town supports the tax increase.
b. What is the probability that a randomly selected voter does not support the tax increase?
c. Suppose you find a voter at random who supports the tax increase. What is the probability he or she is a registered Independent?
Answer:
a) 0.513 = 51.3% probability that a randomly selected voter in the town supports the tax increase.
b) 0.487 = 48.7% probability that a randomly selected voter does not support the tax increase.
c) 0.1777 = 17.77% probability he or she is a registered Independent.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
Question a:
57% of 46%(democrats)
38% of 42%(republicans)
76% of 12%(independents)
So
[tex]P = 0.57*0.46 + 0.38*0.42 + 0.76*0.12 = 0.513[/tex]
0.513 = 51.3% probability that a randomly selected voter in the town supports the tax increase.
Question b:
1 - 0.513 = 0.487
0.487 = 48.7% probability that a randomly selected voter does not support the tax increase.
c. Suppose you find a voter at random who supports the tax increase. What is the probability he or she is a registered Independent?
Event A: Supports the tax increase.
Event B: Is a independent.
0.513 = 51.3% probability that a randomly selected voter in the town supports the tax increase.
This means that [tex]P(A) = 0.513[/tex]
Probability it supports a tax increase and is a independent:
76% of 12%, so:
[tex]P(A \cap B) = 0.76*0.12[/tex]
Thus
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.76*0.12}{0.513} = 0.1777[/tex]
0.1777 = 17.77% probability he or she is a registered Independent.
The length of a rectangle is 6 meters more than its width. The area of the rectangle is 114 square meters. Which of the following quadratic equations represents the area of the rectangle? Suppose x is the width of the rectangle. x 2-6x - 114 = 0
A) x^2-6x-114=0
B) x^2-6x+114=0
C) x^2+6x+114=0
D) x^2+6x-114=0
Answer:
last one
Step-by-step explanation:
x = width
x+6 = length
Area = length times width
x(x + 6) = [tex]x^{2}[/tex] + 6x
[tex]x^{2}[/tex] + 6x = 114 (subtract 114 from both sides)
[tex]x^{2}[/tex] + 6x -114 = 0
Given a parametric curve
{x = 2 cost
{y = 4 sint 0 <= t <= π
a. Set up but do NOT evaluate an integral to find the area of the region enclosed by the curve and the x-axis.
b. Set up but do NOT evaluate an integral to find the area of the surface obtained by rotating the curve about the x-axis.
(a) The area of the region would be given by the integral
[tex]\displaystyle\int_0^\pi y(t)\left|x'(t)\right|\,\mathrm dt = 8 \int_0^\pi \sin^2(t)\,\mathrm dt[/tex]
(b) The area of the surface of revolution would be given by
[tex]\displaystyle\int_0^\pi y(t)\sqrt{x'(t)^2+y'(t)^2}\,\mathrm dt = 4\int_0^\pi\sin(t)\sqrt{4\sin^2(t)+16\cos^2(t)}\,\mathrm dt[/tex]
Solve the expression using the correct order of operations.
0.75x3.2+ (9.1)2-((-2.3)-(-0.9))2
Answer:
[tex]0.75 * 3.2+ (9.1)^2-((-2.3)-(-0.9))^2 = 83.25[/tex]
Step-by-step explanation:
Given
[tex]0.75 * 3.2+ (9.1)^2-((-2.3)-(-0.9))^2[/tex]
Required
Solve
Start with the bracket
[tex]0.75 * 3.2+ (9.1)^2-((-2.3)-(-0.9))^2 = 0.75 * 3.2+ (9.1)^2-(-1.4)^2[/tex]
Evaluate all exponents
[tex]0.75 * 3.2+ (9.1)^2-((-2.3)-(-0.9))^2 = 0.75 * 3.2+ 82.81-1.96[/tex]
Evaluate all products
[tex]0.75 * 3.2+ (9.1)^2-((-2.3)-(-0.9))^2 = 2.4+ 82.81-1.96[/tex]
[tex]0.75 * 3.2+ (9.1)^2-((-2.3)-(-0.9))^2 = 83.25[/tex]
A boat travels 8 miles north from point A to point B. Then it moves in the direction S 40°W and reaches point Finally, it turns S 40°E and returns to point A
The total distance covered by the boat is______miles
A. 14.95
B. 18.44
C. 20.04
D. 25.88
Answer:
B.18. 44 miles
Step-by-step explanation:
We are given that
Distance between A and B=8 miles
Angle B=Angle BCQ=40 degree (Alternate interior angles)
Angle ACB=180-Angle ACP-Angle BCQ
Angle ACB=180-40-40=100 degree
In triangle ABC
Angle A+ Angle B +Angle C=180 degree using sum of angles of triangle property
Substitute the values
[tex]\angle A+40+100=180[/tex]
[tex]\angle A+140=180[/tex]
[tex]\angle A=180-140[/tex]
[tex]\angle A=40[/tex] degree
Angle A=Angle B
When two angles are equal of a triangle then the triangle is isosceles triangle.
Therefore, triangle ABC is an isosceles triangle.
[tex]\implies BC=AC [/tex]
Now, Sine law
[tex]\frac{a}{sin A}=\frac{b}{sin B}=\frac{c}{sin C}[/tex]
Using the sine law
[tex]\frac{BC}{sin 40}=\frac{AB}{sin 100}[/tex]
[tex]\frac{BC}{sin 40}=\frac{8}{sin 100}[/tex]
[tex]BC=\frac{8\times sin40}{sin 100}[/tex]
BC=5.22
AC=BC=5.22 miles
Now, total distance covered by the boat=AB+BC+AC
Total distance covered by the boat=8+5.22+5.22=18.44 miles
Hence, option B is correct.
find 9 rational no. between 8/7 and 17/10.
Answer:
[tex]\dfrac{81}{70},\dfrac{82}{70},\dfrac{83}{70},\dfrac{84}{70},\dfrac{85}{70},\dfrac{86}{70},\dfrac{87}{70},\dfrac{88}{70},\dfrac{89}{70}[/tex]
Step-by-step explanation:
We need to find 9 rational number between [tex]\dfrac{8}{7}\ \text{and}\ \dfrac{17}{10}[/tex]
We make the denominators of both fractions same. So,
[tex]\dfrac{8}{7}\times \dfrac{10}{10}=\dfrac{80}{70}[/tex]
and
[tex]\dfrac{17}{10}\times \dfrac{7}{7}=\dfrac{119}{70}[/tex]
The rational number are:
[tex]\dfrac{81}{70},\dfrac{82}{70},\dfrac{83}{70},\dfrac{84}{70},\dfrac{85}{70},\dfrac{86}{70},\dfrac{87}{70},\dfrac{88}{70},\dfrac{89}{70}[/tex]
If 89 babies are sampled at random from the hospital, what is the probability that the mean weight of the sample babies would differ from the population mean by less than 48 grams
Answer:
0.6836
Step-by-step explanation:
(weight - mean weight) = 48
Variance, s² = 204,304
Sample size, n = 89
We need to obtain the Zscore :
Zscore = (X - mean) / standard Error
Zscore = (weight - mean weight ) / (s/√n)
s = √204304 = 452
The difference from the meanncoukdnbe either to the right or left :
Zscore = - 48 / (452/√89) OR 48 / (452/√89)
Zscore = - 48 / 47.911904 OR - 48 / 47.911904
Zscore = - 1.002 or 1.002
P(Z < - 1.002) = 0.1582 (using Z table)
P(Z < 1.002) = 0.8418
P(Z < 1.002) - P(Z < - 1.002)
0.8418 - 0.1582
= 0.6836
PLEASE HELP, according to this function, which is a true statement???????
Answer:
function ar true in the mach on which
Answer:
i think three one is right answer...
Prove that the square of an odd number is always 1 more than a multiple of 4
Answer:
By these examples you are able to see that the square of an odd number is always 1 more than a multiple of 4.
Step-by-step explanation:
For examples,
Let's consider squares of 3, 11, 25, 37 and 131.
[tex] {3}^{2} = 9[/tex]
8 is a multiple of 4, and 9 is more than 8.
[tex] {11}^{2} = 121[/tex]
120 is a multiple of 4 and 121 is one more than it.
[tex] {25}^{2} = 625[/tex]
624 is a multiple of 4 and 625 is one more than it.
[tex] {37}^{2} = 1369[/tex]
1368 is a multiple of 4 and 1369 is one more than 1368.
[tex] {131}^{2} = 17161[/tex]
17160 is a multiple of 4.
Find the greatest common factor of 15 x²y³ and -18 x³yz .
Answer:
3 x² y¹
Step-by-step explanation:
15 x²y³ = 3. 5. x². y³
-18x³yz = -2. 3². x³. y¹. z¹
so, the GCF = 3. x². y¹
Answer:
Solution given:
15x²y³=3*5*x*x*y*y*y
-18x³yz=-3*2*3*x*x*x*y*z
over here common is
3*x*x*y
so
greatest common factor is 3x²y¹
work out the value of 5x8 x 5-2/5x4
Answer:
=6
Step-by-step explanation:
(5×8)×(5-2)/(5×4)
Numerator =40×3
=120
Denominator = 5×4
=20
simplifying 120/20
=6
Answer:
6
follow the BDMAS rule
bracket ,division ,multiplication, addition and last subtraction
you won't get any maths problem wrong
Which triangle must be a right triangle and why?
O AA'B'C' is right because it is the image of AABC.
O AADC is right because AA' intersects AC at A.
O ABCC' is right because B lies of the line of
reflection.
O ABGC is right because G. CC')
Answer:
it would be the last one.
Step-by-step explanation:
its looking for a right triangle, a right triangle has one 90 degree angle. all of the other triagles have acute angles making them smaller than 90 degrees
Triangle BGC is the right triangle, because BG is perpendicular to CC'.
The line passing through points E, F, and G in the image is now perpendicular to the lines is DF and CG.
So we know that our triangle will be made with some of these lines.
For example, the right triangles in the figure are:
BFD, BGC, B'FD', and B'GC'.
Then, the concluded statement is ΔBGC, because BG ⊥CC.
There says that "Triangle BGC is the Right because BG is perpendicular to CC.
Learn more about right triangle here:
brainly.com/question/2217700
#SPJ7
HELP ME PLEASE ASAP! So the answer for the question I got is 113.1. Is my answer correct or is it wrong? Please let me know how to solve this problem if the answer is wrong. Thank you for your time.
Answer: 113.01m - You are almost right
Step-by-step explanation:
Simply by using pir^2, you get the number you calculated, but it is asking for at least 2 decimal places. So it would be "113.01"
Find the number of integers n that satisfy n^2 < 100.
Answer:
n=-9,-8,-7
Step-by-step explanation:
n<100
but that is the positive square root
\(-10 n is between the negative and positive square root of 100
thus, n=-9,-8,-7
The solution of the inequality n² < 100 will be less than 10.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The inequality is given below.
n² < 100
Simplify the equation, then we have
n² < 100
n² < 10²
n < 10
The solution of the inequality n² < 100 will be less than 10.
More about the inequality link is given below.
https://brainly.com/question/19491153
#SPJ2
If F is the function defined by F(x)=3x−1, find the solution set for F(x)=0.
The solution for set F(x) is -1
The value of Tonya's car is $21,000. The car's value depreciates at a rate of 15% per year.
Which function represents the value of the car after t years?
f(t)=0.85(21,000)t
f(t)=1.15(21,000)t
f(t)=21,000(0.85)t
f(t)=21,000(1.15)t
9514 1404 393
Answer:
(c) f(t)=21,000(0.85)^t
Step-by-step explanation:
Each year, the value is multiplied by 1-15% = 85% = 0.85. This is correctly shown in the function ...
f(t)=21,000(0.85)^t
Please help! Variables!!
Answer:
-x^4, and (2√x)/x
Step-by-step explanation:
4. [tex]- \sqrt{ x^{8} } = - \sqrt{x^{4} *x^{4} } = -x^{4}[/tex]
x^8 = x*x*x*x*x*x*x*x = (x*x*x*x)(x*x*x*x) = (x^4)(x^4)
5.
[tex]\sqrt{\frac{4}{x} } = \frac{\sqrt{4} }{\sqrt{x} } = \frac{2}{\sqrt{x} } \\\\\\\frac{2}{\sqrt{x} } * \frac{\sqrt{x} }{\sqrt{x} } = \frac{2\sqrt{x} }{x}[/tex]
write the following in set builder form C={1,4,9,16,25}
Answer:
C={n : n=i^2 where i belongs to Natural_numbers and 1 <= i <= 5}
Solve: |4x+3|=|2x+1|
Step-by-step explanation:
|4x+3|=|2x+1|THERE ARE TWO UNIQUE EQUATIONs
4x+3=2x+1
2x=-2
x=-1
(or)
4x+3= -(2x+1)
4x+3=-2x-1
6x=-4
x=-2/3
Therefore x=-1 , -2/3A projectile is fired from ground level with an initial velocity of 35 m/s at an angle of 35° with the horizontal. How long
will it take for the projectile to reach the ground?
Answer:
Step-by-step explanation:
We will work in the y-dimension only here. What we need to remember is that acceleration in this dimension is -9.8 m/s/s and that when the projectile reaches its max height, it is here that the final velocity = 0. Another thing we have to remember is that an object reaches its max height exactly halfway through its travels. Putting all of that together, we will solve for t using the following equation.
[tex]v=v_0+at[/tex]
BUT we do not have the upwards velocity of the projectile, we only have the "blanket" velocity. Initial velocity is different in both the x and y dimension. We have formulas to find the initial velocity having been given the "blanket" (or generic) velocity and the angle of inclination. Since we are only working in the y dimension, the formula is
[tex]v_{0y}=V_0sin\theta[/tex] so solving for this initial velocity specific to the y dimension:
[tex]v_{0y}=35sin(35)[/tex] so
[tex]v_{0y}=[/tex] 2.0 × 10¹ m/s
NOW we can fill in our equation from above:
0 = 2.0 × 10¹ + (-9.8)t and
-2.0 × 10¹ = -9.8t so
t = 2.0 seconds
This is how long it takes for the projectile to reach its max height. It will then fall back down to the ground for a total time of 4.0 seconds.
The sum of 7/3 and four times a number is equal to 2/3 subtracted from five times the number?
Answer:
-3
Step-by-step explanation:
When 4 times a positive number is subtracted from the square of the number, the result is 5. Find the number.
Answer:
5
Step-by-step explanation:
x² - 4x = 5
x² - 4x - 5 = 0
the solution of a quadratic equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
a = 1
b = -4
c = -5
x = (4 ± sqrt(16 + 20))/2 = (4 ± sqrt(36))/2
x1 = (4 + 6)/2 = 5
x2 = (4 - 6)/2 = -1
since we are looking only for a positive number, x=5 is the answer.
Let F(x) = x^2 – 15 and
G(x)= 4 - x
Find (F/G)(–7) =
Answer:
[tex]\displaystyle \bigg( \frac{F}{G} \bigg)(-7) = \frac{34}{11}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
FunctionsFunction NotationStep-by-step explanation:
Step 1: Define
Identify
F(x) = x² - 15
G(x) = 4 - x
Step 2: Find
Substitute in functions: [tex]\displaystyle \bigg( \frac{F}{G} \bigg)(x) = \frac{x^2 - 15}{4 - x}[/tex]Step 3: Evaluate
Substitute in x [Function (F/G)(x)]: [tex]\displaystyle \bigg( \frac{F}{G} \bigg)(-7) = \frac{(-7)^2 - 15}{4 - (-7)}[/tex]Exponents: [tex]\displaystyle \bigg( \frac{F}{G} \bigg)(-7) = \frac{49 - 15}{4 - (-7)}[/tex]Subtract: [tex]\displaystyle \bigg( \frac{F}{G} \bigg)(-7) = \frac{34}{11}[/tex]* Insert a digit to make numbers that are divisible by 6 if it is possible:
234_6
Answer:
i put in 3 to make 23436 because 36 is divisible by 6
Which of the following are integer solutions to the inequality below?
−2≤×<3
Answer:
-2, - 1, 0, 1, 2
Step-by-step explanation:
The greater than or equal to sign (≤) demonstrates that the unknown is equal to -2 and greater, but is less than 3, so the largest integer solution is 2, not 3
Four cups of pure water are added to a 20-cup bowl of punch that is 75% juice. What percentage of the new punch is juice?
Amount of Juice
15
0
Amount of Punch
20
4
27%
37.5%
62.5%
75%
Answer:
62.5%
Step-by-step explanation:
Given that :
20 cup bowl of punch = 75% Juice
We can infer that :
The number of cups of JUICE is :
75% * 20 = 0.75 * 20 = 15 cups
Adding 4 cups of water to the 20 cups, we have = 24 cups
With 15 cups of JUICE ;
The percentage of the new punch that is juice will be x
x% of 24 cups = 15 cups
x/100 * 24 = 15
0.01x * 24 = 15
0.24x = 15
x = 15 / 0.24
x = 62.5
x = 62.5%
Answer:
It's C
62.5% btw
Step-by-step explanation:
Did the quiz lol
What is the equation, in the point-slope form, of the line that is parallel to the given and passes through the point (-1,-1)?
Answer:
y + 1 = 3(x+ 1)
Step-by-step explanation:
(2,3) , (0 ,-3)
Slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]= \frac{-3-3}{0-2}\\\\=\frac{-6}{-2}\\\\= 3[/tex]
m = 3
Parallel lines have same slope.
m = 3; (-1 , -1)
y -y1 = m (x -x1)
y -[-1] = 3(x -[-1])
y + 1 = 3(x+ 1)
Answer:
D. y+1=3(x+1)
Need help on this ASAP
Answer:
The answer is C
Step-by-step explanation:
The intersection of those figures results to a point
In studying the sampling distribution of the mean, you were asked to list all the different possible samples from a small population and then find the mean
of each of them. Consider the following:
Personal phone calls received in the last three days by a new employee were 2. 4, and 7. Assume that samples of size 2 are randomly selected with replacement from
this population of three values
What different samples could be chosen? What would be their sample means?
O A. Possible samples 2-4, 2-74-2: 4-7, 7-2,7-4
Sample means: 3,45,55
O B. Possible samples: 2-2.2-4,2-74-2, 4-4 4-7,7-2,7-4.7-7
Sample means: 2, 3, 4, 4.5,55,7
OC. Possible samples: 2-4 2-7, 4-7
Sample means: 3.4,45
a
Q
rd
What is the following product?(2square root 7 +3square root 6)(5square root2+4square root3)
Answer:
[tex]10\sqrt{14} + 8\sqrt{21} + 30 \sqrt{3} +36\sqrt{2}\\\\[/tex]
Step-by-step explanation:
[tex]( 2 \sqrt7 + 3 \sqrt6)(5\sqrt2 + 4\sqrt3)\\\\= 2\sqrt7(5\sqrt2 + 4\sqrt3) + 3\sqrt6 ( 5\sqrt2 + 4\sqrt3)\\\\=10\sqrt{7 \times 2} + 8\sqrt{7 \times 3} + 15\sqrt{6 \times 2} + 12\sqrt{ 6\times 3}\\\\=10\sqrt{14} + 8\sqrt{21} + 15 \sqrt{12} +12\sqrt{18}\\\\= 10\sqrt{14} + 8\sqrt{21} + 15 \sqrt{4 \times 3 } +12\sqrt{9 \times 2}\\\\= 10\sqrt{14} + 8\sqrt{21} + 15 \sqrt{2^2 \times 3} +12\sqrt{3^2 \times 2}\\\\= 10\sqrt{14} + 8\sqrt{21} + 30 \sqrt{3} +36\sqrt{2}\\\\[/tex]