Answer:
9/20
Step-by-step explanation:
450/1000
this is not the answer, because it is not simplified
so here we have to find common factor and simplifying
________________________________________________
450/1000 is simplified to 9/20, and it can no longer be simplified.
Giving a test to a group of students, the grades and gender are summarized below
A B C Total
Male 19 4 12 35
Female 3 13 5 21
Total 22 17 17 56
Let pp represent the percentage of all male students who would receive a grade of A on this test. Use a 99.5% confidence interval to estimate p to three decimal places.
Enter your answer as a tri-linear inequality using decimals (not percents).
< p
Answer:
Using Anova for a tri linear probability at ∝= 0.005
Step-by-step explanation:
Here simple probability cannot be used because we want to enter your answer as a tri-linear inequality using decimals (not percents).
So we can use ANOVA
Null hypothesis
H0: µA = µB=µC
all the means are equal
Alternative hypothesis
H1: Not all means are equal.
The significance level is set at α-0.005
The test statistic to use is
F = sb²/ sw²
Which if H0 is true has an F distribution with v₁=k-1 and v₂= n-k degrees of freedom .
The computations are as follows
XA (XA)² XB (XB)² XC (XC)² Total ∑X²
Male 19(361) 4(16) 12(144) 35 521
Female 3(9) 13 (169) 5 (25) 21 203
TotalTj 22 17 17 56 724
T²j (22)(22)
484 289 289 1062
∑X² 370 285 169
Correction Factor = CF = Tj²/n = (56)²/6= 522.67
Total SS ∑∑X²- C. F = 724- 522.67= 201.33
Between SS ∑T²j/r - C.F = 1062/ 2 - 522.877 =8.33
Within SS = Total SS - Between SS
=201.33- 8.33= 193
The Analysis of Variance Table is
Source Of Sum of Mean Computed
Variation d.f Squares Squares F
Between
Samples 1 8.33 8.33 8.33/ 48.25= 0.1726
Within
Samples 4 193 48.25
The critical region is F >F ₀.₀₀₅ (1,4) = 31.3328
Calculated value of F = 0.1726
Since it is smaller than 5 % reject H0.
However the decimal probability will be
Male 19 4 12 35
Female 3 13 5 21
Total 22 17 17 56
There are total 22 people who get an A but only 19 males who get an A
So the probability that a male gets an A is = 19/22= 0.8636
PLEASE ANSWER ASAP THANK YOU!!! How much money will be in a bank account after 3 years if $9 is deposited at an interest rate of 5% compounded annually? Round to the nearest dollar.....
Answer:
10 bucks
Step-by-step explanation:
Money=9*(1+0.05)^3
Money=9*(1.05)^3=10.41≈10
Find the maximum and minimum values of the function f(x,y)=2x2+3y2−4x−5 on the domain x2+y2≤100. The maximum value of f(x,y) is:
First find the critical points of f :
[tex]f(x,y)=2x^2+3y^2-4x-5=2(x-1)^2+3y^2-7[/tex]
[tex]\dfrac{\partial f}{\partial x}=2(x-1)=0\implies x=1[/tex]
[tex]\dfrac{\partial f}{\partial y}=6y=0\implies y=0[/tex]
so the point (1, 0) is the only critical point, at which we have
[tex]f(1,0)=-7[/tex]
Next check for critical points along the boundary, which can be found by converting to polar coordinates:
[tex]f(x,y)=f(10\cos t,10\sin t)=g(t)=295-40\cos t-100\cos^2t[/tex]
Find the critical points of g :
[tex]\dfrac{\mathrm dg}{\mathrm dt}=40\sin t+200\sin t\cos t=40\sin t(1+5\cos t)=0[/tex]
[tex]\implies\sin t=0\text{ OR }1+5\cos t=0[/tex]
[tex]\implies t=n\pi\text{ OR }t=\cos^{-1}\left(-\dfrac15\right)+2n\pi\text{ OR }t=-\cos^{-1}\left(-\dfrac15\right)+2n\pi[/tex]
where n is any integer. We get 4 critical points in the interval [0, 2π) at
[tex]t=0\implies f(10,0)=155[/tex]
[tex]t=\cos^{-1}\left(-\dfrac15\right)\implies f(-2,4\sqrt6)=299[/tex]
[tex]t=\pi\implies f(-10,0)=235[/tex]
[tex]t=2\pi-\cos^{-1}\left(-\dfrac15\right)\implies f(-2,-4\sqrt6)=299[/tex]
So f has a minimum of -7 and a maximum of 299.
In 2018, the population of a district was 25,000. With a continuous annual growth rate of approximately 4%, what will the
population be in 2033 according to the exponential growth function?
Round the answer to the nearest whole number.
Answer:
40,000 populationsStep-by-step explanation:
Initial population in 2018 = 25,000
Annual growth rate (in %) = 4%
Yearly Increment in population = 4% of 25000
= 4/100 * 25000
= 250*4
= 1000
This means that the population increases by 1000 on yearly basis.
To determine what the population will be in 2033, we need to first know the amount of years we have between 2018 and 2033.
Amount of years we have between 2018 and 2033 = 2033-2018
= 15 years
After 15 years, the population will have increased by 15*1000 i.e 15,000 more than the initial population.
Hence the population in 2033 will be Initial population + Increment after 15years = 25,000+15000 = 40,000 population.
A ball is dropped from a height of 14 ft. The elasticity of the ball is such that it always bounces up one-third the distance it has fallen. (a) Find the total distance the ball has traveled at the instant it hits the ground the fourth time. (Enter an exact number.)
Answer:
Hello,
742/27 (ft)
Step-by-step explanation:
[tex]h_1=14\\\\h_2=\dfrac{14}{3} \\\\h_3=\dfrac{14}{9} \\\\h_4=\dfrac{14}{27} \\\\[/tex]
[tex]d=14+2*\dfrac{14}{3} +2*\dfrac{14}{9} +2*\dfrac{14}{27} \\=14*(1+\dfrac{1}{3}+\dfrac{2}{9} +\dfrac{2}{27} )\\=14*\dfrac{53}{27} \\=\dfrac{742}{27} \\[/tex]
The total distance the ball has traveled at the instant it hits the ground the fourth time [tex]28ft.[/tex]
What is the total distance?
Distance is a numerical measurement of how far apart objects or points are. It is the actual length of the path travelled from one point to another.
Here given that,
A ball is dropped from a height of [tex]14[/tex] ft. The elasticity of the ball is such that it always bounces up one-third the distance it has fallen.
So, after striking with the ground it covers the distance [tex]14[/tex] ft. so it rebounds to the height is [tex]\frac{1}{3}(14)[/tex].
Then again it hits the ground and covers the distance [tex]\frac{1}{3}(14)[/tex] and again after rebounding it goes to the height is
[tex]\frac{1(1)}{3(3)}.(14)=\frac{(1)^2}{(3)^2}(14)[/tex]
Then it falls the same distance and goes back to the height
[tex]\frac{1}{3}[/tex] ×[tex](\frac{(1)^2}{(3)^2})[/tex] ×[tex]14[/tex] = [tex]\frac{(1)^3}{(3)^3}(14)[/tex]
So, the total distance travelled is
[tex]14+2[\frac{1}{3}(14)+(\frac{1}{3})^2(14)+(\frac{1}{3})^3(14)+...][/tex]
We take the sum is twice because it goes back to the particular height and falls to the same distance.
[tex]S=14+2(\frac{\frac{1}{3}(14)}{1-\frac{1}{3}})\\\\\\S=\frac{a}{1-r}\\\\\\S=14+2(\frac{\frac{14}{3}}{\frac{2}{3}})\\\\S=14+2(\frac{14}{2})\\\\S=14+2(7)\\\\S=14+14\\\\S=28ft[/tex]
Hence, the total distance the ball has traveled at the instant it hits the ground the fourth time [tex]28ft.[/tex]
To know more about thetotal distance
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Express the quotient of z1 and z2 in standard form given that [tex]z_{1} = -3[cos(\frac{-\pi }{4} )+isin(\frac{-\pi }{4} )][/tex] and [tex]z_{2} = 2\sqrt{2} [cos(\frac{-\pi }{2} )+isin(\frac{-\pi }{2} )][/tex]
Answer:
Solution : [tex]-\frac{3}{4}-\frac{3}{4}i[/tex]
Step-by-step explanation:
[tex]-3\left[\cos \left(\frac{-\pi }{4}\right)+i\sin \left(\frac{-\pi \:}{4}\right)\right]\:\div \:2\sqrt{2}\left[\cos \left(\frac{-\pi \:\:}{2}\right)+i\sin \left(\frac{-\pi \:\:\:}{2}\right)\right][/tex]
Let's apply trivial identities here. We know that cos(-π / 4) = √2 / 2, sin(-π / 4) = - √2 / 2, cos(-π / 2) = 0, sin(-π / 2) = - 1. Let's substitute those values,
[tex]\frac{-3\left(\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}i\right)}{2\sqrt{2}\left(0-1\right)i}[/tex]
=[tex]-3\left(\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}i\right)[/tex] ÷ [tex]2\sqrt{2}\left(0-1\right)i[/tex]
= [tex]3\left(-\frac{\sqrt{2}i}{2}+\frac{\sqrt{2}}{2}\right)[/tex] ÷ [tex]-2\sqrt{2}i[/tex]
= [tex]\frac{3\left(1-i\right)}{\sqrt{2}}[/tex]÷ [tex]2\sqrt{2}i[/tex] = [tex]-3-3i[/tex] ÷ [tex]4[/tex] = [tex]-\frac{3}{4}-\frac{3}{4}i[/tex]
As you can see your solution is the last option.
Let x1 represent a quantitative independent variable and x2 represent a dummy variable for a 2-level qualitative independent variable. Which of the following models is the equation that produces two parallel curves, one for each level of your QL variable?
A. E(y) = ?0 + ?1x1 + ?2x12 + ?3x2
B. E(y) = ?0 + ?1x1 + ?3x2
C. E(y) = ?0 + ?x11 + ?3x2 + ?4x1x2
D. E(y) = ?0 + ?1x1 + ?2x12 + ?3x2 + ?4x1x2 + ?5x12x2
Answer:
D. E(y) = ?0 + ?1x1 + ?2x12 + ?3x2 + ?4x1x2 + ?5x12x2
Step-by-step explanation:
Quantitative variables are measured in terms of numbers, and figures. Independent variables are those which are reason for change in other variables. Dummy variables are numerical that represents categorical data. The range of these variables is small and they can take on only two quantitative values.
For a certain instant lottery game, the odds in favor of a win are given as 81 to 19. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive.
Answer: 0.81
Step-by-step explanation:
[tex]81:19\ \text{can be written as the fraction}\ \dfrac{81}{81+19}=\dfrac{81}{100}=\large\boxed{0.81}[/tex]
A list of pulse rates is 70, 64, 80, 74,92. What is the median for this list?
Answer:
64 70 74 80 92
Answer = 74
Step-by-step explanation:
The median is when you have an order of numbers in ascending order (smallest to largest) then you find the middle number
Hope this helps :)
If anything is incorrect then please comment and I shall change the answer to the correct one
Median for the given data 70, 64, 80, 74,92 is equals to 74.
What is median?"Median is defined as the central value of the given data after arranging them into ascending or descending order."
According to the question,
Given data for pulse rates = 70, 64, 80, 74,92
Arrange the data in ascending order we get,
64, 70 , 74, 80, 92
Number of pulse rate reading is 5 , which is an odd number.
Therefore, median is the central value.
Median for the given data = 74
Hence, median for the given data 70, 64, 80, 74,92 is equals to 74.
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look the image below
Answer:
Does the answer help you?
Does the answer help you?Please choose my answer as a brainliest answer and please rate.
Does the answer help you?Please choose my answer as a brainliest answer and please rate.It take a few mins to solve your question.
Answer:
V≈696.91
Step-by-step explanation:
V=4
3πr3=4
3·π·5.53≈696.90997
Evaluate the expression for q = -2. 8q=
Answer:
-16
Step-by-step explanation:
8q
Let q = -2
8*-2
-16
plz help brainliest to correct answer
Answer:
-2 would be right next to -3 because its negative and -1 would be right next to -2, 2 would be two points away from 0 bc its a whole number
A population culture begins with 20 strands of bacteria and then doubles every 4 hours. This can be modeled by , where t is time in hours. How many strands of bacteria are present at 20 hours?
Question 13 options:
A)
425 strands of bacteria
B)
567 strands of bacteria
C)
640 strands of bacteria
D)
375 strands of bacteria
Answer:
C) 640 strands of bacteria
Step-by-step explanation:
We are told in the question that the population doubles every 4 hours
Hence, formula to solve this question =
P(t) = Po × 2^t/k
From the question, we have the following information:
Beginning amount (Po) = 20 strands of bacteria
Rate(k) = 4 hours
Time(t) = 20 hours
Ending time (P(t)) = unknown
Ending amount = 20 × 2^20/4
= 20 × 2^5
= 20 × 320
= 640 strands of bacteria.
Therefore, the number of strands left after 20 hours is 640 strands of bacteria.
Please help me with this on the picture
9514 1404 393
Answer:
(x, y) ⇒ (y+1, 7-x) . . . rotation 90° CW about (4, 3)
or
(x, y) ⇒ (y+1, x+1) . . . glide reflection across y=x; and translation (1, 1)
Step-by-step explanation:
The figure is apparently rotated 90° clockwise. This can be accomplished a couple of ways: (1) rotation 90° CW about some center; (2) reflection across the line y=x. Because of the symmetry of the figure, we cannot tell which of these is used.
Rotation
The center of rotation can be found by looking at the perpendicular bisectors of the segments joining a vertex and its image. One such segment has endpoints (1, 6) and (7, 6), so is a horizontal line with midpoint (4, 6). The perpendicular bisector of that is x=4.
Another segment joining a point with its image has endpoints (5, 6) and (7, 2). Its midpoint is (6, 4), and the slope of the bisector through that point is 1/2. It intersects the line x=4 at (4, 3), the center of rotation.
Rotation 90° CW about the origin is the transformation (x, y) ⇒ (y, -x), so rotation of (x, y) 90° about the point (4, 3) will be the transformation ...
(x, y) ⇒ ((y -3) +4, (-(x -4) +3) = (y +1, 7 -x)
The transformation A to B is rotation 90° CW about (4, 3):
(x, y) ⇒ (y +1, 7 -x).
__
Reflection
Simple reflection across the line y=x is the transformation (x, y) ⇒ (y, x). Applying that transformation, we see that an additional translation of 1 unit right and one unit up is required. The complete transformation is a "glide reflection", a reflection followed by a translation.
The transformation A to B is a glide reflection across the line y=x with a translation up 1 and right 1:
(x, y) ⇒ (y +1, x +1).
On a coordinate plane, line P Q goes through (negative 6, 4) and (4, negative 4). Point R On a coordinate plane, a line goes through (negative 4, 0) and (4, negative 4). A point is at (2, 3). What is the equation of the line that is parallel to the given line and passes through the point (2, 3)? x + 2y = 4 x + 2y = 8 2x + y = 4 2x + y = 8
Answer:
x + 2y = 8.
Step-by-step explanation:
Line goes through (-4, 0) and (4, -4).
The slope is (-4 - 0) / (4 - -4) = -4 / (4 + 4) = -4 / 8 = -1/2.
Since we are looking for the equation of the line parallel to that line, the slope will be the same.
We have an equation of y = -1/2x + b. We have a point at (2, 3). We can then say that y = 3 when x = 2.
3 = (-1/2) * 2 + b
b - 1 = 3
b = 4.
So, we have y = -1/2x + 4.
1/2x + y = 4
x + 2y = 8.
Hope this helps!
ANSWEAr
x + 2y = 8
because it is
What is the difference in their elevations?
An airplane flies at an altitude of 26,000 feet. A submarine dives to a depth of 700 feet below sea level
Answer:
their difference in elevations are: they both don't fly one fly and one dive if you take the airplane it works quicker but if you take the submarine you won't reach faster
Find x. A. 3√3 B. 3 C. 2√3/3 D. √63
Answer:
[tex]\huge\boxed{\sf x = 3\sqrt{3}}[/tex]
Step-by-step explanation:
Cos 30 = Adjacent / Hypotenuse
Where Adjacent = x , Hypotenuse = 6
[tex]\frac{\sqrt{3} }{2}[/tex] = x / 6
x = [tex]\frac{\sqrt{3} }{2}[/tex] * 6
[tex]\sf x = 3\sqrt{3}[/tex]
What is the slope of the line showed?
Answer:
2
Step-by-step explanation:
The formula for the slope of a line is rise over run. We know that the slope of the line will be positive because the line is going up from left to right.
Rise is the change on the y-axis, going up and down. Run is the change on the x-axis, going from left to right.
Let's start from the origin (0,0). To reach the next point on the line, we have to go up two points (rise) and over one point (run).
Slope = rise/run
Slope = 2/1
Slope = 2
Hope that helps.
Answer:
slope=2
Step-by-step explanation:
take two points from graph (0,0) and (1,2)
m=y2-y1/x2-x1
m=2-0/1-0
m=2
Find 14.6 + 8.52
I really need help !!!!
Answer:
[tex]14.6 + 8.52 \\ = 23.12[/tex]
To prove a statement by mathematical induction, all we have to do is show that it is true for n+1. (True or False)
Answer:
False
Step-by-step explanation:
We also need to show that it is true for n=1
and for n=k+1
Solve x/10 = -7 A. x = 3 B. x = -0.7 C. x = -17 D. x = -70
Answer:
x = -70
Step-by-step explanation:
x/10 = -7
Multiply each side by 10
x/10*10 = -7*10
x = -70
What is the volume of the sphere shown below with a radius of 6?
A. 483 Cu, units
B. 2887 cu units
C. 1627 cu units
D. 14431 Cu, units
Answer:
B
Step-by-step explanation:
Volume of the sphere = (4/3)*pi*6^3=288*pi
Answer:
288 pi units^3
Step-by-step explanation:
The volume of a sphere is given by
V = 4/3 pi r^3
V = 4/3 pi (6)^3
V = 4/3 pi (216)
V = 288 pi units^3
A chemical company makes two brands
of antifreeze. The first brand is 30% pure
antifreeze, and the second brand i$ 80% pure
antifreeze. In order to obtain 80 gallons of a
mixture that contains 70o£ pure antifreeze, hov
mabry gallons of each band ot antifneze must
bo used?
Answer:
16 bags for the first(30% pure) and 64 bags of the second(80% pure)
Step-by-step explanation:
If they are mixed in a ratio of x bags to y bags
(0.3x+0.8y)/(x+y) = 0.7
0.3x + 0.8y = 0.7(x+y)
Multiply both sides with 10
3x + 8y = 7(x+y)
4x = y ——(1)
x + y = 80 ——(2)
Solve simultaneously
x + 4x = 80
5x = 80
x = 16 bags
y = 4x = 64 bags
Consider the given function and the given interval.
f(x) = 8 sin x - 4 sin 2x, [0,pi]
(a) Find the average value f ave of f on the given interval.
(b) Find c such that f ave = f(c).
(a) The average value of f(x) on the closed interval [0, π] is
[tex]\displaystyle\frac1{\pi-0}\int_0^\pi f(x)\,\mathrm dx = \frac1\pi\int_0^\pi(8\sin(x)-4\sin(2x))\,\mathrm dx = \boxed{\frac{16}\pi}[/tex]
(b) By the mean value theorem, there is some c in the open interval (0, π) such that f(c) = 16/π. Solve for c :
8 sin(c) - 4 sin(2c) = 16/π
8 sin(c) - 8 sin(c) cos(c) = 16/π
sin(c) - sin(c) cos(c) = 2/π
Use a calculator to solve this. You should get two solutions, c ≈ 1.2382 and c ≈ 2.8081.
A portion of the quadratic formula proof is shown. Fill in the missing reason.
Answer:
Find a common denominator on the right side of the equation
Step-by-step explanation:
The equation before the problem is
X² + b/a(x) + (b/2a)²= -c/a + b²/4a²
The next step in solving the above equation is to fibd tge common denominator on the right side of the equation.
X² + b/a(x) + (b/2a)²= -c/a + b²/4a²
X² + b/a(x) + (b/2a)²= -4ac/4a² + b²/4a²
X² + b/a(x) + (b/2a)²=( b²-4ac)/4a²
The right side of the equation now has a common denominator
The next step is to factorize the left side of the equation.
(X+b/2a)²= ( b²-4ac)/4a²
Squaring both sides
X+b/2a= √(b²-4ac)/√4a²
Final equation
X=( -b+√(b²-4ac))/2a
Or
X=( -b-√(b²-4ac))/2a
Fill in the blanks and explain the pattern
0,1,1,2,3,5,__,__,21,34,55
Answer:
8,13
Step-by-step explanation:
Look at the pattern :
0,1,1,2,3,5,...,...,21,34,55.
As you see the number in the pattern was made by the sum of 2 numbers behind it. Then, the blanks must be filled by :
3 + 5 = 88 + 5 = 13So, the blanks must be filled by 8 and 13
Answer:
In the two blanks would be 8, 13.
The pattern is practically the Fibonacci Code.
Step-by-step explanation:
The Fibonacci Code is a mathematical sequencing in which you start with two numbers and add them together to make the third number, then you add the third number and the second number together. Practically you keep adding each new sum and the number before it in the sequence to find the next new sum.
After 55 in this pattern, the pattern would go 89, 144, 233, 377, 610, 987,...
x power 8 + x power 4 + 1
factorize
Answer:
[tex]1(x {}^{8} + x {}^{4} + 1)[/tex]
Step-by-step explanation:
[tex]x {}^{8} + {x}^{4} + 1 =1( x {}^{8} + x {}^{2} + 1)[/tex]
Hope this helps ;) ❤❤❤
Let me know if there is an error in my answer.
Find the value of x.
A. 86
B. 172
C. 94
D. 188
Answer:
188
Step-by-step explanation:
Tangent Chord Angle = 1/2Intercepted Arc
94 = 1/2 x
Multiply by 2
2*94 =x
188 =x
Select the best answer for the question . 7. At a public swimming pool , the probability that an employee is a lifeguard is P(L) = 0.85 , and the probability that an employee is a teenager is P(T) = 0.58 . What's the probability that an employee is a lifeguard , given that the employee is a teenager ? O A. There isn't enough information given. O B. 1.47 OC. 0.68 O D.0.49
Answer:
D) 0.49
Step-by-step explanation:
0.85 * 0.58 = 0.49
The probability is:
D 0.49
A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 407 gram setting. It is believed that the machine is underfilling the bags. A 20 bag sample had a mean of 397 grams with a standard deviation of 13. A level of significance of 0.05 will be used. Assume the population distribution is approximately normal. State the null and alternative hypotheses.
Answer:
Null hypothesis: μ = 407
Alternative hypothesis: μ < 407.
Step-by-step explanation:
In this case, the machine is SUPPOSED to fill the bag so that the bag weighs 407 grams. So, the null hypothesis will be that the machine is doing what it is supposed to be doing. And so, μ = 407 grams would be the null.
The worker thinks the machine is filling the bags to LESS THAN what it is supposed to. So, the alternative hypothesis is that the machine is NOT doing what it is supposed to and μ < 407 grams.
Hope this helps!