10. Look at the graphs below. The graph on the left is the pre-image and the graph on the right
is the image. Using a scale factor, what are the coordinates of H'.
شے کے مر 1 2
765432
-1
-2
5
3
2
H
X
5
4
3
2
-1
-2
H
Y

To add polynomials in a horizontal method, combine like terms. For the vertical method, write the polynomials in standard form and align like terms in columns, and combine like terms. To subtract polynomials in a horizontal method, find the negative (opposite)  of the polynomial that is being subtracted and then combine like terms. For the vertical method, write the polynomials in standard form, align like terms, and subtract by adding the negative (opposite).

To add polynomials vertically,  one need to write them in standard form and align like terms in the columns. Combine like terms and add them to the polynomial.

Therefore, note that Polynomials are seen as expressions with variables and coefficients. Combine or subtract like terms when adding or subtracting them.

Learn more about polynomials   from

https://brainly.com/question/4142886

#SPJ1

WRITE Describe how to add and subtract polynomials using both the vertical and horizontal methods.

To add polynomials in a horizontal method, combine  ----- For the vertical method, write the polynomials in  --------  align like terms in columns, and combine like terms. To subtract polynomials in a horizontal method, find the ------ of the polynomial that is being and then combine like terms. For the vertical method, write the polynomials in standard form, align like terms and  and subtract by adding the  -------

The solution of the quadratic equations are shown below.

There are various methods that we could use when we want to solve a quadratic equation and these include;

1) Formula method

2) Graphical method

3) Completing the square method

4) Factor method

We have solved the following quadratic equations by factoring.

1)  3x^2 + 13x +10 = 0

x = - 1 and -10/3

2)  12n²-11n +2=0

n = 2/3 and 1/4

3) 5x^2 + 8x +3=0

x = -3/5 and -1

4)  10a²+ a -2=0

a = 2/5 and -1/2

5) 8x^2 + 10x + 3 = 0

x = -1/2 and -3/4

Learn more about quadratic equation:https://brainly.com/question/30098550

#SPJ1

The probability that the mean weight of 12 fruit will be between 681 and 682 grams is 0.0184.

We can solve this problem by using the central limit theorem, which tells us that the distribution of sample means will be approximately normal if the sample size is sufficiently large.

First, we need to calculate the standard error of the mean:

standard error of the mean = standard deviation / sqrt(sample size)

= 23 / sqrt(12)

= 6.639

Next, we can standardize the sample mean using the formula:

z = (x - mu) / (standard error of the mean)

where x is the sample mean, mu is the population mean, and the standard error of the mean is calculated above.

z1 = (681 - 692) / 6.639 = -1.656

z2 = (682 - 692) / 6.639 = -1.506

Using a standard normal distribution table or calculator, we can find the probabilities corresponding to these z-scores:

P(z < -1.656) = 0.0484

P(z < -1.506) = 0.0668

The probability of the sample mean being between 681 and 682 grams is the difference between these probabilities:

P(-1.656 < z < -1.506) = P(z < -1.506) - P(z < -1.656)

= 0.0668 - 0.0484

= 0.0184

Therefore, the probability that the mean weight of 12 fruit will be between 681 and 682 grams is 0.0184.

To learn more about corresponding visit:

https://brainly.com/question/1597341

#SPJ11

The three pairs of fraction whose sum is 3/5 are

We have to find pairs of fractions that have a sum of 3/5.

First pair:

1/5 + 2/5

= 3/5

Second pair:

= -2/5 + 1

= -2/5+ 5/5

= 3/5

Third pair:

= -6/5 + 9/5

= 3/5

Learn more about Fraction here:

https://brainly.com/question/10354322

#SPJ1

In the short run, if a contractionary fiscal policy is followed by an expansionary monetary policy, the nominal interest rate is likely to decrease and employment is likely to increase.

The contractionary fiscal policy initially reduces government spending and may also increase taxes, which slows down economic growth and leads to higher unemployment. However, the subsequent expansionary monetary policy, which involves the central bank increasing the money supply and lowering interest rates, encourages borrowing and investment, stimulating economic activity and leading to job creation. The combined effect of these policies would result in lower nominal interest rates and higher employment in the short run.

Know more about fiscal policy here:

https://brainly.com/question/27250647

#SPJ11

Answer: 32 km

Step-by-step explanation:

If he travelled 4/5 of the trip by bike, then he travelled 1/5 on foot.

so he travelled 160/5 = 32 km on foot. Phew! thats a long walk.

We can interpret this confidence interval as: With 95% confidence, we can say that the true difference between

a) Hypothesis test for comparing variances between two data sets:

Null hypothesis: The variance of data set A is equal to the variance of data set B.

Alternative hypothesis: The variance of data set A is not equal to the variance of data set B.

We can use the F-test to compare the variances between the two data sets. The test statistic is calculated as:

[tex]F = s1^2 / s2^2[/tex]

where [tex]s1^2[/tex] is the sample variance of data set A and [tex]s2^2[/tex] is the sample variance of data set B.

Using the given information, we can calculate the test statistic as:

F = 0.45 / 0.32 = 1.41

Using an alpha level of 0.05 and degrees of freedom of 28 and 21 (n1-1 and n2-1), we can find the critical values for F as 0.46 and 2.33.

Since the calculated F value of 1.41 falls between the critical values, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the variance of data set A is different from the variance of data set B.

b) Hypothesis test for comparing means between two data sets:

Null hypothesis: The mean weight of newborns whose parents smoke cigarettes is equal to the mean weight of newborns whose parents do not smoke cigarettes.

Alternative hypothesis: The mean weight of newborns whose parents smoke cigarettes is not equal to the mean weight of newborns whose parents do not smoke cigarettes.

Since the variances of the two data sets are not significantly different from each other, we can use a two-sample t-test assuming equal variances to compare the means between the two data sets.

Using the given information, we can calculate the test statistic as:

t = (x1bar - x2bar) / (sqrt[([tex]s^2[/tex] / n1) + ([tex]s^2[/tex] / n2)])

where x1bar and x2bar are the sample means,[tex]s^2[/tex] is the pooled sample variance, n1 and n2 are the sample sizes.

Using an alpha level of 0.05 and degrees of freedom of 48 (n1 + n2 - 2), we can find the critical values for t as ±2.01.

Using the given information, we can calculate the test statistic as:

t = (7.25 - 7.68) / (sqrt[(0.[tex]385^2[/tex] / 30) + ([tex]0.28^2[/tex] / 23)]) = -1.2

Since the calculated t value of -1.23 falls between the critical values, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the mean weight of newborns whose parents smoke cigarettes is different from the mean weight of newborns whose parents do not smoke cigarettes.

c) Confidence interval for the difference between means:

Using the given information, we can calculate the 95% confidence interval for the difference between means as:

(x1bar - x2bar) ± tα/2,df * (sqrt[([tex]s^2 / n1[/tex]) + (s^2 / n2)])

where tα/2,df is the t-value for the given alpha level and degrees of freedom.

Using the calculated values from part b), we can find the 95% confidence interval as:

(7.25 - 7.68) ± 2.01 * (sqrt[(0.385^2 / 30) + ([tex]0.28^2[/tex] / 23)]) = (-0.779, 0.179)

We can interpret this confidence interval as: With 95% confidence, we can say that the true difference between

To learn more about  confidence visit:

https://brainly.com/question/28969535

#SPJ11

Answer:  A

Step-by-step explanation:

It would take 4 pipes with a radius of 4cm to replace one pipe with a radius of 8cm and provide the same amount of water flow.

We have,

The volume of water that can flow through a pipe is proportional to the cross-sectional area of the pipe.

The formula for the area of a circle is:

A = πr²

where A is the area of the circle and r is the radius of the circle.

For a pipe with a radius of 8cm, the cross-sectional area is:

A_8cm = π(8cm)²

     = 64π cm²

For a pipe with a radius of 4cm, the cross-sectional area is:

A_4cm = π(4cm)²

     = 16π cm²

To find out how many 4cm pipes would be needed to replace one 8cm pipe, we can compare the areas of the two pipes:

Number of 4cm pipes

= A_8cm / A_4 cm

= (64π) / (16π)

= 4

Therefore,

It would take 4 pipes with a radius of 4cm to replace one pipe with a radius of 8cm and provide the same amount of water flow.

Learn more about pipes here:

https://brainly.com/question/31180984

#SPJ1

Answer:

[tex]3x - 12 = 4x - 24[/tex]

[tex]x = 12[/tex]

To find the value of x in the given parallelogram, set up an equation using the given sides and solve for x. The value of x is 12.

To find the value of x in the given parallelogram, we need to use the properties of a parallelogram. In a parallelogram, opposite sides are equal in length. So, we can set up an equation using the given sides:

3x - 12 = 4x - 24

Now, we can solve the equation to find the value of x:

3x - 4x = -24 + 12

-x = -12

x = 12

Therefore, the value of x is 12.

https://brainly.com/question/31342904

#SPJ2

This means that there exists a nonzero vector x such that Ax=0x, which implies that λ=0 is an eigenvalue of A with a corresponding eigenvector x.

a. If Ax-Ax for some vector x, then à is an eigenvalue of A. - True.

This statement is true because if Ax = λ.x for some vector x, then we can rewrite Ax-Ax = λ.x - λ.x as (A-I)x = 0. This means that the matrix A-I is singular, and therefore its determinant is 0. So, we have det(A-I) = 0, which implies that λ = 1 is an eigenvalue of A.

b. A matrix A is not invertible if and only if 0 is an eigenvalue of A. - False.

This statement is false because a matrix A is not invertible if and only if its determinant is 0, which means that the equation Ax = 0 has a nontrivial solution. This implies that 0 is an eigenvalue of A, but the converse is not necessarily true.

c. If 0 is an eigenvalue of A, then the equation Ax-ox has only the trivial solution. The equation Ax-0x is equivalent to the equation Ax-o and Ax-o - True.

This statement is true because if λ=0 is an eigenvalue of A, then we have (A-0I)x = Ax = 0x, which means that the matrix A-0I is singular, and therefore its determinant is 0. So, we have det(A-0I) = 0, which implies that the equation Ax = 0 has a nontrivial solution. However, if A is invertible, then the only solution to the equation Ax=0 is the trivial solution, which means that Ax-0x = Ax = 0x has only the trivial solution.

d. If 0 is an eigenvalue of A, then there are nontrivial solutions to the equation Ax=0x. The equation Ax-0x is equivalent to the equation Ax=0 - True.

This statement is true because if λ=0 is an eigenvalue of A, then we have (A-0I)x = Ax = 0x, which means that the matrix A-0I is singular, and therefore its determinant is 0. So, we have det(A-0I) = 0, which implies that the equation Ax = 0 has a nontrivial solution. This means that there exists a nonzero vector x such that Ax=0x, which implies that λ=0 is an eigenvalue of A with a corresponding eigenvector x.

To learn more about statement visit:

https://brainly.com/question/2285414

#SPJ11

The number line represents all possible numbers of signatures Ali could collect is Number line A.

We have,

Ali currently has 520 signatures.

Now, number of signatures Ali need

= 1,000 - 520

= 480

So, the possible number depending on how many weeks he wants to spend getting signatures.

480/6 = 80

480/5 = 96

480/4 = 120

480/3 = 160

480/2 = 240

480/1 = 480

Learn more about Number line here:

https://brainly.com/question/16191404

#SPJ1

Answer:

To solve this problem, we need to use the concept of hypergeometric distribution, which gives the probability of selecting a certain number of objects with a specific characteristic from a population of known size without replacement. We will use the formula:

P(X = k) = [ C(M, k) * C(N - M, n - k) ] / C(N, n)

where:

P(X = k) is the probability of selecting k objects with the desired characteristic;

C(M, k) is the number of ways to select k objects with the desired characteristic from a population of M objects;

C(N - M, n - k) is the number of ways to select n - k objects without the desired characteristic from a population of N - M objects;

C(N, n) is the total number of ways to select n objects from a population of N objects.

In our case, we want to select 5 rats out of a population of 80, and we want exactly 3 of them to have 2 genetic mutations. We can calculate this probability as follows:

P(3 rats have exactly 2 mutations) = [ C(12, 3) * C(68, 2) ] / C(80, 5)

where:

M is the number of rats that have exactly 2 mutations, which is the sum of the rats that have mutations AB, AC, AD, BC, BD, and CD, or M = 5 + 6 + 4 + 3 + 3 + 1 = 22;

N - M is the number of rats that do not have exactly 2 mutations, which is the remaining population of 80 - 22 = 58 rats;

n is the number of rats we want to select, which is 5.

We can simplify this expression as follows:

P(3 rats have exactly 2 mutations) = [ C(12, 3) * C(68, 2) ] / C(80, 5)

= [ (12! / (3! * 9!)) * (68! / (2! * 66!)) ] / (80! / (5! * 75!))

= 0.03617

Therefore, the probability that if 5 rats are selected at random, 3 will have exactly 2 genetic mutations is 0.03617 (rounded to five decimal places).

To solve this problem, we need to find the z-score corresponding to the 14th percentile of the normal distribution. We can then use this z-score to find the corresponding value of K.

First, we find the z-score corresponding to the 14th percentile using a standard normal distribution table or calculator. The 14th percentile is equivalent to a cumulative probability of 0.14, which corresponds to a z-score of approximately -1.08.

Next, we use the formula z = (x - μ) / σ to find the corresponding value of K. Rearranging this formula, we get x = μ + z * σ. Plugging in the values we know, we get:

K = 11 + (-1.08) * 0.25
K = 10.73 cm

Therefore, there is a 14% chance that a randomly selected cylindrical metal bar has a length longer than 10.73 cm.

Learn more about normal distribution: https://brainly.com/question/4079902

#SPJ11

There is a 90% probability that a resident has at least one of the two services, and a 62.5% probability that a resident has Internet service given that they already have television service.

To answer your question, we will use the formula for the probability of the union of two events: P(A ∪ B) = P(A) + P(B) - P(A ∩ B), where A represents having Internet service and B represents having television service.

The probability of having at least one of the two services is:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
= 0.60 (Internet) + 0.80 (television) - 0.50 (both)
= 1.40 - 0.50
= 0.90 or 90%

Now, to find the probability of having Internet service given that the resident already has television service, we'll use the conditional probability formula: P(A | B) = P(A ∩ B) / P(B)

P(Internet | Television) = P(Internet ∩ Television) / P(Television)
= 0.50 (both) / 0.80 (television)
= 0.625 or 62.5%

So, there is a 90% probability that a resident has at least one of the two services, and a 62.5% probability that a resident has Internet service given that they already have television service.

Learn more about "probability": https://brainly.com/question/13604758

#SPJ11

To select one junior and one senior there are 30 different choices and to select exactly one student there are 11 different choices.

(a) Given that there is a total of 5 juniors and 6 seniors volunteering for the committee, and the committee decides to select one junior and one senior, you can calculate the different choices by multiplying the number of juniors by the number of seniors. In this case, it would be 5 juniors * 6 seniors = 30 different choices.

(b) If the committee decides to select exactly one student, you would simply add the number of juniors and seniors together. In this case, it would be 5 juniors + 6 seniors = 11 different choices.

So, there are 30 different choices when selecting one junior and one senior, and 11 different choices when selecting exactly one student.

Learn more about: Permutation & Combination - https://brainly.com/question/28065038

#SPJ11

The joint distribution for (X,Y) is given by the table below, and the marginal distributions for X and Y are given by the tables below.

Y P(Y)

0 0

1 0.3686

2 0.0588

To determine the joint distribution for (X,Y), we need to calculate the probability of each possible outcome. There are 4 kings in the deck and 13 diamonds. We can use the formula for calculating probabilities of combinations to find the probabilities of each possible combination of kings and diamonds:

P(X = 0, Y = 0) = 36/52 * 35/51 = 0.5098

P(X = 0, Y = 1) = 36/52 * 16/51 = 0.2353

P(X = 0, Y = 2) = 36/52 * 1/51 = 0.0055

P(X = 1, Y = 0) = 16/52 * 36/51 = 0.2353

P(X = 1, Y = 1) = 16/52 * 15/51 = 0.0588

P(X = 1, Y = 2) = 16/52 * 0 = 0

P(X = 2, Y = 0) = 1/52 * 36/51 = 0.0055

P(X = 2, Y = 1) = 1/52 * 15/51 = 0.0007

P(X = 2, Y = 2) = 1/52 * 0 = 0

Therefore, the joint distribution for (X,Y) is:

To find the marginal distribution for X, we can sum the probabilities for each possible value of X:

P(X = 0) = 0.5098 + 0.2353 + 0.0055 = 0.7506

P(X = 1) = 0.2353 + 0.0588 + 0 = 0.2941

P(X = 2) = 0.0055 + 0.0007 + 0 = 0.0062

Therefore, the marginal distribution for X is:

To find the marginal distribution for Y, we can sum the probabilities for each possible value of Y:

P(Y = 0) = 0.5098 + 0.2353 + 0.0055 = 0.7506

P(Y = 1) = 0.2353 + 0.0588 + 0.0007 = 0.2948

P(Y = 2) = 0.0055 + 0 + 0 = 0.0055

Therefore, the marginal distribution for Y is:

To learn more about diamonds visit:

https://brainly.com/question/29775108

#SPJ11

To find dx/dt and dy/dt for the given curve with parametric equations y = Int and x = 4ts, we can use the chain rule of differentiation.

First, let's find dx/dt:

dx/dt = d/dt (4ts)

Using the product rule of differentiation, we get:

dx/dt = 4s + 4t(ds/dt)

However, we don't know what ds/dt is. But we do know that s = x/4t, so we can use the quotient rule of differentiation to find ds/dt:

ds/dt = d/dt (x/4t)

ds/dt = (4t(dx/dt) - x(4(dt/dt))) / (4t)^2

Simplifying this expression, we get:

ds/dt = (dx/dt)/t - x/(4t^2)

Substituting this back into the expression for dx/dt, we get:

dx/dt = 4s + 4t[(dx/dt)/t - x/(4t^2)]

Simplifying this expression, we get:

dx/dt = 4s - (x/t)

Next, let's find dy/dt:

dy/dt = d/dt(Int)

Since Int is a constant, its derivative with respect to t is 0. Therefore,

dy/dt = 0

In summary, we have found that:

dx/dt = 4s - (x/t)

dy/dt = 0

This means that the slope of the curve at any point is given by dx/dt, and that the curve is horizontal (i.e. dy/dt = 0) at every point.

Explaining this in 200 words:

To find the derivative of a curve with parametric equations, we use the chain rule of differentiation. By differentiating x and y with respect to t, we can express dx/dt and dy/dt in terms of s and t. In this particular example, we first found dx/dt using the product rule of differentiation. We then used the quotient rule to find ds/dt, which allowed us to substitute back into the expression for dx/dt. Finally, we found dy/dt by differentiating the constant Int with respect to t.

The resulting expressions for dx/dt and dy/dt tell us important information about the curve. The slope of the curve at any point is given by dx/dt, which we found to be 4s - (x/t). This means that the slope of the curve varies depending on the values of s and t. The curve is horizontal (i.e. dy/dt = 0) at every point, which means that it does not rise or fall as t changes. Overall, finding the derivatives of parametric curves allows us to better understand their behavior and properties.

More on parametric equation: https://brainly.com/question/30451972

#SPJ11

We can see that the maximum height attained by the cannonball is 20 meters, which is less than the maximum height of 25 meters in part (b) of Problem 36.  As a result, the cannonball does not reach the same height as in the case of no air resistance.

To modify the differential equation in Problem 35, we use the same approach as in Problem 36, but with air resistance proportional to instantaneous velocity.

Let v be the velocity of the cannonball and g be the acceleration due to gravity. Then, the force due to air resistance is proportional to v, so we can write:

F = -kv

where k is the constant of proportionality. The negative sign indicates that the force due to air resistance opposes the motion of the cannonball.

Using Newton's second law, we have:

ma = -mg - kv

where m is the mass of the cannonball and a is its acceleration. Dividing both sides by m, we get:

a = -g - (k/m)v

This is a first-order linear differential equation, which we can solve using the same method as in Problem 36. The solution is:

v(t) = (mg/k) + Ce[tex]^(-kt/m)[/tex]

where C is a constant determined by the initial conditions.

To find the maximum height attained by the cannonball, we need to integrate the velocity function to get the height function. However, this cannot be done in closed form, so we need to use numerical methods. We can use Euler's method, which is a simple and efficient way to approximate the solution of a differential equation.

Using Euler's method with a step size of 0.1 seconds, we obtain the following values for the velocity and height of the cannonball:

t = 0, v = 50, h = 0

t = 0.1, v = 45, h = 0.5

t = 0.2, v = 40, h = 1.5

t = 0.3, v = 35, h = 2.9

t = 0.4, v = 30, h = 4.6

t = 0.5, v = 25, h = 6.5

t = 0.6, v = 20, h = 8.7

t = 0.7, v = 15, h = 11.1

t = 0.8, v = 10, h = 13.8

t = 0.9, v = 5, h = 16.8

t = 1.0, v = 0, h = 20.0

We can see that the maximum height attained by the cannonball is 20 meters, which is less than the maximum height of 25 meters in part (b) of Problem 36. This is because air resistance slows down the cannonball more quickly when it is moving upward than when it is moving downward. As a result, the cannonball does not reach the same height as in the case of no air resistance.

Learn more about differential equation ,

https://brainly.com/question/31583235

#SPJ4

The probability that z lies between -0.55 and 0.55 is 0.4176. So, the correct option is option OD. 0.4176.

To find the probability that z lies between -0.55 and 0.55 for a standard normal variable, we'll use the standard normal table (also known as the z-table).

Step 1: Look up the z-score of -0.55 in the z-table. This gives us the area to the left of -0.55, which is 0.2912.

Step 2: Look up the z-score of 0.55 in the z-table. This gives us the area to the left of 0.55, which is 0.7088.

Step 3: Subtract the area to the left of -0.55 from the area to the left of 0.55 to find the probability between the two z-scores: 0.7088 - 0.2912 = 0.4176.

Therefore, the probability that z lies between -0.55 and 0.55 for a standard normal variable is approximately 0.4176 (rounded to four decimal places).

Know more about probability here:

https://brainly.com/question/13604758

#SPJ11

Answer:

1/6561

Step-by-Step Explanation:

you get 1/6561 when you simplify 9^-4

Answer:

Step-by-step explanation:

You want the present value and the lower-cost choice for two payment plans:

The present value of 20 semiannual payments of $2500 discounted at the rate of 5% can be found by a financial calculator to be $38,973. Together with the $7500 down payment, the present value of Option 2 is ...

  Option 2 = $7500 +38,973 = $46,473

The present value of $30,000 cash is $30,000.

Option 1 has a present value of $30,000.

Option 2 has a present value of $46,473.

Option 1 will save your parents the most money.

__

Additional comment

The total cash outlay for option 2 is $7500 + 20×2500 = $57,500. For this option to be the same cost as option 1, the account would need to earn interest at the rate of 18.4%.

There are various ways to estimate the interest earned. One of them is to compute half the value of simple interest on the interval. That is, the interest could be estimated as (1/2)(5%/yr)(10 yr) = 25%. This suggests the PV would be about 1/1.25 times the sum of payments, or 40000. That's close enough to the actual value of 39000 to tell you that Option 1 is the better choice.

Answer:

[tex] v = \frac{1}{3} h\pi \: r { }^{2} \\ = \frac{1}{3} \times 3 \times \pi \times2 ^{2} \\ \frac{1}{3 } \times 3 \times \pi \times 4 \\ \frac{1}{3} \times 12\pi \\ 4\pi \: cm {}^{3} is \: the \: answer[/tex]

the answer is 4 pie cm cube

may I get branliest

Answer:

At Marco Market, a chewy toy costs $2 and a cat collar costs $6. Meanwhile, at Sonia Superstore, a chewy toy for dogs costs $4 and a cat collar costs $4. To represent the quantities of each item that can be purchased at each store, an equation can be used.

Step-by-step explanation:

At Marco Market, a chewy toy costs $2 and a cat collar costs $6. Meanwhile, at Sonia Superstore, a chewy toy for dogs costs $4 and a cat collar costs $4. To represent the quantities of each item that can be purchased at each store, an equation can be used.

The percent of increase from 25 to 34 to the nearest tenth of percent is 36.

In order to find the percent of increase from 25 to 34, we first need to find the amount of increase, which is:

34 - 25 = 9

Next, we divide the amount of increase by the original value, and then multiply by 100 to express the result as a percentage:

(9 / 25) x 100 ≈ 36

Therefore, the percent of increase from 25 to 34 is approximately 36%.

More on percent calculation can be found here: https://brainly.com/question/14697226

#SPJ1

Jonty is correct as the original cost of paint is £196 which is less than £200 as said by him.

The area of part of cuboid to be painted will be the sum of all the unpainted areas. So, the area remaining to be painted will be = (2 × 3 × 2.5) + (2 × 3 × 12) + (12 × 2.5)

Remaining area = 15 + 72 + 30

Remaining area = 117 m²

Let us assume the original cost of paint be x. So,

x + 10%x = 26.95

110x = 26.95 × 100

110x = 2695

x = £24.5

Now, number of required tins = total unpainted area/area covered by one tin

Number of required tins = 117/15

Number of required tins = 7.8 tins

Taking it as 8 tins.

Previous cost of tins = 8 × 24.5

Previous cost = £196

Since the original cost is less than £200, Jonty is stating truth.

Learn more about area -

https://brainly.com/question/25292087

#SPJ4

The complete question is attached in figure.

The SDSM approaches normality, the sample mean becomes a better estimator of the population mean, and the confidence intervals become narrower, increasing the likelihood of capturing the true population mean.

a. With the exponential population distribution and a small sample size of 5, the 95% confidence intervals do not perform well at capturing the true population mean. This is because the exponential distribution is highly skewed and not symmetric, so the sample mean is not necessarily a good estimator of the population mean. Additionally, with a small sample size, there is more variability in the sample means, so the confidence intervals are wider and less likely to capture the true population mean.

b. With a larger sample size of 40, the intervals are more likely to capture the true population value. This is because the Sampling Distribution of Sample Means (SDSM) approaches a normal distribution as the sample size increases, regardless of the underlying population distribution. This is known as the Central Limit Theorem. As the SDSM approaches normality, the sample mean becomes a better estimator of the population mean, and the confidence intervals become narrower, increasing the likelihood of capturing the true population mean.

To learn more about population visit:

https://brainly.com/question/31544819

#SPJ11

The test statistic is -5.02

To test the hypothesis that the proportion of men who own cats is smaller than the proportion of women who own cats, we can use a two-sample z-test for the difference in proportions.

The null hypothesis is that the proportion of men who own cats is equal to or greater than the proportion of women who own cats, while the alternative hypothesis is that the proportion of men who own cats is smaller than the proportion of women who own cats.

We can calculate the test statistic using the following formula:

z = (p1 - p2) / sqrt(p*(1-p)*(1/n1 + 1/n2))

where

p1 is the proportion of men who own cats (0.35)

p2 is the proportion of women who own cats (0.9)

p is the pooled proportion [(x1 + x2) / (n1 + n2)] = [(0.35100 + 0.980)/(100+80)] = 0.62

n1 is the sample size of men (100)

n2 is the sample size of women (80)

Plugging in the values, we get:

z = (0.35 - 0.9) / sqrt(0.62*(1-0.62)*(1/100 + 1/80)) = -5.02

Rounding this to two decimal places, the test statistic is -5.02.

To learn more about statistics, click here:

https://brainly.com/question/31577270

#SPJ11