Answer:
a. Pr(They both have type O)
= Pr(They both have type O)
= 0.35 x 0.45
= 0.1575 = 15.75%
b. Pr( they both have the same blood type)
= Pr( they both have the same blood type)
= 2/8
= 0.25 = 25%
c. Pr( at least one person has type O)
= Pr (at least one person has type O)
= 1 - 0.3575
= 0.6425 = 64.25%
Step-by-step explanation:
a) Data:
O A B AB
Chinese 0.35 0.27 0.26 0.12
American 0.45 0.4 0.11 0.04
b) Calculations:
i. Pr(They both have type O)
= Probability of Chinese with O multiplied by Probability of American with O
= 0.35 * 0.45
= 0.1575 = 15.75%
ii. Pr( they both have the same blood type)
= Probability of two out of 8 outcomes
= 2/8
= 0.25 = 25%
iii. Pr( at least one person has type O)
= Probability of (1 – p(none) )
The probability of none = p(none O blood type)
= p(none)
for Chinese = (0.27 + 0.26 + 0.12) * for American ( 0.4 + 0.11 + 0.04)
= 0.65 * 0.55 = 0.3575
Pr (at least one person has type O) = 1 - 0.3575
= 0.6425
simplify theta(sin theta) ²/2tan theta
Step-by-step explanation:
When θ is very small, θ ≈ sin θ ≈ tan θ.
θ (sin θ)² / (2 tan θ)
θ³ / (2θ)
θ² / 2
g natasha is in a class of 30 students that selects 4 leaders. How many ways are there to select the 4 leaders so that natasha is one of the leaders
Answer:
3,654 different ways.Step-by-step explanation:
If there are 30 students in a class with natasha in the class and natasha is to select four leaders in the class of which she is already part of the selection, this means there are 3 more leaders needed to be selected among the remaining 29 students (natasha being an exception).
Using the combination formula since we are selecting and combination has to do with selection, If r object are to selected from n pool of objects, this can be done in nCr number of ways.
nCr = n!/(n-r)!r!
Sinca natasha is to select 3 more leaders from the remaining 29students, this can be done in 29C3 number of ways.
29C3 = 29!/(29-3)!3!
29C3 = 29!/(26!)!3!
29C3 = 29*28*27*26!/26!3*2
29C3 = 29*28*27/6
29C3 = 3,654 different ways.
This means that there are 3,654 different ways to select the 4 leaders so that natasha is one of the leaders
PLZ HELP ASAP (Algebra)
Answer:
Step-by-step explanation:
Whenever you add two number x and -x and it becomes 0 . IT is the identity property.
Ex:
-1/3 + 1/3 = 0
-1 + 1 = 0
-58 + 58 = 0
Please answer! I am struggling with this question! Please show ALL work! <3 (the answer choices are provided on a separate image)
Answer:
The radius is 18 inches
Step-by-step explanation:
The circumference of a circle is given by
C = 2 * pi *r
36 pi = 2 * pi *r
Divide each side by pi
36 = 2r
Divide each side by 2
18 =r
Answer:
The answer is option CStep-by-step explanation:
Circumference of a circle = 2πr
where
r is the radius of the circle
From the question
Circumference = 36π inches
To find the radius substitute the value of the circumference into the above formula and solve for the radius
That's
[tex]36\pi = 2\pi r[/tex]Divide both sides by 2π
We have
[tex] \frac{36\pi}{2\pi} = \frac{2\pi \: r}{2\pi} [/tex]We have the final answer as
r = 18 inchesHope this helps you
I require someone to answer this question for me ASAP please?
Answer:
x has to be less than 3
Step-by-step explanation:
Answer:
x < 3
I hope this helps!
What is 5% added to $194?
Answer:
203.7
Step-by-step explanation:
5% of 194 added to 194 =
= 5% * 194 + 194
= 0.05 * 194 + 194
= 9.7 + 194
= 203.7
What is the slope of a line perpendicular to y=-7/4x
O A.
IN
O B.
7
O c.
4
-
O D.
7
4
Answer:
y=4/7x
Step-by-step explanation:
perpendicular lines have opposite slopes. that means reciprocal and opposite sign.
Ellen is making jewelry sets that contain a bracelet and a pair of earrings. Each bracelet uses 3 times as many beads as one earring. Each bracelet uses 3 as times as many beads as one earring . Ellen uses 13 beads for each earring. How many beads does Ellen need to make one jewelry set?
It's given that the Bracelet uses 3 times the number of beads that's used in making a single earring.
It's also given that one single earing has 13 beads. So a single bracelet would have (3×13) beads .... and that's equal to 39.
Making a single set of jewellery needs a pair of earrings and a Bracelet.
So total number of required beads will be =
39 + 13 + 13 = 65Find the measure of b. A. 63 B. 27 C. 31.5 D. 126
Answer:
126°
Step-by-step explanation:
If that angle is 27, so is angle a.
180-27-27=126
A 20-foot ladder is placed against a tree. The bottom is located 5 feet from the base of the tree and the top of the ladder is 5√15 feet up the tree. Use tangent to find the angle created between the ladder and tree. Include a sketch that shows all known information and clearly shows what you need to find. Show all work and give the answer rounded to the nearest tenth of a degree.
Answer:
14.5°
Step-by-step explanation:
The sketch results in an angle of depression problem.
In this case, the opposite side of the triangle formed is 5 ft
The hypotenuse side is 20 ft
The adjacent side is the [tex]5\sqrt{15}[/tex] ft
Using tangent θ = opp/adj
tangent θ = 5/[tex]5\sqrt{15}[/tex] = [tex]\frac{1}{\sqrt{15} }[/tex] = 0.258
θ = [tex]tangent^{-1}[/tex] 0.258 = 14.5°
3(x–6)=18 help plese
Answer:
x = 12
Step-by-step explanation:
3(x–6)=18
x-6 = 18:3
x-6 = 6
x = 6+6
x = 12
Answer:
x=12
Step-by-step explanation:
it is 235 miles from tulsa to dallas. it is 390 miles from dallas to houston. a) what is the total distance of a trip from tulsa to dallas to houston? b) what is the total distance from houston to dallas to tulsa? c) explain how you can tell whether the distances described in parts (a) and (b) are equal by using reasoning.
Answer:
a- tulsa to dallas to houston is 235+390 which is 625 miles
b - houston to dallas to tulsa is 390+235 miles which is 625 miles
c - by using reasoning both are same because they are just rewritten differently but the equation is same
please give me brainliest
hope it helps buddy
A hypothesis test is to be performed to test the equality of two population means. The sample sizes are large and the samples are independent. A 95% confidence interval for the difference between the population means is (1.4, 8.7). If the hypothesis test is based on the same samples, which of the following do you know for sure:
A: The hypothesis µ1 = µ2 would be rejected at the 5% level of significance.
B: The hypothesis µ1 = µ2 would be rejected at the 10% level of significance.
C: The hypothesis µ1 = µ2 would be rejected at the 1% level of significance.
A) A and B
B) A and C
C) A only
D) A, B, and C
Answer:
C) A only
Step-by-step explanation:
In statistics, the null hypothesis is the default hypothesis and the alternative hypothesis is the research hypothesis. The alternative hypothesis usually comes in place to challenge the null hypothesis in order to determine if the test is statistically significant or not.
Similarly,
In hypothesis testing, the confidence interval consist of all reasonable value of the population mean. Values for which the null hypothesis will be rejected [tex]H_o[/tex] .
Given that:
At 95% confidence interval for the difference between the population means is (1.4, 8.7).
The level of significance = 1 - 0.95 = 0.05 = 5%
So , If the hypothesis test is based on the same samples, The hypothesis µ1 = µ2 would be rejected at the 5% level of significance.
To measure Monarch butterfly migration,
scientist tag and release 100 butterflies in
Kansas and Missouri before traveling to
Mexico. While in Mexico, the same
scientist captured another 100 butterflies
of which 15 are tagged. Based on this
information, how many butterflies would
you predict start in Kansas and Missouri
and migrate to Mexico?
the answer is 667.
100/x = 15/100
it’s a proportion so you cross multiply. after cross multiplying you get 15x = 10,000. divided both sides by 15 and you get x = 66.6 (continuation of the 6). since it’s repeating, round it and you get 667.
by the way this is actually one of my homework questions for today ;)
The predicted number of butterflies that starts from Kansas and Missouri and migrate to Mexico is 667.
The Aim of the experiment is to measure the Monarch butterfly migration
number of butterflies tagged and released in Kansas and Missouri = 100 number of tagged butterflies captured in Mexico = 15 Let the number of butterflies that start from Kansas and Missouri and end in Mexico = xPredicting the number of butterflies
= [tex]\frac{100}{x} = \frac{15}{100}[/tex]
= [tex]15x = ( 100 * 100)[/tex]
∴ x( predicted value ) = [tex]\frac{10000}{15 } = 667[/tex]
hence the approximate value of the number of butterflies that migrate to Mexico from Kansas and Missouri is 667
learn more about migration : https://brainly.com/question/23903333
The length of a rectangle is twice its width. If the perimeter of the rectangle is 30m, find its area.
Answer:
If the perimeter of the rectangle is 30cm , find its area. W=5 FOR THE WIDTH. 5*10=50 FOR THE AREA.
Step-by-step explanation:
The area of the Rectangle is 50 sq.m
What is the formula of Area of Rectangle?The area of rectangle for a rectangle of length L and width W is given by
A = L* W
It is measured in square units.
Let the length of the rectangle be L
The width of the rectangle is W
The length of a rectangle is twice its width
L = 2W
Perimeter of the Rectangle is 2( Length + Width)
30 = 2 (L +W)
15 = L + W
15 = 2W +W
15 = 3W
W = 5m
L = 10m
The area of the rectangle is Length * Width
Area = 10 *5
Area = 50 sq.m
To know more about Area of Rectangle
brainly.com/question/20693059
#SPJ2
una compañía sabe que si produce "x" unidades mensuales su utilidad "u" se podría calcular con la expresión:
u(x)=-0.04x^2+44x-4000
donde "u" se expresa en dólares. Determine la razón del cambio promedio de la utilidad cuando el nivel de producción cambia de 600 a 620 unidades mensuales. Recuerde que la pendiente de la recta secante a la gráfica de la función representa a la razón de cambio promedio.
porfavor alguien que me explique el procedimiento :(
Answer:
Δf(u) /Δx = 92,8 ( razón de cambio promedio)
Step-by-step explanation:
La expresión de la utilidad de la empresa u(x) en función de la cantidad de unidades producidas "x" es:
u(x) = 0,04*x² + 44*x -4000
Entonces la razón de cambio promedio en un intervalo (a ; b) en este caso ( 620 ; 600 ) viene dada por la expresión:
Δf(x)/ Δx = [ f(b) - f(a) ]/( b - a )
en donde f(b) y f(a) se obtienen por sustitución de los valores a y b es decir 600 y 620 respectivamente en la función f(x) = u(x) entonces
Δf(u) /Δx = [ u(b) - u(a) ]/( b -a ) (1)
u(b) = 0,04*(620)² + 44*(620) - 4000
u(b) = 15376 + 27280 -4000
u(b) = 2656 unidades
u(a) = 0,04* (600)² + 44* 600 - 4000
u(a) = 14400 + 26400 - 4000
u(a) = 800
Sustituyendo esos valores en la ecuación 1
Δf(u) /Δx = 2656 - 800 / 620 - 600
Δf(u) /Δx = 92,8
10 easy points!!!! What is the x-intercept of the line?
Answer:
Step-by-step explanation:
As x increases from -74 to -54 (a 'run' of 20), y decreases from 18 to 12 (a 'rise' of -6. Thus, the slope of this line is m = rise/run = -6/20 = -13/10.
From y = mx + b we get 12 = (-13/10)(12) + b, or (after dividing all terms by 12)
1 = -13/10 + b/12, or
60 = -3(6) + 5b, or
42 = - 5b, or b = -42/5
The line is y = (-13/10)x - 42/5.
At the x-intercept, y = 0. Setting y = 0, we get:
(13/10)X = -42/5, or 13x = -84.
Thus, x = -84/13 = -6.46
and so the x-intercept of the line is (-6.46, 0)
Consider the line =−−7x4y−6.
What is the slope of a line parallel to this line?
What is the slope of a line perpendicular to this line?
Answer:
4/7
Step-by-step explanation:
Original equation, in general form: -7x - 4y - 6
Rearrange to get: 4y = -7x - 6
Divide both sides by 4 to get: y = -7/4(x) - 1.5
To find the slope of a line perpendicular to another line, take the original gradient, and find the negative inverse
So for here,
Original gradient: -7/4
Negative: 7/4
Negative Inverse: 4/7 (which is our gradient)
Done!
Eliminate the parameter for the following set of parametric equations: x= t + 6 y= 3t – 1
Answer:
Solution : Option A
Step-by-step explanation:
What we want to do here is eliminate the parameter t. In order to do that, we can isolate t in our first equation x = t + 6 ----- ( 1 ) and then plug that value for t in the second equation y = 3t - 1. Our solution will be an equation that is not present with t.
( 1 ) x = t + 6, t = x - 6
( 2 ) y = 3( x - 6 ) - 1 ( Distribute the " 3 " in 3( x - 6 ) )
y = 3x - 18 - 1 ( Combine like terms )
y = 3x - 19
As you can see our result will be option a, y = 3x - 19.
How do u solve A/B + C/D = E
What is the probability that a randomly selected individual on this campus weighs more than 166 pounds? (express in decimal form and round final answer to 4 decimal places)
Answer:
hello attached is the missing part of your question and the answer of the question asked
answer : 0.2951
Step-by-step explanation:
Given data:
number of persons allowed in the elevator = 15
weight limit of elevator = 2500 pounds
average weight of individuals = 152 pounds
standard deviation = 26 pounds
probability that an individual selected weighs more than 166 pounds
std = 26 , number of persons(x) = 15, average weight of individuals(u) = 152 pounds
p( x > 166 ) = p( x-u / std, 166 - u/ std )
= p ( z > [tex]\frac{166-152}{26}[/tex] )
= 1 - p( z < 0.5385 )
p( x > 166 ) = 1 - 0.70488 = 0.2951
The following sample contains the scores of 6 students selected at random in Mathematics and English. Use the scores in English as the dependent variable Y.
Mathematics score (X) 70 92 80 74 65 83
English score 74 84 63 87 78 90
Σx =464 Σy=476 Σx^2= 36354 Σy^2=38254 Σxy= 36926
Find the sample coefficient of determination and interpret.
a. 0.0575 and prediction accuracy is 5.75%
b. 0.2397 and prediction accuracy is 23.97%
c. 0.0575 and prediction accuracy is 94.25%
d. 0.2397 and prediction accuracy is 76.03%
Answer:
d the answer is d
Step-by-step explanation:
Average of 44.64, 43.45, 42.79, 42.28
Answer:
43.29Step-by-step explanation:
[tex]44.64+ 43.45+42.79+42.28\\\\= \frac{44.64+ 43.45+42.79+42.28}{4} \\\\\\= \frac{173.16}{4} \\\\= 43.29\\[/tex]
Tierra's THR zone is 135-185 bpm (beats per minute). What might Tierra's heart rate be to
indicate that she was working too hard?
A. 145 bpm
B. 195 bpm
C. 175 bpm
D. 130 bpm
The correct answer is B. 195 bpm
Explanation:
In health and related areas, THR or Target Heart Rate zone refers to the range of heart rate an individual should have including the maximum heart rate. In the case of Tierra, her THR zone indicates her maximum heart rate should be 185 beats per minute.
In this context, a heart rate above this number shows Tierra is working too hard or that his heart is doing too much effort, which is dangerous for her health. Thus, the heart rate that shows she is doing too hard is 195 bmp as this is the only one that is above the ideal rate.
Find the mass and center of mass of the solid E with the given density rho. E is the cube 0 ≤ x ≤ a, 0 ≤ y ≤ a, 0 ≤ z ≤ a; rho(x, y, z) = 9x2 + 9y2 + 9z2.
Answer:
mass = 9a^5
center of mass = [tex]\frac{7a}{12}, \frac{7a}{12}, \frac{7a}{12}[/tex]
Step-by-step explanation:
Finding the mass of the solid E
given density function : p ( x,y,z ) = [tex]9x^2 + 9y^2 + 9z^2[/tex]
Mass = [tex]\int\limits^a_0 \int\limits^a_0 \int\limits^a_0 {9(x^2+y^2+z^2)} \, dx dydz[/tex] [tex]= \int\limits^a_0 \int\limits^a_0 {9(\frac{a^3}{3}+ay^2+az^2 )} \, dydz[/tex]
[tex]= \int\limits^a_0 {9(\frac{a^4}{3}+\frac{a^4}{3} +a^2z^2 )} \, dz[/tex] [tex]= \int\limits^a_0 {9(\frac{2a^4}{3}+a^2z^2 )} \, dz[/tex] [tex]= 9 ( \frac{2a^5}{3} + \frac{a^5}{3} )[/tex]
( taking limits as a and 0 )
hence Mass = 9 [tex](a^5)[/tex]
finding the center of mass
attached below is solution
BRAINLEST Find the sum of the first 6 terms of the infinite series: 1 - 2 + 4 - 8+...
Answer:
-21
Step-by-step explanation:
1-2+4-8+16-32
=-21
Answer:
The sum of the first 6 terms of the infinite series will be - 21.
Step-by-step explanation:
In this case, the infinite geometric series 1 - 2 + 4 - 8 + ... is represented by the following summation,
[tex]\sum _{{k=0}}^{{n}}(-2)^{k}[/tex]
Therefore if we continue this pattern, the first 6 terms will be 1 - 2 + 4 - 8 + 16 - 32. Adding these terms,
1 - 2 + 4 - 8 + 16 - 32
= - 1 + 4 - 8 + 16 - 32
= 3 - 8 + 16 - 32 = - 5 + 16 - 32
= 11 - 32 = Solution : - 21
Find the doubling time of an investment earning 8% interest if interest is compounded continuously. The doubling time of an investment earning 8% interest if interest is compounded continuously is ____ years.
Answer:
8.66 years
Step-by-step explanation:
Given that:
Interest rate = 8%
Using the exponential growth function:
A = Ao * e^(rt)
Where A = final amount
Ao = Initial amount
r = growth rate
t = time
Here we are to calculate the time it takes an investment earning 8% interest to double;
rate (r) = 8% = 0.08
2A = A * e^(rt)
Divide both sides by A
2 = e^(rt)
2 = e^(0.08 * t)
2 = e^(0.08t)
In(2) = 0.08t
0.6931471 = 0.08t
Divide both sides by 0.08
0.6931471 / 0.08 = 0.08t / 0.08
8.6643397 = t
t = 8.66 years
Answer:
symbolically, the answer would be t= ln(2)/(.08)
Step-by-step explanation:
start by writing out your variables:
rate= .08
*dont forget the investment doubles too, thats where 2P is in the bottom equation
equation should look like:
[tex]2P=Pe^{.08t}[/tex]
then you solve, so divide P on the right and left:
[tex]\frac{2p}{p} = \frac{Pe^{.08t}}{p}[/tex]
now it looks like: [tex]2=e^{.08t}[/tex]
you can take the natural log (ln) of 2 to get the exponent by itself .08t
ln(2)=.08t
then divide .08 to get t by itself
[tex]\frac{ln(2)}{.08} =\frac{.08t}{.08}[/tex]
so symbolically, your equation should be:
[tex]t=\frac{ln(2)}{.08}[/tex]
to get t as your answer you can plug this equation into your calculator to get:
t=8.66 years so approximently 8 years
The parallelogram to be a square,x=?
Answer:
7°
Step-by-step explanation:
for this paralellogram to be a square, the sides should be perpendicular.
Woch means that 4x+17° = 45°
● 4x +17° = 45°
Substract 17 from both sides.
● 4x +17°-17° = 45°-17°
● 4x = 28°
Divide both sides by 4
● 4x/4 = 28°/ 4
● x = 7°
Apply the distributive property to factor out the greatest common factor. 40f+30 =
Answer:
10(4f+3)
Step-by-step explanation:
boo
f(x)=3x2+10x-25 g(x)=9x2-25 Find (f/g)(x).
Answer:
[tex](f/g)(x) = \frac{x + 5}{3x + 5} [/tex]
Step-by-step explanation:
f(x) = 3x² + 10x - 25
g(x) = 9x² - 25
To find (f/g)(x) divide f(x) by g(x)
That's
[tex](f/g)(x) = \frac{3 {x}^{2} + 10x - 25 }{9 {x}^{2} - 25 } [/tex]
Factorize both the numerator and the denominator
For the numerator
3x² + 10x - 25
3x² + 15x - 5x - 25
3x ( x + 5) - 5( x + 5)
(3x - 5 ) ( x + 5)
For the denominator
9x² - 25
(3x)² - 5²
Using the formula
a² - b² = ( a + b)(a - b)
(3x)² - 5² = (3x + 5)(3x - 5)
So we have
[tex](f/g)(x) = \frac{(3x - 5)(x + 5)}{(3x + 5)(3x - 5)} [/tex]
Simplify
We have the final answer as
[tex](f/g)(x) = \frac{x + 5}{3x + 5} [/tex]
Hope this helps you
