Answer:
a
The null hypothesis is
[tex]H_o : \mu = 21[/tex]
The Alternative hypothesis is
[tex]H_a : \mu< 21[/tex]
b
[tex]\sigma_{\= x} = 0.8944[/tex]
c
[tex]t = -2.236[/tex]
d
Yes the mean population is significantly less than 21.
Step-by-step explanation:
From the question we are given
a set of data
20 18 17 22 18
The confidence level is 90%
The sample size is n = 5
Generally the mean of the sample is mathematically evaluated as
[tex]\= x = \frac{20 + 18 + 17 + 22 + 18}{5}[/tex]
[tex]\= x = 19[/tex]
The standard deviation is evaluated as
[tex]\sigma = \sqrt{ \frac{\sum (x_i - \= x)^2}{n} }[/tex]
[tex]\sigma = \sqrt{ \frac{ ( 20- 19 )^2 + ( 18- 19 )^2 +( 17- 19 )^2 +( 22- 19 )^2 +( 18- 19 )^2 }{5} }[/tex]
[tex]\sigma = 2[/tex]
Now the confidence level is given as 90 % hence the level of significance can be evaluated as
[tex]\alpha = 100 - 90[/tex]
[tex]\alpha = 10[/tex]%
[tex]\alpha =0.10[/tex]
Now the null hypothesis is
[tex]H_o : \mu = 21[/tex]
the Alternative hypothesis is
[tex]H_a : \mu< 21[/tex]
The standard error of mean is mathematically evaluated as
[tex]\sigma_{\= x} = \frac{\sigma}{ \sqrt{n} }[/tex]
substituting values
[tex]\sigma_{\= x} = \frac{2}{ \sqrt{5 } }[/tex]
[tex]\sigma_{\= x} = 0.8944[/tex]
The test statistic is evaluated as
[tex]t = \frac{\= x - \mu }{ \frac{\sigma }{\sqrt{n} } }[/tex]
substituting values
[tex]t = \frac{ 19 - 21 }{ 0.8944 }[/tex]
[tex]t = -2.236[/tex]
The critical value of the level of significance is obtained from the critical value table for z values as
[tex]z_{0.10} = 1.28[/tex]
Looking at the obtained value we see that [tex]z_{0.10}[/tex] is greater than the test statistics value so the null hypothesis is rejected
In order to sustain itself in its cold habitat, a Siberian tiger requires 25 pounds of meat per day.
How much meat would seven Siberian tigers need for the month of April?
Select one:
a. 750 pounds
b. 175 pounds
c. 5425 pounds
d. 5250 pounds
Answer:
d. 5250 pounds
Step-by-step explanation:
25 lbs per day
There are 30 days in april
25 lbs/ day * 30 days
1 tiger would eat 750 lbs
There are 7 tigers
7 * 750 =5250 lbs
Answer:
D. 5250 pounds
Step-by-step explanation:
What you need to do is multiply 25 pounds by 30 because there are 30 days in the month of April.
25 x 30 = 750
Then multiply that amount by seven because there are 7 tigers.
750 x 7 = 5250
Find the midpoint of AC.
B (0, a)
C (a, a)
A(0, 0) D (a,0)
Answer:
[tex]\huge\boxed{\bigg(\dfrac{a}{2};\ \dfrac{a}{2}\bigg)}[/tex]
Step-by-step explanation:
The formula of a midpoint:
[tex]M\bigg(\dfrac{x+1+x+2}{2};\ \dfrac{y_1+y_2}{2}\bigg)[/tex]
We have the points
[tex]A(0;\ 0)\to x_1=0;\ y_1=0\\\\C(a;\ a)\to x_2=a;\ y_2=a[/tex]
Substitute:
[tex]\dfrac{x_1+x_2}{2}=\dfrac{0+a}{2}=\dfrac{a}{2}\\\\\dfrac{y_1+y_2}{2}=\dfrac{0+a}{2}=\dfrac{a}{2}[/tex]
Answer:
The answer is (a/2,a/2)
Step-by-step explanation:
Fill in 2 then a
In conclusion (a/2,a/2)
For the functions f(x)=4x+5 and g(x)=6x+4,find (f•g)(0)and (g•f)(0)
Answer:
Step-by-step explanation:
f(x)=4x+5
g(x)=6x+4,
first: (f*g)=(4x+5) (6x+4)=24x²+46x+20
next:(f*g)(0)=((g*f)=24x²+46x+20=20
Hi,
f°g means : apply first g then f . so calculate "g" and then use result as "x" in f.
g°f means : you apply first f then g
so : f°g = 4 (g (x)) +5
4 (6x+4) +5 = 24x+16+5 = 24x+21
If (x+1) is the factor of polynomial p(x) = ax²+x+1, then find a.
Answer:
a = 0
Step-by-step explanation:
p(x) = ax²+x+1
Let x+1 = 0 => x = -1
Putting in the above polynomial
=> p(-1) = a(-1)^2+(-1)+1
By Remainder Theorem, Remainder will be zero
=> 0 = a(1) -1+1
=> 0 = a
OR
=> a = 0
Answer:
a = 1Step-by-step explanation:
Factors are what we can multiply to get the number.
x² + x + 1
Factor the polynomial.
x(x+1) + 1
ax² + x = x(x + 1)
ax² + x = x² + x
[tex]a=\frac{x^2 +x}{x^2 +x}[/tex]
a = 1
In a certain country the life expectancy for women in 1990 was 45 and in 2000 it was 85?years. Assuming that life expectancy between 2000 and 2100 increases by the same percentage as it did between 1900 and 2000,what will life expectancy be for women in 2100? Assuming the life expectancy between 2000 and 2100 will increase by the same percentage as it did between 1900 and 2000, the life expectancy for women will be —— years
Answer:
49145 years
Step-by-step explanation:
In a certain country the life expectancy for women in 1990 was 45 and in 2000 it was 85?years.
Assuming that life expectancy between 2000 and 2100 increases by the same percentage as it did between 1900 and 2000,what will life expectancy be for women in 2100?
In 10 years, the expectancy increased by 85/45 = 17/9
between 2000 and 2100, it will increas by 10 time 10 years, so expected expectancy is [tex]85*(\frac{85}{45})^{10} = 49145[/tex] years
The life expectancy for women will be 49145 years when It will increase by ten times between 2000 and 2100.
What is an exponential function?An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.
It is a relation of the form y = aˣ in mathematics, where x is the independent variable
In one country, women's life expectancy was 45 years in 1990 and 85 years in 2000.
Assuming that life expectancy grows by the same proportion between 2000 and 2100 as it did between 1900 and 2000, we have to determine the life would expectancy for women in 2100
Over a ten-year period, life expectancy rose by 85/45 = 17/9.
It will increase by ten times between 2000 and 2100, therefore the anticipated life expectancy will be
⇒ 85×(85/45)¹⁰
⇒ 85×(1.88)¹⁰
⇒ 49145 years
Hence, the life expectancy for women will be 49145 years
Learn more about exponential function here:
brainly.com/question/11487261
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The function f is defined as follows.
f(x) =4x²+6
If the graph of f is translated vertically upward by 4 units, It becomes the graph of a function g.
Find the expression for g(x).
Answer:
g ( x ) = 4x^2 + 10
Step-by-step explanation:
Solution:-
The translation of a function f ( x ) in the cartesian coordinate domain can be done by following the given guidelines:
Translation guidelines
Horizontal shifts
Right : f ( x ) -> f ( x - a )Left : f ( x ) - > f ( x + a )
Vertical shifts
Up : f ( x ) -> f ( x ) + bDown : f ( x ) - > f ( x ) - bGeneral shift ( Horizontal and Vertical shift )
f ( x ) - > f ( x ± a ) ± b
We are given a function f ( x ) which is to be translated vertically upward 4 units. We will use the guidelines for Vertical shifts, where in this case the magnitude of b = 4.
f ( x ) = 4x^2 + 6
f ( x ) - > f ( x ) + b
g ( x ) = f ( x ) + 4
g ( x ) = 4x^2 + 6 + 4
g ( x ) = 4x^2 + 10 ... Answer
Which ordered pair is a solution to the system of linear equations? 2x + 3y= 6 –3x + 5y = 10
Answer:
(0,2)
Step-by-step explanation:
solve by addition/elimination
2x + 3y= 6
–3x + 5y = 10
multiply first equation by 3 and second one by 2 to eliminate x)
6x+9y=18
-6x+10y=20 (add the two equations)
6x+9y-6x+10y=38
19y=38
y=38/19=2
2x+3y=6
2x=6-6
x=0
Answer:
a
Step-by-step explanation:
Marie is saving money for home repairs. So far, she has saved $1,558. She needs at least $2,158 for the repairs. She plans to
add $60 per week to her current savings until she can afford the repairs.
In this activity, you will algebraically model and solve an inequality based on this situation and interpret the solutions within
realistic guidelines
Part A
Question
Given the situation, which inequality models the number of additional weeks Marie needs to continue saving to afford the
home repairs?
Select the correct answer.
1,558 + 60x 22,158
60x + 1,558 5 2,158
1,558 - 60x s 2,158
2,158 - 60x 2 1,558
Answer:
Inequality: [tex]1558 + 60 x \geq 2158[/tex]
Number of Weeks: [tex]x \geq 10[/tex]
Step-by-step explanation:
Given
[tex]Initial\ Savings = \$1558[/tex]
[tex]Amount\ Needed = \$2158[/tex]
[tex]Additional\ Savings = \$60\ weekly[/tex]
Required
Represent this using an inequality
Represent the number of weeks as x;
This implies that, She'll save $60 * x in x weeks
Her total savings after x weeks would be
[tex]Initial\ Savings + 60 * x[/tex]
From the question, we understand that she needs at least 2158;
Mathematically, this can be represented as (greater than or equal to 2158)
[tex]\geq 2158[/tex]
Bringing the two expressions together;
[tex]Initial\ Savings + 60 * x \geq 2158[/tex]
Substitute 1558 for Initial Savings
[tex]1558 + 60 * x \geq 2158[/tex]
[tex]1558 + 60 x \geq 2158[/tex]
Hence, the inequality that represents the situation is [tex]1558 + 60 x \geq 2158[/tex]
Solving further for x (number of weeks)
[tex]1558 + 60 x \geq 2158[/tex]
Subtract 1558 from both sides
[tex]1558- 1558 + 60 x \geq 2158 - 1558[/tex]
[tex]60x \geq 600[/tex]
Divide both sides by 60
[tex]\frac{60x}{60} \geq \frac{600}{60}[/tex]
[tex]x \geq 10[/tex]
This means that she needs to save $60 for at least 10 weeks
Answer:
Its the first one
Step-by-step explanation:
I just did it lol
A right triangle has legs with lengths equal to 10 inches and 9x inches. Its hypotenuse measures (x + 10) inches. What is the approximate value of the hypotenuse? 10 inches 10.25 inches 20.25 inches 81 inches
Answer:
10.25 inchesStep-by-step explanation:
Given,
Perpendicular ( p ) = 9x
Base ( b ) = 10
Hypotenuse ( h ) = x + 10
Now, let's find the value of x
Using Pythagoras theorem:
[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]
Plug the values
[tex] {(x + 10)}^{2} = {(9x)}^{2} + {(10)}^{2} [/tex]
Using [tex] {(a + b)}^{2} = {a}^{2} + 2ab + {b}^{2} [/tex] , expand the expression
[tex] {x}^{2} + 20x + 100 = {(9x)}^{2} + {10}^{2} [/tex]
To raise a product to a power , raise each factor to that power
[tex] {x}^{2} + 20x + 100 = 81 {x}^{2} + {10}^{2} [/tex]
Evaluate the power
[tex] {x}^{2} + 20x + 100 = 81 {x}^{2} + 100[/tex]
Cancel equal terms on both sides of the equation
[tex] {x}^{2} + 20x = 81 {x}^{2} [/tex]
Move x² to R.H.S and change its sign
[tex]20x = 81 {x}^{2} - {x}^{2} [/tex]
Calculate
[tex]20x = 80 {x}^{2} [/tex]
Swap both sides of the equation and cancel both on both sides
[tex]80x = 20[/tex]
Divide both sides of the equation by 80
[tex] \frac{80x}{80} = \frac{20}{80} [/tex]
Calculate
[tex]x = \frac{20}{80} [/tex]
Reduce the numbers with 20
[tex]x = \frac{1}{4} [/tex]
The value of X is [tex] \frac{1}{4} [/tex]
Now, let's replace the value of x to find the approximate value of hypotenuse
Hypotenuse = [tex] \frac{1}{4} + 10[/tex]
Write all numerators above the common denominator
[tex] \frac{1 + 40}{4} [/tex]
Add the numbers
[tex] \frac{41}{4} [/tex]
[tex] = 10.25[/tex] inches
Hope this helps..
best regards!!
Answer:
10.25
Step-by-step explanation:
because I said so ya skoozie
A college graduate is curious about the proportion of graduates who have loan debt 20 years after graduating. Let the proportion of graduates who have loan debt 20 years after graduating be p. If the college graduate wishes to know if the proportion of graduates who have loan debt 20 years after graduating is less than 18%, what are the null and alternative hypotheses?
Answer: Null Hypothesis [tex]H_{0}[/tex]: p = 0.18
Alternative Hypothesis [tex]H_{a}[/tex]: p < 0.18
Step-by-step explanation: When doing an experiment, first define the hypotheses you want to test. These hypotheses are Null Hypothesis and Alternative Hypothesis
Null Hypothesis is a general assumption and discloses that there is no relationship between the conditions under consideration. It is the hypothesis the researcher is trying to disprove. It is denoted by the symbol [tex]H_{0}[/tex].
For the college graduate curiosity, the hypothesis the graduate is trying to disprove is that the proportion of students who have loan debt after 20 years of graduation is 18%. Then, Null Hypothesis is [tex]H_{0}[/tex]: p = 0.18
Alternative Hypothesis is the a statement describing a relationship between the collected data. It is what researches try to prove and the results are observations of real causes. It is denoted by the symbol [tex]H_{a}[/tex].
For the graduate study, the alternative is that the proportion is less tahn 18% or 0.18. Then, Alternative Hypothesis: [tex]H_{a}[/tex]: p < 0.18
In △ABC, m∠A=27 °, c=14 , and m∠B=25 °. Find a to the nearest tenth.
Answer:
a = 8.1
Step-by-step explanation:
Firstly, since we have a triangle, automatically, we have 3 interior angles
Mathematically the sum of these angles = 180
A + B + C = 180
27 + 25 + C = 180
52 + C = 180
C = 180-52
C = 128
We use the sine rule to find a
The sine rule posits that the ratio of a side to the sine of the angle facing that side is equal for all the sides of a triangle
Thus, mathematically according to the sine rule;
c/Sin C = a/Sin A
14/sin 128 = a/sin 27
a = 14sin27/sin 128 = 8.0657
which to the nearest tenth is 8.1
2. Write as a complex number.
Answer:
Your answer is correct ✔️
Step-by-step explanation:
Hope this is correct and helpful
HAVE A GOOD DAY!
Answer:
2√3 + 3i is the answer
Step-by-step explanation:
People start waiting in line for the release of the newest cell phone at 5\text{ a.m.}5 a.m.5, start text, space, a, point, m, point, end text The equation above gives the number of people, PPP, in line between the hours, hhh, of 6\text{ a.m.}6 a.m.6, start text, space, a, point, m, point, end text and 11\text{ a.m.}11 a.m.11, start text, space, a, point, m, point, end text, when the doors open. Assume that 6\text{ a.m.}6 a.m.6, start text, space, a, point, m, point, end text is when time h = 1h=1h, equals, 1. What does the 232323 mean in the equation above?
Answer:
There are 23 people in line at 6:00 A.M
Step-by-step explanation:
When you plug in h=1, we get 23 people
h corresponds with the time 6:00 am, as a result there are 23 people in line
The equation represents how many people will come as the hour increases.
23 represents the initial amount of people in line.
(got this from Khan academy too:))
16. Find the equation of a parabola with a focus at (3,1) and a directrix at y = 3.
A) y = 1∕4(x – 3)^2 + 3
B) y = –1∕4 (x – 3)^2 + 3
C) y = –1∕4 (x – 3)^2 + 2
D) y = 1∕4(x – 3)^2 + 2
Answer:
C
Step-by-step explanation:
Any point (x, y) on the parabola is equidistant from the focus and the directrix.
Using the distance formula
[tex]\sqrt{(x-3)^2+(y-1)^2}[/tex] = | y - 3 | ← square both sides
(x - 3)² + (y - 1)² = (y - 3)² ← expand the y- factors
(x - 3)² + y² - 2y + 1 = y² - 6y + 9 ← subtract y² - 2y + 1 from both sides
(x - 3)² = - 4y + 8 ( subtract 8 from both sides )
(x - 3)² - 8 = - 4y ( divide both sides by - 4 )
- [tex]\frac{1}{4}[/tex] (x - 3)² + 2 = y, that is
y = - [tex]\frac{1}{4}[/tex] (x - 3)² + 2 → C
Answer:
Step-by-step explanation:
C) y = –1∕4 (x – 3)^2 + 2
Which point is a solution to y<=3x-4?
Answer:
(3, 1)
Step-by-step explanation:
Plug-in points and see which one works. (x, y). <= means less than or equal to.
Answer:
D. (3,1) is the correct answer
Step-by-step explanation: Just graph this question on a graph, and you will find that (3,1) is in the shaded region, which means it is part of the solution
Please answer this correctly without making mistakes I want expert genius or ace people to answer this correctly
Answer:
45.5 km
Step-by-step explanation:
18.3 km + 27.2 km = 45.5 km or 45 km and 500 m
Answer:
45.5km
Step-by-step explanation:
The distance between the locksmith and the furniture=18.3km
The distance between the furniture and the hotel=27.2km
S(locksmith)+S(furniture)=S(hotel)
18.3km+27.2km=45.5km
Hope this helps ;) ❤❤❤
Let me know if there is an error in my answer.
The equation 6x2 - 132 +5 -0 has solutions of the form
NVD
M
(A) Use the quadratic formula to solve this equation and find the appropriate integer values of N.M and D. Do not worry about simplifying the VD yet in this part of the problem.
N = ]:D
M
(B) Now simplify the radical and the resulting solutions. Enter your answers as a list of integers or reduced fractions, separated with commas. Example: -5/2-3/4
Preview
Answer:
(A)
[tex]N = -b = -(-13) = 13\\\\[/tex]
[tex]D =b^2 -4ac = (-13)^2 - 4(6)(5) = 169- 120 = 49[/tex]
[tex]M = 2a = 2(6) = 12[/tex]
(B)
[tex]$ x = (\frac{5}{3} , \: \frac{1}{2}) $[/tex]
Step-by-step explanation:
The given equation is
[tex]6x^2 - 13x + 5 = 0[/tex]
The solution is of the form as given by
[tex]$x=\frac{N\pm\sqrt{D}}{M}$[/tex]
(A) Use the quadratic formula to solve this equation and find the appropriate integer values of N, M and D. Do not worry about simplifying the VD yet in this part of the problem.
The quadratic formula is given by
[tex]$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$[/tex]
The equations of N, M and D are
[tex]N = -b[/tex]
[tex]D =b^2 -4ac[/tex]
[tex]M = 2a[/tex]
The values of a, b and c are
[tex]a = 6 \\\\b = -13 \\\\c = 5[/tex]
So,
[tex]N = -b = -(-13) = 13\\\\[/tex]
[tex]D =b^2 -4ac = (-13)^2 - 4(6)(5) = 169- 120 = 49[/tex]
[tex]M = 2a = 2(6) = 12[/tex]
(B) Now simplify the radical and the resulting solutions. Enter your answers as a list of integers or reduced fractions, separated with commas. Example: -5/2-3/4
N = 13
D = 49
M = 12
[tex]$x=\frac{13\pm\sqrt{49}}{12}$[/tex]
[tex]$x=\frac{13\pm7}{12}$[/tex]
[tex]$ x=\frac{13+7}{12} $[/tex] and [tex]$ x=\frac{13-7}{12} $[/tex]
[tex]$ x=\frac{20}{12} $[/tex] and [tex]$ x=\frac{6}{12} $[/tex]
[tex]$ x=\frac{5}{3} $[/tex] and [tex]$ x=\frac{1}{2} $[/tex]
[tex]$ x = (\frac{5}{3} , \: \frac{1}{2}) $[/tex]
please help answer this!!!
Answer:
49) [tex]12\,b^4[/tex]
50) [tex]200\,x^6[/tex]
Step-by-step explanation:
Use the properties of exponent to reduce this expressions:
a) [tex]3\,b\,*\,4 \,b^3=(3\,*\,4)\,(b\,*\,b^3)=12\,b^{(1+3)}=12\,b^4[/tex]
b) [tex]5\,x^2\,*\,8\,x\,5\,*\,x^3=(5\,*\,8\,*\,5)\,(x^2\,*\,x\,*\,x^3)=200\,x^{(2+1+3)}= 200\,x^6[/tex]
the product of two consequtive integers is 72 the equation x(x+1)=72 represents the situation, where x represents the smaller integer, which equation can be factor and solve for the smaller integer?
Answer:
x² + x - 72 = 0 can be factored into (x - 8)(x + 9) = 0 to find your answer.
Step-by-step explanation:
Step 1: Distribute x
x² + x = 72
Step 2: Move 72 over
x² + x - 72 = 0
Step 3: Factor
(x - 8)(x + 9) = 0
Step 4: Find roots
x - 8 = 0
x = 8
x + 9 = 0
x = -9
Answer:
x² + x - 72 = 0 ⇒ (x - 8)(x + 9) = 0
Step-by-step explanation:
Let the first consecutive integer be x.
Let the second consecutive integer be x+1.
The product of the two consecutive integers is 72.
x(x + 1) = 72
x² + x = 72
Subtracting 72 from both sides.
x² + x - 72 = 0
Factor left side of the equation.
(x - 8)(x + 9) = 0
Set factors equal to 0.
x - 8 = 0
x = 8
x + 9 = 0
x = -9
8 and -9 are not consecutive integers.
Try 8 and 9 to check.
x = 8
x + 1 = 9
x(x+1) = 72
8(9) = 72
72 = 72
True!
The two consecutive integers are 8 and 9.
what is the answer 2×3+4×100-50+10
Answer:
366
Step-by-step explanation:
2×3+4×100-50+10
PEMDAS says multiply and divide from left to right
6 + 400 - 50 +10
Then add and subtract
406-50+10
356+10
366
Answer:
[tex]\boxed{366}[/tex]
Step-by-step explanation:
[tex]2 \times 3+4 \times 100-50+10[/tex]
Multiplication is first.
[tex]6+400-50+10[/tex]
Add or subtract the numbers.
[tex]350+10+6[/tex]
[tex]366[/tex]
A sample of radioactive material disintegrates from 6 to 4 grams in 100 days. After how many days will just 3 grams remain?
Answer:
150 days
Step-by-step explanation:
6-4=2
100/2=50
50*3=150
The number of days for the radioactive material to disintegrate to 3 grams is 173.077 days.
The rate of disintegration varies directly proportional to the quantity of the material.
As such, we can say:
[tex]\mathbf{=\dfrac{dN}{dt}\ \alpha \ N}[/tex]
[tex]\mathbf{\implies \dfrac{dN}{N}\ = k dt}[/tex]
Taking the integral form;
[tex]\mathbf{\implies \int \dfrac{dN}{N}\ =\int k dt}[/tex]
[tex]\mathbf{\implies In N =kt+ C---- (1)}[/tex]
When t = 0, N = 6 grams
In(6) = C
∴
When t = 100, N = 4 grams
In (4) = 100k + In6
100 k = 1n (4) - In(6)
[tex]\mathbf{100 k = In (\dfrac{4}{6})}[/tex]
[tex]\mathbf{k = \dfrac{1}{100} In(\dfrac{4}{6})}[/tex]
∴
From equation (1):
[tex]\mathbf{In N = \dfrac{t}{100} In(\dfrac{4}{6})+ In 6}[/tex]
when,
n = 3 grams; we have:[tex]\mathbf{In (3) = \dfrac{t}{100} In(\dfrac{4}{6})+ In 6}[/tex]
[tex]\mathbf{\implies \dfrac{t}{100} In(\dfrac{4}{6}) = In \dfrac{ 3}{ 6}}[/tex]
[tex]\mathbf{t = 100\times \Big ( \dfrac{In (\dfrac{ 3}{ 6})}{ In(\dfrac{4}{6}) }\Big) }[/tex]
[tex]\mathbf{t = 100\times \Big ( \dfrac{0.69314}{ 0.40048}\Big) }[/tex]
t = 173.077 days
Therefore, the number of days for the radioactive material to disintegrate to 3 grams is 173.077 days.
Learn more about radioactive materials here:
https://brainly.com/question/24339152?referrer=searchResults
The four-member math team at Pecanridge Middle School is chosen from the math club, which has three girls and five boys. How many different teams made up of two girls and two boys could be chosen?
Answer:
[tex]Total\ Selection = 30\ ways[/tex]
Step-by-step explanation:
Given
Girls = 3
Boys = 5
Required
How many ways can 2 boys and girls be chosen?
The keyword in the question is chosen;
This implies combination and will be calculated as thus;
[tex]Selection =\ ^nC_r = \frac{n!}{(n-r)!r!}[/tex]
For Boys;
n = 5 and r = 2
[tex]Selection =\ ^5C_2[/tex]
[tex]Selection = \frac{5!}{(5-2)!2!}[/tex]
[tex]Selection = \frac{5!}{3!2!}[/tex]
[tex]Selection = \frac{5 * 4 * 3!}{3!*2 * 1}[/tex]
[tex]Selection = \frac{20}{2}[/tex]
[tex]Selection = 10[/tex]
For Girls;
n = 3 and r = 2
[tex]Selection =\ ^3C_2[/tex]
[tex]Selection = \frac{3!}{(3-2)!2!}[/tex]
[tex]Selection = \frac{3!}{1!2!}[/tex]
[tex]Selection = \frac{3 * 2!}{1 *2!}[/tex]
[tex]Selection = \frac{3}{1}[/tex]
[tex]Selection = 3[/tex]
Total Selection is calculated as thus;
[tex]Total\ Selection = Boys\ Selection * Girls\ Selection[/tex]
[tex]Total\ Selection = 10 * 3[/tex]
[tex]Total\ Selection = 30\ ways[/tex]
prove that 1/3 root2 is irrational
Step-by-step explanation:
Let us assume that 1/2+root 3 is rational . So 1/2+root 3 = a/b where a and b are irrationals. since rhs is a rational number root 3 should be also rational .
Which graph best models the inequality y<_ -2/5x+2
Answer:
Step-by-step explanation:
Simplify each term.
y ≤ −2x/5 + 2
Find the slope and the y-intercept for the boundary line.
Slope: -2/5
Y-intercept: 2
Graph a solid line, then shade the area below the boundary line since
y is less than -2x/5 + 2
y ≤ −2x/5 + 2
Hope this can help
f(n)=4n-3 find the 15th term of the sequence defined by the explicit rule
Answer:
57
Step-by-step explanation:
f(15)=4(15)-3
f(15)=60-3
f(15)=57
Hope that helps, tell me if you need more help
Answer:
57
Step-by-step explanation:
If you plug 15 into the equation, you get f(15)=4(15)-3
60-3
57
:)
What is the correlation coefficient for the data in the table?
–0.57
–0.28
0.28
0.57
Answer: i believe it’s 0.28, but tbh i’m on a unit test so i can’t see what’s wrong and what’s right. good luck!
Step-by-step explanation:
Answer:
c- 0.28
Step-by-step explanation:
The Orchard Cafe has found that about 15% of the diners who make reservations don't show up. If 77 reservations have been made, how many diners can be expected to show up? Find the standard deviation of this distribution
Answer:
65 dinners are expected to show up
The standard deviation of the distribution is 3.13
Step-by-step explanation:
Given
Proportion = 15%
Population = 77
Required
Expected Number that'll show up
Standard Deviation
If 15% won't show up; then
100% - 15% = 85% will show up
Expected Number, E(x) of Dinner is calculated as thus;
[tex]E(x) = np[/tex]
Where [tex]p = 85\%[/tex] (calculated above)
and [tex]n = 77[/tex]
Convert p to decimal
[tex]p = 0.85[/tex]
So;
[tex]E(x) = 0.85 * 77[/tex]
[tex]E(x) = 65.45[/tex]
[tex]E(x) = 65[/tex]
65 dinners are expected to show up
Calculating Standard Deviation, SD
Standard Deviation is calculated as;
[tex]SD = \sqrt{np(1-p)}[/tex]
Substitute 0.85 for p and 77 for n
[tex]SD = \sqrt{77 * 0.85 * (1-0.85)}[/tex]
[tex]SD = \sqrt{77 * 0.85 * 0.15}[/tex]
[tex]SD = \sqrt{9.8175}[/tex]
[tex]SD = 3.13328900678[/tex]
[tex]SD = 3.13[/tex] (Approximated)
The standard deviation of the distribution is 3.13
Assume that there is a 6% rate of disk drive failure in a year. a. If all your computer data is stored on a hard disk drive with a copy stored on a second hard disk drive, what is the probability that during a year, you can avoid catastrophe with at least one working drive? b. If copies of all your computer data are stored on independent hard disk drives, what is the probability that during a year, you can avoid catastrophe with at least one working drive? four a. With two hard disk drives, the probability that catastrophe can be avoided is . (Round to four decimal places as needed.) b. With four hard disk drives, the probability that catastrophe can be avoided is . (Round to six decimal places as needed.)
Answer: 0.9964
Step-by-step explanation:
Consider,
P (disk failure) = 0.06
q = 0.06
p = 1- q
p = 1- 0.06,
p = 0.94
Step 2
Whereas p represents the probability that a disk does not fail. (i.e. working entire year).
a)
Step 3
a)
n = 2,
let x be a random variable for number...
Continuation in the attached document
Jamie's dog eats 3/4 pound of dog food each day. How many pounds of dog
food does Jamie's dog eat in 4 days?
Answer:
The dog will eat 3 lbs
Step-by-step explanation:
Take the amount eaten per day and multiply by the number of days
3/4 * 4 = 3
The dog will eat 3 lbs
Answer:
3 pounds
Step-by-step explanation:
Multiply the amount of dog food per day with the number of days.
[tex]\frac{3}{4} \times 4[/tex]
[tex]\frac{12}{4} =3[/tex]
In 4 days, Jamie's dog will eat 3 pounds of dog food.
The head of maintenance at XYZ Rent-A-Car believes that the mean number of miles between services is 4178 miles, with a variance of 124,609. If he is correct, what is the probability that the mean of a sample of 40 cars would be less than 4265 miles? Round your answer to four decimal places.
Answer:
P(X' < 4265) = 0.9418
Step-by-step explanation:
Due to the fact that the population is normal, the distribution of the sample mean of 40 cars is;
X' = (x1 + x2 + x3....... + x40)/40
We are given;
Normal mean;μ = 4178 miles
Variance = 124,609
Standard deviation; σ = √variance = √124609 = 353
Formula for standard error of mean = σ/√n = 353/√40 = 55.814
So from the formula;
z = (x - μ)/(σ/√n)
So for P(X' < 4265) we have;
z-value of P(X' < 4265) = (4265 - 4178)/55.814 ≈ 1.56
From the z-table attached, we have for P(z < 1.56) = 0.94179
Approximating to 4 decimal places gives 0.9418