There is a total of 190 ways to share apples between them.
What is a ball-and-urn method?
The ball-and-urn method often referred to as stars-and-bars, sticks-and-stones, or dots-and-dividers is a typical combinatorial method.
It is used to resolve issues of the following type: in how many different ways can one divide 'k' undifferentiable items into 'n' distinct bins?
Use the ball-and-urn method, Let Alice get 'x' apples, Becky get 'y' apples, and Chris get 'z' apples.
⇒x + y + z = 24
We can manipulate this into an equation that can be solved using the ball-and-urn method
All of them get at least 2 apples, so we can subtract 2 from x, 2 from y, and 2 from z.
⇒(x - 2) + (y - 2) + (z - 2) = 18
Let x' = x - 2, y' = y - 2, z' = z - 2.
⇒ x' + y' + z' = 18
We can allow either of them to equal 0, hence this can be solved by the ball-and-urn method.
By the ball-and-urn method, we get
[tex]$\binom{18 + 3 - 1}{3 - 1} = \binom{20}{2} = \ 190}$.[/tex]
Hence, there are 190 ways to split the apples among them.
To learn more about a ball-and-urn method
https://brainly.com/question/29242782
#SPJ4
The two polygons are similar, find the missing length. (the ?)
The required measure of the missing length is given as 14 units.
Given that,
The figure of two similar triangles is given, and the missing length of the figure is to be determined.
The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°
Here,
Let the missing length be x,
So by property of proportions,
20/8 = [49 - x] / x
20x = 392 - 8x
28x = 392
x = 14
Thus, the required measure of the missing length is given as 14 units.
Learn more about triangles here:
https://brainly.com/question/2773823
#SPJ1
8^x/2=2^3/8×4^3/4 find x
The solution to the equation 8^x/2=2^3/8×4^3/4 is x = 15/14
What is Simplify?To simplify an expression: to remove brackets, unnecessary terms and numbers
[tex]8^{x/2} = 2^{3/8} * 4^{3/4}[/tex]
[tex]2^{3x/2} = 2^{3/8} * 2^{2 (3/4)}[/tex]
using law of Indices
[tex]2^{3x/2} = 2^{3/8 + 6/4}[/tex]
[tex]\frac{3x}{2} = \frac{3}{8} + \frac{3}{2}[/tex]
[tex]\frac{3x}{2} = \frac{3+12}{8}[/tex]
[tex]\frac{3x}{2} = \frac{15}{8}[/tex]
cross multiply
24x =30
Divide both sides by 24
[tex]\frac{24x}{24} = \frac{30}{28}[/tex]
x = 15/14
Therefore, the solution to the equation is x = 15/14
Learn more about simplification here; https://brainly.com/question/28595186
#SPJ1
mr. imani wants to purchase paper and notebooks for his classroom. at dollar discount he can buy packs of paper, p, for $1.25 each and notebooks, n, for $2.50 each. this is modeled by 1.25p + 2.50n. evaluate for p = 10 and n=30 to find how much it will cost mr. imani to purchase 10 packs of paper and 30 notebooks.
1.$450.00
2.$62.50
3.$43.75
4.$87.50
The total cost for buying 10 packs of paper and 30 notebooks is $87.50.
What is equation?The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that, Mr. Imani wants to purchase paper and notebooks for his classroom. at dollar discount he can buy packs of paper, p, for $1.25 each and notebooks, n, for $2.50 each. this is modelled by 1.25p + 2.50n. evaluate for p = 10 and n=30
Putting p = 10 and n = 30, we get,
1.25*10+2.50*30 = 87.50
Hence, The total cost for buying 10 packs of paper and 30 notebooks is $87.50.
For more references on equation, click;
https://brainly.com/question/10413253
#SPJ1
Why is partitioning a directed line segment into a ratio of 1/2 is not the same as finding half the length of the directed line segment?.
The difference between partitioning into a ratio of 1/2 and finding half of a line segment is that partitioning in that ratio means one part is longer than the other, whereas finding half the length means both parts are the same length.
What is the partition of the line?
Partition means to separate or to divide. A line segment can be partitioned into smaller segments which are compared as ratios.
When we say we want to partition a line into a ratio of say x/y, it means that the line has been divided in that ratio and as such, the total number of parts is x + y.
Similarly, when we partition a line in the ratio 1/2, it implies that the total number of parts of the line segment is 1 + 2 = 3.
This means one part of the divided segment is bigger than the other one.
In contrast, half of the line segment means that the line segment is divided into two equal parts.
Thus, the fundamental difference between partitioning into a ratio of 1/2 and finding half of the line segment is that partitioning in that ratio means one part is longer than the other while half the length means that both parts are the same length.
To learn more about the partition of the line visit,
brainly.com/question/11902987
#SPJ1
Because 1:2 is not a fraction while 1/2 is, you cannot assume that 1:2 is one-half of a line or anything that is being delt with in fact. The length of the line might be 18 units, and if it says that there needs to be some sort of action with a ratio of 1:2, you are not splitting that length in half, you are taking one unit from the left side, and two from the right, which does not equal the length of half of 18 units.
at a large conference of teachers from a variety of subjects, a random sample of 50 mathematics teachers attending the conference was selected. among the selected mathematics teachers, 28 percent had taken one or more courses in statistics. for which of the following populations is 28 percent a reasonable estimate of the percentage of those who have taken one or more courses in statistics?
The Population set for a sample of 28 percent is a reasonable estimate sample of the percentage of those who have taken one or more courses in statistics is "all mathematics teachers who have taken one or more courses in statistics".
So, Correct option is option (C) .
We have given that ,
There is a large conference of teachers from a variety of subjects.
Random sample size = 50 mathematics teachers who attended the conference is selected.
Population set : A population is the entire group that you want to draw conclusions about, that is here population set contains all teachers who attand the conference .
Sample : It is defined as subset of population set in a representative manner. It is taken from large population.
here, sample is 50 selected mathematics teachers.
On reading the provided data we conclude that The required population set for given sample is All mathematics teachers who have taken one or more course in statistics.
To learn more about Sample and population set, refer:
https://brainly.com/question/28435521
#SPJ4
Complete question:
At a large conference of teachers from a variety of subjects, a random sample of 50 mathematics teachers attending the conference was selected. Among the selected mathematics teachers, 28 percent had taken one or more courses in statistics. For which of the following populations is 28 percent a reasonable estimate of the percentage of those who have taken one or more courses in statistics?
A. All mathematics teachers
B. All mathematics teachers who attended the conference
C. all mathematics teachers who have taken one or more courses in statistics
D. All teachers who attended the conference
E. All teachers
Is it a zero if it touches the x-axis?.
At the zero point the curve can either cross the x-axis or just touch it. The root of the function is the number c with f(c) = 0.
If the graph intersects the x-axis and looks nearly linear at the intersection, it is a single root. Even multiplicity zero if the graph touches the x-axis and bounces off the axis.
Different graphs with different x-intercepts. The graph may intersect the x-axis at the intersection. Otherwise, the graph touches the x-axis and bounces.
For example, suppose you plot a function.
f (x) = (x + 1) (x - 2)²
See the figure above to see how the function behaves differently for different x intercepts.
x intercept at x = -1 is the solution of the equation
x + 1 = 0 , graph goes straight through the x intercept at x= −1 . We call it a single zero because zero corresponds to a single factor in the function.
x intercept at x = 2 is the iterative solution of the equation ( x - 2 )= 0
The graph touches the axis at the intercept and changes direction. The coefficients are quadratic (order 2), so, (x-2)²= (x - 2 )(x - 2)
coefficients are repeated and appears twice. The number of times a given factor appears in the factored form of a polynomial equation is called its multiplicity. Zero associated with this factor, the factor is (x-2), occurs twice, and has a multiplicity of 2 .
thus, the behaviour of graph shows that any point of f(x) which touch or intersect x-axis is call zero of f(x).
To learn more about Zeros of fiction , refer:
https://brainly.com/question/14074587
#SPJ4
A Three integers have a mean of 10, a median of 12 and a range of 10. Find the three integers.
Answer:
4 , 12 , 14
Step-by-step explanation:
1) We are told that the median (middle number) is 12 and that the mean is 10
This means that the numbers added together, divided by 3 which equals to ten. From this we can understand that the numbers should add up to 30 as 30 divided by 3 is 10
2) We already know one of the middle numbers which is 12 so the next step would be to subtract 12 from 30 which would be 18.
3) We are also told that the range is 10 meaning that the difference between the smallest and biggest number is 10. If the difference between the smallest and biggest is 10 and the number that they can add to is 18, all we have to do to get our numbers subtract 10 from 18 which is 8 and divide it by 2 which is 4. We have to divide it because we need to find two more numbers
4) From the information we have so far we know that one of our numbers is 4 and the other is 12. To get the final number, add 12 and 4 together which is 16, and subtract that from 30 which is 14. Meaning our numbers are 4 , 12 and 14
5) To check if this is right we can see that the range is 10 (14 - 4 = 10) the mean is 10 (4 + 12 + 14 = 30) and the median is 12!!
Hope this helps, have a great day!
find the area of the triangle below. carry your intermediate computations to at least four decimal places. round your answer to the nearest hundredth.
The area of the given triangle is 20 square kilometers.
Here, we are given a triangle as shown in the figure below.
There are many ways of calculating the area of a triangle but since here, we are given only one angle and 2 sides of the triangle we will use the following formula to calculate the area-
area of triangle = 1/2 × sinФ × side 1 × side 2
where, Ф = angle formed by side 1 and side 2
Here, Ф = 35
Sin 35 = 0.5736
Thus, the area of the triangle will be-
1/2 × 0.5736 × 7 × 10
= 35 × 0.5736
= 20.076
20.076 rounded off to nearest hundredth is 20
Thus, the area of the given triangle is 20 square kilometers.
Learn more about triangles here-
https://brainly.com/question/1058720
#SPJ4
Your question was incomplete. Check for the missing figure below
(a) use the extended euclidean algorithm to find the greatest common divisor of the given numbers and express it as the following linear combination of the two numbers. 6,066s 2,286t, where s
the Greatest Common Divisor is 252 and it can be expressed as the linear combination -2 * 6,066 + 3 * 2,286.
What is GCD?The greatest common divisor (GCD) is the biggest positive integer that divides two or more integers without leaving a remainder. It's also referred to as the greatest common factor (GCF) or the highest common factor (HCF). The Euclidean procedure, which continually divides the greater of the two integers by the smaller until a remainder of zero is obtained, is one way to calculate the GCD. The GCD is a crucial idea in mathematics, notably in number theory, and it has several applications in other disciplines, such as computer science and encryption. Finding the greatest common divisor of the coefficients of a linear equation in two variables is another popular geometry task.
How to solve?
The Greatest Common Divisor of 6,066 and 2,286 can be expressed as 252 = 6,066 * (-2) + 2,286 * 3. So, the GCD is 252 and it can be expressed as the linear combination -2 * 6,066 + 3 * 2,286.
To learn more about GCD, visit:
https://brainly.com/question/27227228
#SPJ4
Suppose A is a 2×2 real matrix with an eigenvalue λ=1+5i and corresponding eigenvector v⃗ =[−1+ii]. Determine a fundamental set (i.e., linearly independent set) of solutions for y⃗ ′=Ay⃗ , where the fundamental set consists entirely of real solutions. Enter your solutions below. Use t as the independent variable in your answers. y⃗ 1(t)= y⃗ 2(t)=
λ = 1 + 5i and ∨ = [ -1 + i , i ]
The first solution is[tex]y(t)=e^{\lambda t}\eta^1=e^{(1+5i)t}\begin{bmatrix} -1+i\\ i \end{bmatrix}\\y(t)=e^{t}(e^{5t}\begin{bmatrix} -1+i\\ i \end{bmatrix})[/tex]
Expanding the e^((5t)i) by Eulers Formula[tex]y(t) e(cos(5t) isin(5t) \begin{bmatrix} -1+i\\ i \end{bmatrix}\\\\y(t)=e^t\begin{bmatrix} (cos(5t)i+i^2sin(5t))-(cos(5t)+isin(5t))\\ cos(5t)i+i^2sin(5t)) \end{bmatrix}\\y(t)=e^t\begin{bmatrix} (-sin(5t)-cos(5t)+(cos(5t)-sin(5t))i\\ -sin(5t)+(cos(5t))i \end{bmatrix}[/tex]
Write the above solution x+yi[tex]y(t)=\left ( e^t \begin{bmatrix} -(sin(5t)+cos(5t))\\ -sin(5t) \end{bmatrix} \right )+\left ( e^t\begin{bmatrix} (cos(5t)-sin(5t))\\ cos(5t) \end{bmatrix} \right ) i[/tex]
The solution of the DE are[tex]y_{1}(t)= -e^t \begin{bmatrix} sin(5t)+cos(5t)\\ sin(5t) \end{bmatrix}\ and \ y_{2}(t)= e^t\begin{bmatrix} cos(5t)-sin(5t)\\ cos(5t) \end{bmatrix}[/tex]
Learn more about eigenvalue in brainly: https://brainly.com/question/15586347
#SPJ4
the othes solution in this picture: ↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓
Write an equation of a line in lope-intercept for that i perpendicular to the line y=1/2x-5 and pae through the point (1, -2)
Step-by-step explanation:
the slope-intercept form is
y = ax + b
"a" being the slope, "b" being the y-intercept (the y-value when x = 0).
to find the slope of the target line we use the slope of the given line : 1/2.
remember, the slope is expressed as ratio (y coordinate change / x coordinate change).
the given line increases the y- value by 1, when the x-value increases by 2.
a perpendicular slope (90°) simply turns y and x upside-down and flips the sign.
so, 1/2 turns into -2/1 = -2.
so, we see our line equation looks like
y = -2x + b
to get b we use the coordinates of the given point :
-2 = -2×1 + b
-2 = -2 + b
0 = b
so thar equation is simply
y = -2x
What are the coordinates of the point on the directed line segment from (−9,−6) to (−2,1) that partitions the segment into a ratio of 3 to 4?
[tex]\textit{internal division of a line segment using ratios} \\\\\\ A(-9,-6)\qquad B(-2,1)\qquad \qquad \stackrel{\textit{ratio from A to B}}{3:4} \\\\\\ \cfrac{A\underline{C}}{\underline{C} B} = \cfrac{3}{4}\implies \cfrac{A}{B} = \cfrac{3}{4}\implies 4A=3B\implies 4(-9,-6)=3(-2,1)[/tex]
[tex](\stackrel{x}{-36}~~,~~ \stackrel{y}{-24})=(\stackrel{x}{-6}~~,~~ \stackrel{y}{3}) \implies C=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{-36 -6}}{3+4}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{-24 +3}}{3+4} \right)} \\\\\\ C=\left( \cfrac{ -42 }{ 7 }~~,~~\cfrac{ -21}{ 7 } \right)\implies \boxed{C=(-6~~,~~-3)}[/tex]
PLSSS SOMEONE HELP ME I JUST NEED HELP PLEASEE!! IM OFFERING 40 PTS FOR THIS!! IM BEGGING YOU!!
Match each description with its corresponding value for the system below:
y = 4 x + 1 and y = -2 x + 7
-2
-1
-7
-5
The y -intercept of the exponential function.
The y -value of the solution in Quadrant I.
The number of points of intersection.
The y -intercept of the linear function.
Which parent function is represented by the graph straight line?.
A linear function is represented by the graph straight line.
In the given question we have to explain which parent function is represented by the graph straight line.
As we know that;
The simplest function in a family of functions, a parent function maintains the definition of the entire family.
There are several basic functions that we run with frequently in math. These fundamental functions include the square root function, basic polynomials, absolute values, and rational and exponential functions.
A linear function with a degree of one that is linear and expressed as f(x)=x. f(x) = x, where the function's graph passes through the origin, is referred to as a linear function.
Hence, a linear function is represented by the graph straight line.
To learn more about parent functions link is here
brainly.com/question/17939507
#SPJ4
Jacob wants to buy a $500,000 15-year term life policy, and the annual premium rate (per $1000 of face value) for his age group is $6. 78. If jacob lives until the end of the term of his policy, how much will jacob have paid in premiums overall? a. $101,700 b. $3,390 c. $50,850 d. $73,746 please select the best answer from the choices provided a b c d.
The required annual premium rate for the given term life policy is $50,850.
Explain term life policy and annual premium rate.Term life insurance covers you for a particular measure of time - basically, the strategy's term. The length of the term can change to suit your specific conditions. You can likewise look over two changed sorts of term disaster protection: diminishing term protection and level term protection.
annual premium rate:Annual Premium Rate implies, if pertinent, the exceptional rate so determined on the Statements Page of this Strategy to be utilized in processing a premium to be transmitted yearly.
According to quetion:Jacob needs to purchase a $500,000 15-year term life strategy, and the yearly superior rate (per $1000 of presumptive worth) for his age bunch is $6. 78.
Number of 1000 of every 500000 will be 500000/1000 = 500
the yearly superior rate (per $1000 of assumed worth) for his age bunch is $6. 78.
Absolute premium is 500 x 6.78 = 3390
The premium each year is 3390
For quite some time, the all out premium is
15 x 3390 = 50850
Thus, over all premium jacob have paid $50850.
To know more about annual premium rate visit:
brainly.com/question/13957713
#SPJ4
what is the probabiluity that in a random sample of 500 adults more than 30 percent do not own a credit card
Using p-hat formula and probability,
we get
a) Sampling distribution of p-hat = 0.02029286
b)The probability that in a random sample of 500 adults more than 30% do not own a credit card is
=0.3121
c) The probability that in a random sample of 500 adults between 25% and 30% do not own a credit card is 0.6635
We have given that
29% of adults do not own a credit card according to creditcard.com.
a) Sample size (n) = 500 of adults have own credit card
sample proportion, for the adults do not own a credit= 29% = 0.29
Normal distribution exits here with p
= 1-0.29=0.71 and
Standard error (p-hat) =sqrt(p(1-p)/n)
=sqrt(0.71× 0.29/500)
p-hat = 0.02029286
b) Now, more than 30% do not have own credit card.
P(p-hat>0.3) = P((phat- p)/sqrt(p×(1-p)/n) >(0.3-0.29)/sqrt(0.29× (1-0.29)/500))
=P(Z>0.49) =0.3121 (from standard normal table)
c) Sample size (n) = 500 and p-hat lies between 25% to 30% .
P(0.25<phat<0.3)
= P((0.25-0.29)/sqrt(0.29*(1-0.29)/500) <Z< (0.3-0.29)/sqrt(0.29*(1-0.29)/500))
=P(-1.97<Z<0.49)
=0.6635 (from standard normal table)
Hence, we calculated all the required probabilities.
a) p-hat = 0.02029286
b) P(p-hat>0.3) =0.3121
c) P(0.25<phat<0.3) =0.6635
To learn more about Standard error or p-hat , refer:
https://brainly.com/question/12360461
#SPJ4
Complete question:
According to creditcard.com, 29% of adults do not own a credit card.
a. Suppose a random sample of 500 adults is asked, "Do you own a credit card?" Describe the sampling distribution of p-hat, the proportion of adults who own a credit card.
b. What is the probability that in a random sample of 500 adults more than 30% do not own a credit card?
c. What is the probability that in a random sample of 500 adults between 25% and 30% do not own a credit card?
Over the summer, paulo opens a dog-washing business and begins with $32. The table shows how much he earns and spends each week. Weekly revenue and expenses revenue expense sales $124 supplies $8 he works for 8 weeks washing dogs. When he starts back at school, he budgets $60 to spend each week. How many weeks pass before he needs to wash more dogs?.
16 weeks would pass before any further dogs need to be bathed.
Define the term profit?Profit is the term used to describe the financial gain experienced when the revenue from a commercial activity exceeds the costs, costs, and taxes associated with maintaining that activity.The parameters being:
Initial investment = $32Eight weeks were worked.From the formula;
Profit = Sales - Expenses.
Weekly profit is $124 - $8 = $116.
Total revenue generated:
Number of weeks Profit per week.:
= $116 × 8
= $928
Total ownership is total revenue plus initial investment.
Owned in total:
$928 + $32 = $960.
The number of weeks until the entire amount owned is spent can be computed as follows:
Total amount owned weekly spending
= ($960 / $60) = 16
Thus, 16 weeks would pass before any further dogs need to be bathed.
To know more about the profit, here
https://brainly.com/question/1078746
#SPJ4
Which is a solution of the equation 3x 14 4?.
Solution of the equation 3x - 14 = 4 will be x=6
What are Equations?
Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.
3x - 14 = 4
⇒3x = 4 +14 (adding 14 on both side)
⇒x = 18 / 3 (dividing 3 from both sides)
⇒x = 6
Hence, Solution to the equation 3x - 14 = 4 will be x=6
Learn more about equations, by the following link
brainly.com/question/2972832
#SPJ4
If their food and beverage cot $25. 30 and there i an 8% meal tax, how much i the bill? After adding a tip, the total lunch cot wa $32. 24. What percentage tip did they give? Enter your anwer to the nearet percentage
The percentage tip did they give is 18%
If their food and beverage cost $25. 30
There i an 8% meal tax
The tax will be
$25.30(0.08) = $2.024.
Then we add the tax to the price such that
The bill will be
$25.30 + 2.024 = $27.32
Tip = 32.24 - 27.32 = 4.92
percentage tip did they give
= tip given /total amount of the bill x 100
= 4.92/27.32 x 100
= 18%
Therefore, If their food and beverage cot $25. 30 and there i an 8% meal tax and after adding a tip, the total lunch cot wa $32. 24.the percentage tip did they give is 18%
To learn more about percentage refer here
https://brainly.com/question/843074
#SPJ4
consider running golden section search on a function that is unimodal. if the method starts with an initial bracket of , what is the length of the bracket after 1 iteration?
The length of the bracket after 1 iteration is 100%.
Let f(x) = x³-15x² + 50x
a = 0, b=10.
Let the golden ratio be
GR=√5-1 / 2=0.618
Now, d = GR (b-a)
= 0.618 (10-0) = 6·18
[tex]x_{1}[/tex]= a+d = 0 + 6·18 = 6.18
[tex]x_{2}[/tex] = b-d = 10- 6·18 = 3.82
f([tex]x_{1}[/tex]) = (6·18)³ - 15 (6·18)² + 50(6·18) = -27.887
f([tex]x_{2}[/tex]) = (3.82)³-15(3.82)²+50(3.82)=27.857
so, f([tex]x_{2}[/tex]) > f([tex]x_{1}[/tex]) new interval is [a,x,]
i.e., maximum lies in [0, 6·18]
so, Xmax = [tex]x_{2}[/tex]= 382
Uncertainty in measurement will be,
∈= [tex]\frac{1-GR) (b-a)}{Xopt}[/tex] =[tex]\frac{((1-0.618) X (10-0)}{382}[/tex] × 100%
∈ = 100%
In arithmetic, quantities are within the golden ratio if their ratio is the same as the ratio in their sum to the larger of the 2 portions. Expressed algebraically, for quantities a and b with [tex]a > b > 0[/tex], [tex]\frac{(a+b)}{a}[/tex] = [tex]\frac{a}{b}[/tex]= φ
The golden ratio turned into known as the acute and suggest ratio by way of Euclid, and the divine proportion using Luca Pacioli, and also is going through numerous other names. The golden ratio seems in some patterns in nature, such as the spiral association of leaves and different elements of plants.
A few twentieth-century artists and architects, together with Le Corbusier and Salvador Dalí, have proportioned their works to approximate the golden ratio, believing them to be aesthetically appealing. these uses often appear in the form of a golden rectangle.
To learn more about the Golden Ratio visit here:
brainly.com/question/12450159
#SPJ4
A sample of 64 observations is selected from a normal population. The sample mean is 215, and the population standard deviation is 15. Conduct the following test of hypothesis using the 0.025 significance level. H0: μ ≥ 220 H1: μ < 220 Is this a one- or two-tailed test? One-tailed test Two-tailed test What is the decision rule? (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.) What is the value of the test statistic? (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.) What is your decision regarding H0? Reject Do not reject What is the p-value? (Round your answer to 4 decimal places.)
Therefore, the p-value is 0.0031, and our decision is to reject the null hypothesis on coducting a one tail test.
What is Hypothesis?A hypothesis is a theory put up to explain a phenomena. A link between two or more variables is described, and the proposition is testable. A hypothesis is an informed estimate or forecast made before undertaking any tests or research to determine its validity. A strong hypothesis should be definable, testable, and supported by prior data. It should also be stated in a way that allows it to be disproven, so that it can be tested using empirical evidence. Generally speaking, a hypothesis serves as the basis for additional research and testing in a scientific endeavour.
How to solve?
The decision rule for a one-tailed test with a significance level of 0.025 is to reject the null hypothesis if the test statistic is less than -1.96.
To calculate the test statistic, we use the formula:
z = (x - μ) / (s / √n)
x = 215, μ = 220, s = 15, and n = 64. Plugging these values into the formula gives:
z = (215 - 220) / (15 / √64) = -5 / (15 / 8) = -5 / 1.875 = -2.67
The test statistic is -2.67, which is less than the critical value of -1.96, so we reject the null hypothesis.
To calculate the p-value, we can use the z-table to look up the area under the normal curve that is to the left of -2.67. This area is approximately 0.0031, which is the p-value.
Therefore, the p-value is 0.0031, and our decision is to reject the null hypothesis.
To learn more about hypothesis, visit:
https://brainly.com/question/896413
#SPJ4
The area of a rectangle is 91 square inches. If the length of the rectangle is 1 less than twice its width, write an equation that could be used to find the width, w, of the rectangle.
The equation that can be used to find the width, w, of the rectangle with the given area is 2w² - w - 91 = 0
To determine the equation that can be used to find the width we use the following formula; Area of a rectangle = length × width
Since the area of the rectangle is 91 square inches and the length of the rectangle is 1 less than twice its width, this can be represented as;
Length of the given rectangle = 2w - 1
Using the area formula the equation to find the width would be:
(2w - 1)(w) = 91
2w² - w - 91 = 0
Hence 2w² - w - 91 = 0, is the equation that can be used to find the width.
To learn more about the area; click here:
https://brainly.com/question/25292087
#SPJ4
suppose the starting pressure in the container p1 is below atmospheric pressure when the stopper is popped. draw the adiabatic and isochoric processes on a p-v diagram.
The diagram of adiabatic and isochoric process on a pv diagram is given below.
In the given question we have to suppose the starting pressure in the container p1 is below atmospheric pressure when the stopper is popped the draw the adiabatic and isochoric processes on a p-v diagram.
The Adiabatic Process
A thermodynamic process known as adiabatic means that no heat is transferred into or out of the system. For an ideal gas, an adiabatic process is a reversible process with constant entropy. The adiabatic process is mathematically represented by the expression ∆Q=0.
The Isochoric Process
A thermodynamic process known as an isochoric process, also known as a constant-volume process, isovolumetric process, or isometric process, occurs when the volume of the closed system undergoing the process remains constant.
The diagram of adiabatic and isochoric process on a pv diagram is given below:
To learn more about adiabatic and isochoric process link is here
brainly.com/question/17407455
#SPJ4
Which linear equations have an infinite number of solutions?.
Linear equations have an infinite number of solutions are-
a) (x – 3\7) = 2\3 (3\2x – 9\14 )
c) 12.3x – 8 = 3(–6 + 4.1x)
What is Linear equations?
A linear equation is an equation within which the very best power of the variable is usually one.
Main body:
A linear equation can be said to have an infinite number of solutions when the number of the right hand side is the same at the number on the left hand side of the equation.
For example:
2 = 2 or x = x or 0 = 0
Solving the question above:
Which linear equations have an infinite number of solutions? Check all that apply.
a) (x – 3\7) = 2\3 (3\2x – 9\14 )
x - 3/7 = 6x/6 - 18/42
x - 3/7 = x - 3/7
Collect like terms
x - x = -3/7 + 3/7
0 = 0
The linear equation in option a has an infinite number of solutions
b) 8(x + 2) = 5x – 14
8x + 16 = 5x - 14
Collect like terms
8x - 5x = -14 - 16
3x = -30
x = -30/3
x = -10.
The linear equation in Option b has a true solution.
c) 12.3x – 18 = 3(–6 + 4.1x)
12.3x - 18 = -18 + 12.3x
Collect like terms
12.3x - 12.3x = -18 + 18
0 = 0
The linear equation in Option c has infinite number of solutions
d) 1\2(6x + 10) = 7(3\7x – 2)
6x/2 + 5 = 21/7x - 14
3x + 5 = 3x - 14
Collect like terms
3x - 3x = -14 - 5
0 = -19
The linear equation Option d has no solution
e) 4.2x – 3.5 = 2.1 (5x + 8)
4.2x - 3.5 = 10.5x + 16.8
Collect like terms
4.2x - 10.5x = 16.8 + 3.5
-6.3x = 20.3
x = -20.3/6.3
x = -3.22
Hence, the linear equation in Option e has a true solution
Therefore, the linear equations have an infinite number of solutions are:
a) (x – 3\7) = 2\3 (3\2x – 9\14 )
c) 12.3x – 18 = 3(–6 + 4.1x)
to know more about linear equation , visit:
https://brainly.com/question/2030026
#SPJ4
Using the ruler postulate, find the distance between -9 and 2
The distance between -9 and 2 using ruler postulate is 11units
What is ruler postulate?Ruler postulate states that the points on a line can be matched one to one with the real numbers. The real number that corresponds to a point is the coordinate of the point. The distance between points A and B, written as AB, is the absolute value of the difference of the coordinates of A and B.
If point A is -9 and point B is 2,
therefore the distance between https://brainly.com/question/28271571 A and B is A-B= -9-2= -11 units
Therefore the absolute value of the distance is 11 units
learn more about ruler postulate from
https://brainly.com/question/28271571
#SPJ1
Suppose X1,X2,X3 are random variables, each with expected value mand variance v, and cov(Xi,Xj) = c, i not equal j. Calculate the covariance and correlation coefficient of U,V , where U = 2−X1−2X2, and V = 3+3X2−X3.
To calculate the covariance and correlation coefficient of U and V, we need to first find the expected value and variance of U and V.
What is covariance?The covariance of two variables is a gauge of their relationship. In other words, it is a measure of how much the values of two variables tend to fluctuate together. Positive covariance shows that the values of the two variables tend to rise or decrease together, whereas negative covariance indicates that the values of one variable tend to increase when the values of the other variable drop. In probability theory and statistics, covariance is frequently employed to determine the association between two variables. It is determined by multiplying the variances of the two variables from their respective means and dividing the result by the total number of observations. This metric can be helpful for seeing trends and patterns in data and aiding analysts in forecasting.
How to solve?
The expected value of U is $E[U] = E[2 - X_1 - 2X_2] = 2 - m - 2m = -2m. Similarly, the expected value of V is $E[V] = E[3 + 3X_2 - X_3] = 3 + 3m - m = 4m.
To learn more about covariance, visit:
https://brainly.com/question/14300312
#SPJ4
To calculate the value of covariance and correlation coefficient of U and V, we have to find their expected value along with variance.
What does covariance mean?A measure of the link between two random variables and how much they fluctuate together is called covariance. Alternately, we may say that it establishes the relationship between the two variables' changes, i.e., that a change in one variable is equivalent to a change in the other.
What does the covariance tell us?When one variable changes, covariance shows the link between the other two variables. Both variables are said to have positive covariance if a rise in one causes an increase in the other. Reduced values of one variable also result in reduced values of the other.
for expected value of U ;
= $E[U]
= E[2 - X_1 - 2X_2]
= 2 - m - 2m = -2m.
Similarly, the expected value of V;
= $E[V]
= E[3 + 3X_2 - X_3]
= 3 + 3m - m
= 4m.
now we can easily calculate the covariance and correlation coefficient of U,V.
To learn more about covariance, visit:
brainly.com/question/14300312
#SPJ4
Frequent food questionnaires (FFQ) are a simple way to obtain information on the foods individuals consume by asking them questions about typical amounts of food consumed in a day or week or month. A more accurate picture is obtained by obtaining a detailed food diary (DR) for several days, randomly chosen over a certain time period. The data obtained from a frequent food questionnaire can be compared with the food diary to assess the validity of the questionnaire. The correlation between alcohol consumption from the food questionnaire and diary was r = 0.89 based on seven individuals. Based on the seven individuals for whom data is available, which statement is INCORRECT?DR8.26FFQ1.680.83020.1315.111.167.497.1812.841.76022.6625.06All of the answer options are correct.Because r > 0, the amount that is truly consumed is always larger than what is stated on the FFQ.Typical consumption as stated on a FFQ is positively associated with what is actually consumed.The FFQ is a reasonable tool to obtain information on the amount of alcohol consumed by individuals.
The amount the is truly consumed is always larger than what is stated on the FFQ. Hence, it is the incorrect statement for the indicated correlation.
What is correlation?
To represent the relationship between continuous variables, correlation is utilized. A numerical value called the correlation illustrates the connection between two variables. The sign affects the kind of relationship that exists between the variables. A direct or positive association would result if the sign is positive. It would be detrimental otherwise.
The correlation is a number which indicates relationship between two variables.
A correlation is used to test the relationship between continuous variables.
A correlation coefficient has a value between -1 and 1 this means there is a perfect negative or positive correlation. These are very high correlation examples.
A positive correlation does not imply that what is truly consumed is always larger than what is stated on the FFQ.
A positive correlation coefficient only implies that with a change in diary readings, the food questionnaire reading will also change in the same manner.
However, this does not reflect anything on the true consumed values and therefore, it cannot be judged whether the truly consumed amount will be larger or not.
The provided options are analyzed by the fact that the positive correlation means the change in the variables is direct rather than indirect.
The positive correlation means the direct change in the variables. Hence, the option is an incorrect one.
The correlation only represents whether the two variables have a positive or negative relationship. It does not tell anything about whether one value is greater or not.
Since, r > 0 the amount the is truly consumed is always larger than what is stated on the FFQ.
Hence, it is the incorrect statement for the indicated correlation.
To know more about the correlation, click on the link
https://brainly.com/question/4219149
#SPJ4
When beth was 9 years old, paul was 3 times younger than her. Now beth is 30 years old, how old is paul?.
Step-by-step explanation:
9÷3=3 so when beth is 30 you need to do 30-6 which is 24
When beth was 9, paul was 3 times younger = 9/3 = 3 years old.
Beth has gained 21 years since, so the age of paul is 3 + 21 = 24 years old.
During a four week period you work the following hour
Week 1: 36 3/8
Week 2: 41 1/4
Week 3: 40 1/2
Week 4: 38 3/8
What i the average number of hour you worked in one week?
You work an average of 39 1/8 hours per week.
The given can be used to calculate the average.
(36 3/8 + 41 1/4 + 40 1/2 + 38 3/8) / 4 =
36 + 41 + 40 + 38 = 155
3/8 + 1/4 + 1/2 + 3/8 = 3/8 + 2/8 + 4/8 + 3/8 = 12/8 = 1 1/2
155 + 1 1/2 = 156 1/2
(156 1/2) / 4 =
313/2 * 1/4 = 313/8 = 39 1/8
average weekly hours are 39 1/8.
Learn more about average here
https://brainly.com/question/12322912
#SPJ4
What is the domain of the square root function graphed?.
The domain of the square root function is x≥0.
What is a function?
A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.
The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.
The square root function's purpose must now be considered. The positive number that results in the input after being squared is returned as the principal root or output. Since y will be bigger than or equal to 0, we may be certain of that.
To find out a perfect square we need to find out square root is an integer.
Hence, The domain of the square root function is x≥0.
Learn more about function, by the following link.
https://brainly.com/question/25638609
#SPJ4
