A number that can be divided exactly only by itself and 1.
For Eg:- 7, 10, 13.
Answer:
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself. However, 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4. Primes are central in number theory because of the fundamental theorem of arithmetic:
A couple has a total household income of $84,000. The husband earns $18,000 less than twice what the wife earns. How much does the wife earn? Select the correct answer below:
Answer:
$34000
Step-by-step explanation:
We can set up a systems of equations, assuming [tex]h[/tex] is the husbands income and [tex]w[/tex] is the wife's income.
h + w = 84000
h = 2w - 18000
We can substitute h into the equation as 2w - 18000:
(2w - 18000) + w = 84000
Combine like terms:
3w - 18000 = 84000
Add 18000 to both sides
3w = 102000
And divide both sides by 3
w = 34000
Now that we know how much the wife earns, we can also find out how much the husband earns by substituting into the equation.
h + 34000 = 84000
h = 50000
Hope this helped!
Activity 12-4: A large monohybrid crossa corn ear with purple and yellow kernels The total number of purple and yellow kernels on 8 different corn ears were counted: Purple kernels 3593 Yellow kernels 1102 What is the ratio of purple kernels to yellow kernels
Complete Question
The complete question is shown on the first uploaded image
Answer:
The correct option is C
Step-by-step explanation:
From the question we are told that
The number of purple kernel is [tex]n_k = 3593[/tex]
The number of yellow kernel is [tex]n_y = 1102[/tex]
Generally the ration of the purple to the yellow kernels is mathematically evaluated as
[tex]r = \frac{n_k}{n_y}[/tex]
substituting values
[tex]r = \frac{3593}{1102}[/tex]
[tex]r = 3.3[/tex]
[tex]r \approx 3[/tex]
Therefore the ratio is
[tex]1 \ Yellow : 3 \ Purple[/tex]
please answer this question please
Step-by-step explanation:
C = Amount (A) - Principal (P)
Where
C is the compound interest
To find the amount we use the formula
[tex]A = P ({1 + \frac{r}{100} })^{n} [/tex]
where
P is the principal
r is the rate
n is the period / time
From the question
P = Rs 12, 000
r = 5%
n = 3 years
Substitute the values into the above formula
That's
[tex]A = 12000 ({1 + \frac{5}{100} })^{3} \\ A = 12000(1 + 0.05)^{3} \\ A = 12000 ({1.05})^{3} [/tex]
We have the answer as
Amount = Rs 13891.50Compound interest = 13891.50 - 12000
Compound interest = Rs 1891.50Hope this helps you
Which option is correct and how would one solve for it?
Answer:
28
Step-by-step explanation:
We need to find the value of [tex]\Sigma_{x=0}^3\ 2x^2[/tex]
We know that,
[tex]\Sigma n^2=\dfrac{n(n+1)(2n+1)}{6}[/tex]
Here, n = 3
So,
[tex]\Sigma n^2=\dfrac{3(3+1)(2(3)+1)}{6}\\\\\Sigma n^2=14[/tex]
So,
[tex]\Sigma_{x=0}^3\ 2x^2=2\times 14\\\\=28[/tex]
So, the value of [tex]\Sigma_{x=0}^3\ 2x^2[/tex] is 28. Hence, the correct option is (d).
If a cube has an edge of 2 feet. The edge is increasing at the rate of 6 feet per minute. How would i express the volume of the cube as a function of m, the number of minutes elapsed. V(m)= ??
Answer:
v(m) = 8 + 48m+ 180m² +216m³
Step-by-step explanation:
Let's first of all represent the edge of the the cube as a function of minutes.
Initially the egde= 2feet
As times elapsed , it increases at the rate of 6 feet per min, that is, for every minute ,there is a 6 feet increase.
Let the the egde be x
X = 2 + 6(m)
Where m represent the minutes elapsed.
So we Al know that the volume of an edge = edge³
but egde = x
V(m) = x³
but x= 2+6(m)
V(m) = (2+6m)³
v(m) = 8 + 48m+ 180m² +216m³
The volume of cube as function of m is, [tex]V(m)=72m[/tex]
Let us consider that edge of cube is a feet.
Since, The edge is increasing at the rate of 6 feet per minute.
[tex]\frac{da}{dt}=6feet/min.[/tex]
Volume of cube , V = [tex]a^{3}[/tex]
[tex]\frac{dV}{dt} =3a^{2} \frac{da}{dt}[/tex]
Substituting the value of da/dt in above equation.
We get, [tex]\frac{dV}{dt}=3a^{2}*(6) =18a^{2} \\\\dV=18a^{2}dt[/tex]
Integrating on both side.
[tex]V=18a^{2}t[/tex]
Since, number of minutes elapsed is m.
Substitute , t = m and a = 2 feet in above equation.
We get, [tex]V=18(2)^{2}*m=72m[/tex]
Thus, the volume of cube as function of m is, [tex]V(m)=72m[/tex]
Learn more:
https://brainly.com/question/14002029
i will rate you brainliest
Answer:
First option
Step-by-step explanation:
Common ratio is greater than 1
Yuko added a 15 percent tip when she paid her cab driver. If the fare was $25.50, what was the total amount she paid? A. $28 B. $30 C. $31
Answer:
B. $30
Step-by-step explanation:
First, find the amount of the tip.
Multiply the tip rate and taxi fare.
tip rate * taxi fare
The tip rate is 15% and the taxi fare is $25.50
15% * 25.50
Convert 15% to a decimal. Divide 15 by 100 or move the decimal place two spots to the left.
15/100=0.15
15.0 ---> 1.5 ---> 0.15
0.15 * 25.50
3.825
The tip amount is $3.825
Next, find the total amount she paid.
Add the taxi fare and the tip amount.
taxi fare + tip amount
The taxi fare is $25.50 and the tip amount is $3.825
$25.50 + $3.825
$29.325
Round to the nearest dollar. Typically, this would round down to $29, but that is not an answer choice. So, if we round up, the next best answer is $30.
Therefore, the best answer choice is B. $30
Please help me guys :)
Question:
In exercises 1 through 4, find the one-sided limits lim x->2(left) f(x) and limx-> 2(right) from the given graph of f and determine whether lim x->2 f(x) exists.
Step-by-step explanation:
For a left-hand limit, we start at the left side and move right, and see where the function goes as we get close to the x value.
For a right-hand limit, we start at the right side and move left, and see where the function goes as we get close to the x value.
If the two limits are equal, then the limit exists. Otherwise, it doesn't.
1. As we approach x = 2 from the left, f(x) approaches -2.
lim(x→2⁻) f(x) = -2
As we approach x = 2 from the right, f(x) approaches 1.
lim(x→2⁺) f(x) = 1
The limits are not the same, so the limit does not exist.
lim(x→2) f(x) = DNE
2. As we approach x = 2 from the left, f(x) approaches 4.
lim(x→2⁻) f(x) = 4
As we approach x = 2 from the right, f(x) approaches 2.
lim(x→2⁺) f(x) = 2
The limits are not the same, so the limit does not exist.
lim(x→2) f(x) = DNE
3. As we approach x = 2 from the left, f(x) approaches 2.
lim(x→2⁻) f(x) = 2
As we approach x = 2 from the right, f(x) approaches 2.
lim(x→2⁺) f(x) = 2
The limits are equal, so the limit exists.
lim(x→2) f(x) = 2
4. As we approach x = 2 from the left, f(x) approaches 2.
lim(x→2⁻) f(x) = 2
As we approach x = 2 from the right, f(x) approaches infinity.
lim(x→2⁺) f(x) = ∞
The limits are not the same, so the limit does not exist.
lim(x→2) f(x) = DNE
Because she has limited shelf space, she can't put out all her copies of the CD at once. On Monday morning, she stocked the display with 40 copies. By the end of the day, some of the copies had been sold. On Tuesday morning, she counted the number of copies left and then added that many more to the shelf. In other words, she doubled the number that was left in the display. At the end of the day, she discovered that she had sold the exact same number of copies as had been sold on Monday. On Wednesday morning, the manager decided to triple the number of copies that had been left in the case after Tuesday. Amazingly, she sold the same number of copies on Wednesday as she had on each of the first two days! But this time, at the end of the day the display case was empty.
Now, it look like there is some information missing in the answer. The whole problem should look like this:
Alicia Keys's new album As I Am is climbing the charts, and the manager of Tip Top Tunes expects to sell a lot of copies. Because she has limited shelf space, she can't put out all her copies of the CD at once. On Monday morning, she stocked the display with 40 copies. By the end of the day, some of the copies had been sold. On Tuesday morning, she counted the number of copies left and then added that many more to the shelf. In other words, she doubled the number that was left in the display. At the end of the day, she discovered that she had sold the exact same number of copies as had been sold on Monday. On Wednesday morning, the manager decided to triple the number of copies that had been left in the case after Tuesday. Amazingly, she sold the same number of copies on Wednesday as she had on each of the first two days! But this time, at the end of the day the display case was empty. How many copies of the As I Am CD did she sell each day?
Answer:
She sold 24 copies of the cd each day.
Step-by-step explanation:
In order to solve this problem we must first set our variable up. In this case, since we need to know what the number of sold cd's per day is, that will just be our variable:
x= Number of copies sold.
So we can start setting our equation up. So we take the first part of the problem:
"On Monday morning, she stocked the display with 40 copies. By the end of the day, some of the copies had been sold."
This can be translated as:
40-x
where this expression represents the number of copies left on the shelf by the end of monday.
"On Tuesday morning, she counted the number of copies left and then added that many more to the shelf."
so we represent it like this:
(40-x)+(40-x)
"In other words, she doubled the number that was left in the display."
so the previous expression can be simplified like this:
2(40-x)
"At the end of the day, she discovered that she had sold the exact same number of copies as had been sold on Monday."
so the expression now turns to:
2(40-x)-x this is the number of copies left by the end of tuesday.
"On Wednesday morning, the manager decided to triple the number of copies that had been left in the case after Tuesday."
this translates to:
3[2(40-x)-x]
This is the number of copies on the shelf by the begining of Wednesday.
"Amazingly, she sold the same number of copies on Wednesday as she had on each of the first two days! But this time, at the end of the day the display case was empty."
this piece of information lets us finish writting our equation:
3[2(40-x)-x] -x = 0
since there were no copies left on the shelf, then the equation is equal to zero.
So now we proceed and solve the equation for x:
3[2(40-x)-x] -x = 0
We simplify it from the inside to the outside.
3[80-2x-x]-x=0
3[80-3x]-x = 0
we now distribute the 3 so we get:
240-9x-x=0
we combine like terms so we get:
240-10x=0
we move the 240 to the other side of the equation so we get:
-10x=-240
and divide both sides into -10 so we get:
x=24
so she sold 24 copies each day.
Amy is a software saleswoman. Let Y represent her total pay (in dollars). Let X represent the number of copies of "English is Fun" she sells. Suppose that X and Y are related by the equation 110X +2300 = Y.
Answer the questions below. Note that a change can be an increase or decrease.
What is the change in Amy's total pay for each copy of "English is Fun"?
What is Amy's total pay if she doesn't sell any copies of "English is Fun"?
Answer:
1) For every copy she sells, her pay increases by $110
2) Her total pay is 2300
Step-by-step explanation:
1) X is the number of copies she sells. In the equation 110X+ 2300 = Y, X will determine how many times 110 is multiplied. So, for every increase by one in X, Y will also go up by 110
eg.
110(50) + 2300 = 7800 -- if she sells 50 copies
110(51) + 2300 = 7910 -- if she sells 51 copies,
2) If she doesn't sell any copies, the equation becomes 110 * 0 + 2300. Anything multiplied by 0 equals 0, so the equation equals 0 + 2300 = 2300 = Y
Therefore, if she doesn't sell any copies, she will get a pay of $2300
An economist is interested in studying the income of consumers in a particular region. The population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in an average income of $15,000. What is the width of the 90% confidence interval
Answer:
The width is [tex]w = 282.8[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 50
The population standard deviation is [tex]\sigma = \$ 1000[/tex]
The sample size is [tex]\= x = \$ 15,000[/tex]
Given that the confidence level is 90% then the level of significance can be mathematically represented as
[tex]\alpha = 100 - 90[/tex]
[tex]\alpha = 10 \%[/tex]
[tex]\alpha = 0.10[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table, the value is
[tex]Z_{\frac{0.10 }{2} } = 1.645[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{0.10}{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]E = 1.645 * \frac{1000 }{\sqrt{50 }}[/tex]
=> [tex]E = 141.42[/tex]
The width of the 90% confidence level is mathematically represented as
[tex]w = 2 * E[/tex]
substituting values
[tex]w = 2 * 141.42[/tex]
[tex]w = 282.8[/tex]
Suppose that you want to estimate the mean pH of rainfalls in an area that suffers from heavy pollution due to the discharge of smoke from a power plant. Assume that σ is in the neighborhood of .5 pH and that you want your estimate to lie within .1 of µ with probability near .95. Approximately how many rainfalls must be included in your sample (one pH reading per rainfall)? Would it be valid to select all of your water specimens from a single rainfall? Explain.
Answer:
The number of rainfalls is [tex]n =96[/tex]
The answer to the second question is no it will not be valid this because from the question we are told that the experiment require one pH reading per rainfall so getting multiply specimens(used for the pH reading) from one rainfall will make the experiment invalid.
Step-by-step explanation:
from the question we are told that
The standard deviation is [tex]\sigma = 0.5[/tex]
The margin of error is [tex]E = 0.1[/tex]
Given that the confidence level is 95% then we can evaluate the level of significance as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5 \%[/tex]
[tex]\alpha =0.05[/tex]
Next we will obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table , the value is [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the sample size is mathematically represented as
[tex]n = [\frac{Z_{\frac{\alpha }{2} * \sigma }}{ E} ]^2[/tex]
substituting values
[tex]n = [\frac{1.96 * 0.5 }{ 0.1} ]^2[/tex]
[tex]n =96[/tex]
The answer to the second question is no the validity is null this because from the question we are told that the experiment require one pH reading per rainfall so getting multiply specimens(used for the pH reading) from one rainfall will make the experiment invalid
5 STARS IF CORRECT! In general, Can you translate a phrase or sentence into symbols? Explain the answer.
Answer:
Step-by-step explanation:
I answered this already a few minutes ago.
Answer:
yes you can
Step-by-step explanation:
you can write algebraic expressions and use variables for the unknown
y varies directly as z, y=180, z=10 , find ywhen z=14
Step-by-step explanation:
To find the value of y when z = 14 we must first find the relationship between them
The statement
y varies directly as z is written as
y = kz
where k is the constant of proportionality
when y = 180
z = 10
180 = 10k
Divide both sides by 10
k = 18
The formula for the variation is
y = 18z
When z = 14
y = 18(14)
y = 252Hope this helps you
Change the polar coordinates (r, θ) to rectangular coordinates (x, y):(-2,sqrt2pi
Step-by-step explanation:
x=rcosθandy=rsinθ,. 7.7. r2=x2+y2andtanθ=yx. 7.8. These formulas can be used to convert from rectangular to polar or from polar to rectangular coordinates.
This person made a mistake. what is the mistake and what is the correct answer?!!
Answer: 44
Step-by-step explanation:
A hot metal bar is submerged in a large reservoir of water whose temperature is 60°F. The temperature of the bar 20 s after submersion is 120°F. After 1 min submerged, the temperature has cooled to 100°F. (Let y be measured in degrees Fahrenheit, and t be measured in seconds.) (a) Determine the cooling constant k. k = s−1 (b) What is the differential equation satisfied by the temperature y(t)? (Use y for y(t).) y'(t) = (c) What is the formula for y(t)? y(t) = (d) Determine the temperature of the bar at the moment it is submerged. (Round your answer to one decimal place.)
Answer:
a. k = -0.01014 s⁻¹
b. [tex]\mathbf{\dfrac{dy}{dt} = - \dfrac{In(\dfrac{3}{2})}{40}(y-60)}[/tex]
c. [tex]\mathbf{y(t) = 60+ \dfrac{60 \sqrt{3}}{\sqrt{2}} \ e^{\dfrac{-In(\dfrac{3}{2})\ t}{40}}}[/tex]
d. y(t) = 130.485°F
Step-by-step explanation:
A hot metal bar is submerged in a large reservoir of water whose temperature is 60°F. The temperature of the bar 20 s after submersion is 120°F. After 1 min submerged, the temperature has cooled to 100°F.
(Let y be measured in degrees Fahrenheit, and t be measured in seconds.)
We are to determine :
a. Determine the cooling constant k. k = s−1
By applying the new law of cooling
[tex]\dfrac{dT}{dt} = k \Delta T[/tex]
[tex]\dfrac{dT}{dt} = k(T_1-T_2)[/tex]
[tex]\dfrac{dT}{dt} = k (T - 60)[/tex]
Taking the integral.
[tex]\int \dfrac{dT}{T-60} = \int kdt[/tex]
㏑ (T -60) = kt + C
T - 60 = [tex]e^{kt+C}[/tex]
[tex]T = 60+ C_1 e^{kt} ---- (1)[/tex]
After 20 seconds, the temperature of the bar submersion is 120°F
T(20) = 120
From equation (1) ,replace t = 20s and T = 120
[tex]120 = 60 + C_1 e^{20 \ k}[/tex]
[tex]120 - 60 = C_1 e^{20 \ k}[/tex]
[tex]60 = C_1 e^{20 \ k} --- (2)[/tex]
After 1 min i.e 60 sec , the temperature = 100
T(60) = 100
From equation (1) ; replace t = 60 s and T = 100
[tex]100 = 60 + c_1 e^{60 \ t}[/tex]
[tex]100 - 60 =c_1 e^{60 \ t}[/tex]
[tex]40 =c_1 e^{60 \ t} --- (3)[/tex]
Dividing equation (2) by (3) , we have:
[tex]\dfrac{60}{40} = \dfrac{C_1e^{20 \ k } }{C_1 e^{60 \ k}}[/tex]
[tex]\dfrac{3}{2} = e^{-40 \ k}[/tex]
[tex]-40 \ k = In (\dfrac{3}{2})[/tex]
- 40 k = 0.4054651
[tex]k = - \dfrac{0.4054651}{ 40}[/tex]
k = -0.01014 s⁻¹
b. What is the differential equation satisfied by the temperature y(t)?
Recall that :
[tex]\dfrac{dT}{dt} = k \Delta T[/tex]
[tex]\dfrac{dT}{dt} = \dfrac{- In (\dfrac{3}{2})}{40}(T-60)[/tex]
Since y is the temperature of the body , then :
[tex]\mathbf{\dfrac{dy}{dt} = - \dfrac{In(\dfrac{3}{2})}{40}(y-60)}[/tex]
(c) What is the formula for y(t)?
From equation (1) ;
where;
[tex]T = 60+ C_1 e^{kt} ---- (1)[/tex]
Let y be measured in degrees Fahrenheit
[tex]y(t) = 60 + C_1 e^{-\dfrac{In (\dfrac{3}{2})}{40}t}[/tex]
From equation (2)
[tex]C_1 = \dfrac{60}{e^{20 \times \dfrac{-In(\dfrac{3}{2})}{40}}}[/tex]
[tex]C_1 = \dfrac{60}{e^{-\dfrac{1}{2} {In(\dfrac{3}{2})}}}[/tex]
[tex]C_1 = \dfrac{60}{e^ {In(\dfrac{3}{2})^{-1/2}}}}[/tex]
[tex]C_1 = \dfrac{60}{\sqrt{\dfrac{2}{3}}}[/tex]
[tex]C_1 = \dfrac{60 \times \sqrt{3}}{\sqrt{2}}}[/tex]
[tex]\mathbf{y(t) = 60+ \dfrac{60 \sqrt{3}}{\sqrt{2}} \ e^{\dfrac{-In(\dfrac{3}{2})\ t}{40}}}[/tex]
(d) Determine the temperature of the bar at the moment it is submerged.
At the moment it is submerged t = 0
[tex]\mathbf{y(0) = 60+ \dfrac{60 \sqrt{3}}{\sqrt{2}} \ e^{\dfrac{-In(\dfrac{3}{2})\ 0}{40}}}[/tex]
[tex]\mathbf{y(t) = 60+ \dfrac{60 \sqrt{3}}{\sqrt{2}} }[/tex]
y(t) = 60 + 70.485
y(t) = 130.485°F
Four couples are at a party. Four of the eight people are randomly selected to win a prize. No person can win more than one prize. What is the probability that both of the members of at least one couple win prizes? Express your answer as common fraction.
Answer:
27/35
Step-by-step explanation:
We use combination to solve for this
C(n, r), =nCr = n!/r!(n - r)!
From the question, we are told that:
Four couples are at a party. Four of the eight people are randomly selected to win a prize.
Four couples = 8 people.
= 8C4 = 8!/4! (8 - 4)!
= 70
No person can win more than one prize. ( No person can win more than one prize of the 4 people selected)
This can happen in 4 ways
[4C1 × 3C2 ] × 4=
[4!/1! ×( 4 - 1)!] × [3!/2! ×(3-2)!] × 4 ways
= 4 × 3 × 4 ways
= 48
The probability that both of the members of at least one couple win prizes
48 + 4C2/ 8C4
4C2 = 4!/2!(4 - 2) !
= 6
8C4 = 8C4 = 8!/4! (8 - 4)!
= 70
48 + 6/ 70
= 54/70
= 27/35
Therefore, the probability that both of the members of at least one couple win prizes is 27/35.
The probability that both of the members of at least one couple win prizes is 27/35 and this can be determined by using the given data.
Given :
Four couples are at a party. Four of the eight people are randomly selected to win a prize. No person can win more than one prize.The following steps can be used in order to determine the probability that both of the members of at least one couple win prizes:
Step 1 - The concept of probability is used in order to determine the probability that both of the members of at least one couple win prizes.
Step 2 - According to the given data, the total number of people is 8.
Step 3 - So, the probability that both of the members of at least one couple win prizes is:
[tex]\rm P =\dfrac{ \;^4C_1\times \;^3C_2\times 4 + \;^4C_2}{\;^8C_4}[/tex]
Step 4 - Simplify the above expression.
[tex]\rm P =\dfrac{48+ 6}{70}[/tex]
[tex]\rm P = \dfrac{27}{35}[/tex]
So, the probability that both of the members of at least one couple win prizes is 27/35.
For more information, refer to the link given below:
https://brainly.com/question/795909
Based on a poll, 40% of adults believe in reincarnation. Assume that 4 adults are randomly selected, and find the indicated probability. Complete parts (a) through (d) below.Required:a. The probability that exactly 3 of the 4 adults believe in reincarnation is? b. The probability that all of the selected adults believe in reincarnation is? c. The probability that at least 3 of the selected adults believe in reincarnation is? d. If 4 adults are randomlyselected, is 3 a significantly high number who believe inreincarnation?
Complete Question
The complete question is shown on the first uploaded image
Answer:
a
[tex]P(3) = 0.154[/tex]
b
[tex]P(4) = 0.026[/tex]
c
[tex]P( X \ge 3 ) = 0.18[/tex]
d
option C is correct
Step-by-step explanation:
From the question we are told that
The probability of success is p = 0.4
The sample size is n= 4
This adults believe follow a binomial distribution is because there are only two outcome one is an adult believes in reincarnation and the second an adult does not believe in reincarnation
The probability of failure is mathematically evaluated as
[tex]q = 1 - p[/tex]
substituting values
[tex]q = 1 - 0.4[/tex]
[tex]q = 0.6[/tex]
Considering a
The probability that exactly 3 of the selected adults believe in reincarnation is mathematically represented as
[tex]P(3) = \left n} \atop {}} \right. C_ 3 * p^3 * q^{n-3}[/tex]
substituting values
[tex]P(3) = \left 4} \atop {}} \right. C_ 3 * (0.40)^3 * (0.60)^{4-3}[/tex]
Here [tex]\left 4} \atop {}} \right.C_3[/tex] means 4 combination 3 . i have calculated this using a calculator and the value is
[tex]\left 4} \atop {}} \right.C_3 = 4[/tex]
So
[tex]P(3) = 4* (0.4)^3 * (0.6)[/tex]
[tex]P(3) = 0.154[/tex]
Considering b
The probability that all of the selected adults believe in reincarnation is mathematically represented as
[tex]P(n) = \left n} \atop {}} \right. C_ n * p^n * q^{n-n}[/tex]
substituting values
[tex]P(4) = \left 4} \atop {}} \right. C_ 4 * (0.40)^4 * (0.60)^{4-4}[/tex]
Here [tex]\left 4} \atop {}} \right.C_3[/tex] means 4 combination . i have calculated this using a calculator and the value is [tex]\left 4} \atop {}} \right.C_4 = 1[/tex]
so
[tex]P(4) = 1* (0.4)^4 * 1[/tex]
=> [tex]P(4) = 0.026[/tex]
Considering c
the probability that at least 3 of the selected adults believe in reincarnation is mathematically represented as
[tex]P( X \ge 3 ) = P(3 ) + P(n )[/tex]
substituting values
[tex]P( X \ge 3 ) = 0.154 + 0.026[/tex]
[tex]P( X \ge 3 ) = 0.18[/tex]
From the calculation the probability that all the 4 randomly selected persons believe in reincarnation is [tex]p(4) = 0.026 < 0.05[/tex]
But the the probability of 3 out of the 4 randomly selected person believing in reincarnation is [tex]P(3) = 0.154 \ which \ is \ > 0.05[/tex]
Hence 3 is not a significantly high number of adults who believe in reincarnation because the probability that 3 or more of the selected adults believe in reincarnation is greater than 0.05.
It is advertised that the average braking distance for a small car traveling at 65 miles per hour equals 122 feet. A transportation researcher wants to determine if the statement made in the advertisement is false. She randomly test drives 38 small cars at 65 miles per hour and records the braking distance. The sample average braking distance is computed as 116 feet. Assume that the population standard deviation is 21 feet. (You may find it useful to reference the appropriate table: z table or t table) a. State the null and the alternative hypotheses for the test.
Complete Question
The complete question is shown on the first uploaded image
Answer:
the null hypothesis is [tex]H_o : \mu = 122[/tex]
the alternative hypothesis is [tex]H_a : \mu \ne 122[/tex]
The test statistics is [tex]t = - 1.761[/tex]
The p-value is [tex]p = P(Z < t ) = 0.039119[/tex]
so
[tex]p \ge 0.01[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 122[/tex]
The sample size is n= 38
The sample mean is [tex]\= x = 116 \ feet[/tex]
The standard deviation is [tex]\sigma = 21[/tex]
Generally the null hypothesis is [tex]H_o : \mu = 122[/tex]
the alternative hypothesis is [tex]H_a : \mu \ne 122[/tex]
Generally the test statistics is mathematically evaluated as
[tex]t = \frac { \= x - \mu }{\frac{ \sigma }{ \sqrt{n} } }[/tex]
substituting values
[tex]t = \frac { 116 - 122 }{\frac{ 21 }{ \sqrt{ 38} } }[/tex]
[tex]t = - 1.761[/tex]
The p-value is mathematically represented as
[tex]p = P(Z < t )[/tex]
From the z- table
[tex]p = P(Z < t ) = 0.039119[/tex]
So
[tex]p \ge 0.01[/tex]
Mr Osei has a rectangular field measured 85m long and 25m wide. How long is the distance around the field?
Answer:
220m
Step-by-step explanation:
l=85m
b=25m
perimeter=2(l+b)
2(85+25)
2(110)
=220m
perimeter is 220m
Answer:
Distance around the field is 220mStep-by-step explanation:
The distance around the field means the perimeter of the field
Since the field is rectangular
Perimeter of a rectangle = 2l + 2w
where l is the length
w is the width
From the question
l = 85m
w = 25m
Perimeter = 2(85) + 2(25)
Perimeter = 170 + 50
The final answer is
Perimeter = 220m
Hope this helps you
4(x/2-2) > 2y-11 which of the following inequalities is equivalent to the inequality above?
1) 4x+2y-3 > 0
2) 4x-2y+3 > 0
3) 2x+2y-3 > 0
4) 2x-26+3 > 0
4) 2x-2y+3 > 0
although it is spelt "26" on the choices
The numbers of words defined on randomly selected pages from a dictionary are shown below. Find the mean, median, mode of the listed numbers. 72 58 62 38 44 66 42 49 76 52 What is the mean? Select the correct choice below and ,if necessary ,fill in the answer box within your choice.(around to one decimal place as needed)
Answer:
Mean: 55.9
Median: 55
Mode: None
Step-by-step explanation:
First, find the mean by dividing the sum by the number of elements:
(72 + 58 + 62 + 38 + 44 + 66 + 42 + 49 + 76 + 52) / 10
= 55.9
Next, find the median by putting the numbers in order and finding the middle one:
38, 42, 44, 49, 52, 58, 62, 66, 72, 76
There is no middle number, so we will take the average of 52 and 58, which is 55.
Lastly, to find the mode, we have to find the number that occurs the most.
All of the numbers occur one time, so there is no mode.
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
Calcule o valor de x nas equações literais: a) 5x – a = x+ 5a b) 4x + 3a = 3x+ 5 c) 2 ( 3x -a ) – 4 ( x- a ) = 3 ( x + a ) d) 2x/5 - (x-2a)/3 = a/2 Resolva as equações fracionárias: a) 3/x + 5/(x+2) = 0 , U = R - {0,-2} b) 7/(x-2) = 5/x , U = R - {0,2} c) 2/(x-3) - 4x/(x²-9) = 7/(x+3) , U = R - {-3,3}
Answer:
1) a) [tex]x = \frac{3}{2}\cdot a[/tex], b) [tex]x = 5-3\cdot a[/tex], c) [tex]x = -a[/tex], d) [tex]x = \frac{5}{2}\cdot a[/tex]
2) a) [tex]x = -\frac{3}{4}[/tex], b) [tex]x = -5[/tex], c) [tex]x = 3[/tex]
Step-by-step explanation:
1) a) [tex]5\cdot x - a = x + 5\cdot a[/tex]
[tex]5\cdot x - x = 5\cdot a + a[/tex]
[tex]4\cdot x = 6\cdot a[/tex]
[tex]x = \frac{3}{2}\cdot a[/tex]
b) [tex]4\cdot x + 3\cdot a = 3\cdot x + 5[/tex]
[tex]4\cdot x - 3\cdot x = 5 - 3\cdot a[/tex]
[tex]x = 5-3\cdot a[/tex]
c) [tex]2\cdot (3\cdot x - a) - 4\cdot (x-a) = 3\cdot (x+a)[/tex]
[tex]6\cdot x -2\cdot a -4\cdot x +4\cdot a = 3\cdot x +3\cdot a[/tex]
[tex]6\cdot x -4\cdot x -3\cdot x = 3\cdot a -4\cdot a +2\cdot a[/tex]
[tex]-x = a[/tex]
[tex]x = -a[/tex]
d) [tex]\frac{2\cdot x}{5} - \frac{x-2\cdot a}{3} = \frac{a}{2}[/tex]
[tex]\frac{6\cdot x-5\cdot (x-2\cdot a)}{15} = \frac{a}{2}[/tex]
[tex]\frac{6\cdot x - 5\cdot x+10\cdot a}{15} = \frac{a}{2}[/tex]
[tex]2\cdot (x+10\cdot a) = 15 \cdot a[/tex]
[tex]2\cdot x = 5\cdot a[/tex]
[tex]x = \frac{5}{2}\cdot a[/tex]
2) a) [tex]\frac{3}{x} + \frac{5}{x+2} = 0[/tex]
[tex]\frac{3\cdot (x+2)+5\cdot x}{x\cdot (x+2)} = 0[/tex]
[tex]3\cdot (x+2) + 5\cdot x = 0[/tex]
[tex]3\cdot x +6 +5\cdot x = 0[/tex]
[tex]8\cdot x = - 6[/tex]
[tex]x = -\frac{3}{4}[/tex]
b) [tex]\frac{7}{x-2} = \frac{5}{x}[/tex]
[tex]7\cdot x = 5\cdot (x-2)[/tex]
[tex]7\cdot x = 5\cdot x -10[/tex]
[tex]2\cdot x = -10[/tex]
[tex]x = -5[/tex]
c) [tex]\frac{2}{x-3}-\frac{4\cdot x}{x^{2}-9} = \frac{7}{x+3}[/tex]
[tex]\frac{2}{x-3} - \frac{4\cdot x}{(x+3)\cdot (x-3)} = \frac{7}{x+3}[/tex]
[tex]\frac{1}{x-3}\cdot \left(2-\frac{4\cdot x}{x+3} \right) = \frac{7}{x+3}[/tex]
[tex]\frac{x+3}{x-3}\cdot \left[\frac{2\cdot (x+3)-4\cdot x}{x+3} \right] = 7[/tex]
[tex]\frac{2\cdot (x+3)-4\cdot x}{x-3} = 7[/tex]
[tex]2\cdot (x+3) -4\cdot x = 7\cdot (x-3)[/tex]
[tex]2\cdot x + 6 - 4\cdot x = 7\cdot x -21[/tex]
[tex]2\cdot x - 4\cdot x -7\cdot x = -21-6[/tex]
[tex]-9\cdot x = -27[/tex]
[tex]x = 3[/tex]
-3(-5x-2u+1) use the distributive property to remove the parentheses
Answer:
15x+6u−3
Step-by-step explanation:
This means -3 times -5x, -3 times -2u, and -3 times 1.
Do this and you have, 15x+6u-3.
Two balls are drawn in succession out of a box containing 5 red and 4 white balls. Find the probability that at least 1 ball was red, given that the first ball was (Upper A )Replaced before the second draw. (Upper B )Not replaced before the second draw. (A) Find the probability that at least 1 ball was red, given that the first ball was replaced before the second draw. StartFraction 24 Over 49 EndFraction (Simplify your answer. Type an integer or a fraction.) (B) Find the probability that at least 1 ball was red, given that the first ball was not replaced before the second draw.
Answer:
The answer is below
Step-by-step explanation:
The box contains 5 red and 4 white balls.
A) The probability that at least 1 ball was red = P(both are red) + P(first is red and second is white) + P(first is white second is red)
Given that the first ball was (Upper A )Replaced before the second draw:
P(both are red) = P(red) × P(red) = 5/9 × 5/9 = 25/81
P(first is red and second is white) = P(red) × P(white) = 5/9 × 4/9 = 20/81
P(first is white and second is red) = P(white) × P(red) = 4/9 × 5/9 = 20/81
The probability that at least 1 ball was red = 25/81 + 20/81 + 20/81 = 65/81
B) The probability that at least 1 ball was red = P(both are red) + P(first is red and second is white) + P(first is white second is red)
Given that the first ball was not Replaced before the second draw:
P(both are red) = P(red) × P(red) = 5/9 × 4/8 = 20/72 (since it was not replaced after the first draw the number of red ball remaining would be 4 and the total ball remaining would be 8)
P(first is red second is white) = P(red) × P(white) = 5/9 × 4/8 = 20/72
P(first is white and second is red) = P(white) × P(red) = 4/9 × 5/8 = 20/72
The probability that at least 1 ball was red = 20/72 + 20/72 + 20/72 = 60/72
Y is the midpoint of XZ. If XZ = 8x − 2 and YZ = 3x + 3, find x.
Answer:
x = 4
Step-by-step explanation:
2( 3x + 3) = 8x - 2
6x + 6 = 8x -2
6x + 8 = 8x
8 = 2x
4 = x
It is given that Y is the midpoint of XZ. If XZ = 8x − 2 and YZ = 3x + 3, So the value of x is x = 4.
What does a midpoint mean?Midpoint, as the word suggests, means the point which lies in the middle of something.
Midpoint of a line segment means a point which lies in the mid of the given line segment.
We have been given that Y is the midpoint of XZ. If XZ = 8x − 2 and YZ = 3x + 3, we need to find x.
We know that;
2(YZ) = XZ
Substitute in the values
2( 3x + 3) = 8x - 2
Use the Distributive Property
6x + 6 = 8x -2
6x + 8 = 8x
8 = 2x
4 = x
Switch the sides to make it easier to read
x = 4
It is given that Y is the midpoint of XZ. If XZ = 8x − 2 and YZ = 3x + 3, So the value of x is x = 4.
To learn more about the midpoint click below;
https://brainly.com/question/1615050
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Your job in a company is to fill quart-size bottles of oil from a full -gallon oil tank. Then you are to pack quarts of oil in a case to ship to a store. How many full cases of oil can you get from a full -gallon tank of oil?
Answer:
See below.
Step-by-step explanation:
1 gal = 4 qt
With a full gallon oil tank, you can fill 4 1-qt bottles.
The problem does not mention the number of quarts that go in a case, so there is not enough information to answer the question.
Also, is the full tank really only 1 gallon, or is there a number missing there too?
A United Nations report shows the mean family income for Mexican migrants to the United States is $26,500 per year. A FLOC (Farm Labor Organizing Committee) evaluation of 24 Mexican family units reveals a mean to be $30,150 with a sample standard deviation of $10,560. State the null hypothesis and the alternate hypothesis.
Answer:
The null hypothesis [tex]\mathtt{H_0 : \mu = 26500}[/tex]
The alternative hypothesis [tex]\mathtt{H_1 : \mu \neq 26500}[/tex]
Step-by-step explanation:
The summary of the given statistics is:
Population Mean = 26,500
Sample Mean = 30,150
Standard deviation = 10560
sample size = 24
The objective is to state the null hypothesis and the alternate hypothesis.
An hypothesis is a claim with insufficient information which tends to be challenged into further testing and experimentation in order to determine if such claim is significant or not.
The null hypothesis is a default hypothesis where there is no statistical significance between the two variables in the hypothesis.
The alternative hypothesis is the research hypothesis that the researcher is trying to prove.
The null hypothesis [tex]\mathtt{H_0 : \mu = 26500}[/tex]
The alternative hypothesis [tex]\mathtt{H_1 : \mu \neq 26500}[/tex]
The test statistic can be computed as follows:
[tex]z = \dfrac{\overline X - \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \dfrac{30150 - 26500}{\dfrac{10560}{\sqrt{24}}}[/tex]
[tex]z = \dfrac{3650}{\dfrac{10560}{4.8989}}[/tex]
[tex]z = \dfrac{3650 \times 4.8989 }{{10560}}[/tex]
z = 1.6933
