Maths qs
Dot diagram and mean mass

Write a function which accepts a nested list of integers and returns the count of all the integers greater than 0. This can be done in a recursive manner by first flattening the nested list and then counting all the integers that are greater than 0.The function can be implemented using any programming language such as Python, Java, or C++.

A nested list is a list that contains other lists. It is a common data structure used in programming languages such as Python, LISP, and Scheme. The task at hand is to write a function that accepts a nested list of integers and returns the count of all the integers greater than 0. To accomplish this task, we can use a recursive approach. The first step is to flatten the nested list into a single list. This can be done by recursively iterating through the list and adding each element to a new list.

Once we have a single list, we can count all the integers that are greater than 0 using a loop or list comprehension. Finally, we return the count as the output of the function. Here is an implementation of the function in Python: def count_positive(lst): flat_list = [] for i in lst: if type(i) == list: flat_list. extend(count _ positive(i)) else: flat _ list. append(i) return len([x for x in flat_list if x > 0])The above function takes a nested list as an argument and returns the count of all the integers greater than 0.

The function first flattens the list and then counts all the integers that are greater than 0 using a list comprehension. The function can be tested using the example given in the question:>>> count_positive([[6,[-3,[1]]],[4,-1,[[0],5]]])5In the above example, there are five integers greater than 0 in the nested list. Therefore, the output of the function is 5.

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The minimum number of dimes that Tyler could have is 9

To solve this word problem, we can use the information given to set up a system of equations. Let N be the number of nickels and D be the number of dimes.

We know that N + D = 17, because Tyler has a maximum of 17 coins.

We also know that (N×$0.05) + (D×$0.10) = $1.15, because the total value of the coins must be at least $1.15.

Substituting the value of N with 4, we get:

4 + D = 17

4× $0.05 + D × $0.10 = $1.15

0.2 + 0.1D = 1.15

0.1D = 1.15 - 0.2

0.1D = 0.95

D = 0.95/0.1

D = 9.5

Since the number of dimes must be an integer, the minimum number of dimes that Tyler could have is 9

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Answer:

y= -5x + 21

Step-by-step explanation:

The equation of the line that passes through (5, -4)  and is perpendicular to line y = 1/5x + 4  is y= -5x + 21

The slope that is perpendicular to the slope 1/5x is -5x.

To find a perpendicular slope, you take the negative reciprocal. (so you change the signs (1/5x is positive so now it would be negative) and -5/1 is basically -5)

However, y = -5x + 4 does NOT pass through (5, -4)

But we still have to write the equation in slope intercept form or the equation of the line

The formula for slope- intercept form is : y= mx + b

So we must plug in (m) which is our -5x and for y we look at the coordinates they gave us ----- (5, -4). -4 is our y. In the coordinates we also have x listed which is 5, so we all plug that in.

y = -5x + b (as you can see -5x is plugged in here)

-4 = -5x + b (as you can see -4 is plugged in here)

4 = -5(5) + b (as you can see 5 is plugged in here)

NOW WE MUST SOLVE!

-4 = -25 + b

Add 25 from both sides.

-4 = -25 + b

+25 25

----------------

21 = b

We can now plug this into our slope intercept formula---y= mx+ b---to find the equation of the line.

Answer:

g=12

Step-by-step explanation:

divide both sides by 13

13g=156

g=156/13

g=12

Answer:

Step 1: Lets say 'x' is the total wage. Then we subtract 1/4 from the total wages.

=> 4x/4 - x/4

=> 3x/4 = Remaining Wages Left.

Step 2: Subtract 20% from 3x/4.

3x/4 - x/5 = Remaining Wages Left.                                 [20% = 20x/100 = x/5]

=> 11x/20 = Remaining Wages Left.

Step 3: Subtract 0.15x from his remaining wages left.

=> 11x/20 - 3x/20 = Remaining Wages Left.                     [0.15 = 15/100 = 3/20]

=> 8x/20 = Remaining Wages Left.

Step 4: Simplify

8x/20 = 2x/5 = 0.40x

=> Simon has saved 2x/5 of the wages.

Please give me brainliest :)

Answer:

Step-by-step explanation:

The total is 100% or 1.

Spent:

Left:

Answer: B) rotation 90 degree clockwise.

If a figure is in quadrant 2, and we rotate 90 degrees clockwise around the origin, then the figure will end up in quadrant 1 instead of quadrant 3. The four quadrants are numbered so that you start in the upper right corner, and move counterclockwise.

Answer:

$21.40

Step-by-step explanation:

7% is equal to .07

multiply .07 times 20

=1.40

add the $1.40 sales tax to the meal price to get 21.40

The values of the mathematical function is a f(-4) = -21,f(-2) = -11,f(0) = -9, f(5) = -4.

According to the statement

We have to find that the value of the function.

So, For this purpose, we know that the

The Mathematical function is an expression that defines a relationship between one variable and another variable.

From the given information:

The statement is a:

5x -1 at the x<-2

And

x -9 at the value of the x is the greater than the equal to the -2.

Then

f(-4) = 5x -1

f(-4) = 5(-4) -1

f(-4) = -20 -1

f(-4) = -21

Then

f(-2) = x -9

f(-2) = -2-9

f(-2) = -11

Then

f(0) = x -9

f(0) = 0-9

f(0) = -9

Then

f(5) = x -9

f(5) = 5-9

f(5) = -4.

So, The values of the mathematical function is a f(-4) = -21,f(-2) = -11,f(0) = -9, f(5) = -4.

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Answer:

translation

Step-by-step explanation:

translation move with same shape and size

Answer:

translation

Step-by-step explanation:

move the same ship and size

Answer:

AC=18

Step-by-step explanation:

To find AC, use the Pythagorean Theorem.  Since the longest side (hypotenuse) is known, instead of a²+b²=c², the equation will be c²-a²=b².  12²-8²=b²

144-64=b²

80=b²

√80=√b²

8.94427191=b

That is for one of the two right triangles that make up the tent.  Since there are 2 triangles, 8.94427191 only equals BC or AB.  So, multiply 8.94427191×2=17.88854382 to find the length of AC.

AC= 18

Arguments are a key component of political campaigns. They are used to convince voters to support a particular candidate or issue. Political campaigns often make claims, which are statements that assert a fact or belief. These claims are backed up by reasoning, which is the evidence or explanation that supports the claim. The conclusion is the result of the reasoning and supports the overall argument.

For example, a candidate may claim that they have a plan to improve the economy. The reasoning may be that the candidate has experience in business and has implemented successful economic policies in the past. The conclusion is that if the candidate is elected, they will be able to improve the economy.
Political campaigns also use arguments to attack opponents and discredit their claims. They may use reasoning to point out flaws in their opponent's plans or past actions. The conclusion is that the opponent is not fit for office and voters should not support them.

Overall, arguments are a crucial tool in political campaigns. They are used to persuade voters and shape public opinion. Successful candidates and campaigns are often those that can make the most convincing arguments and win over the most supporters.

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The Tragedy of the Commons is used to describe when one fisherman exceeds the legal limit for a particular type of fish by one fish, the effect on the fish population might not be harmful, but if many fishermen exceed the limit by one fish, knowing that they are depleting that particular population of fish.

The commons is a situation in which individuals who have access to a resource (also known as the commons) act in their own interests and ultimately release the resource. This economic theory was first proposed by the English writer William Forster Lloyd in 1833. The speed of the resource depends on three important factors: the number of users who want to use the resource in question, the intensity of use, and the resources involved. Fishing is a classic example of the situation of different people who occur when the property is not in full possession and the resources are open. Migration of fish often makes it difficult to establish and protect the right to fish at sea, so fishing laws apply. So giving service is an example of the situation of people who share.

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Answer:

a. True

Step-by-step explanation:

a. True

A cost that changes in total as output changes is indeed a variable cost. Variable costs are expenses that vary in direct proportion to the level of production or business activity. As output increases, variable costs increase, and as output decreases, variable costs decrease. Examples of variable costs include direct labor, raw materials, and sales commissions.

The 95% confidence interval for the amount of time spent on personal issues is (4.805, 4.95).

Mean time that employees spend on personal issues each week(M) = 4.9 hours

Standard deviation = 0.35 hours

The following formula is used to get the confidence interval for the sample mean and standard deviation given:

μ = M ± t(sM)

where; M = sample mean

t = T-statistic based on confidence interval

Degree of freedom = n - 1

From the question, n = 55

Degree of freedom = 55 - 1

Degree of freedom = 54

(Standard errors)sM = √(s^2/n)

Now putting the value

sM = √(0.352/55)

sM = 0.05

t = 2.005 This is determined using the Excel formula =T.INV.2T at a confidence level of 0.95 and a degree of freedom of 55-1=54. (0.05,54)

Now the confidence interval

μ = M ± t(sM)

μ = 4.9 ± 2.005 × 0.05

μ = 4.9 ± 0.095

μ = (4.9 - 0.095, 4.9 + 0.095)

μ = (4.805, 4.95)

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The values of a and b for the function f(x) = (4x+b)/(ax+7) to have x=5 as a vertical asymptote and y=6 as a horizontal asymptote are a=1/6 and b=24.

For the function to have x=5 as a vertical asymptote, the denominator ax+7 must approach 0 as x approaches 5. This means that a must be equal to 1/6 to make ax+7 equal to 0 when x=5.

For the function to have y=6 as a horizontal asymptote, the limit of f(x) as x approaches infinity should be equal to 6. Therefore, we can use the fact that f(x) approaches b/a as x approaches infinity.

If we set b/a = 6, we can solve for b to get b = 6a.

Substituting the value of a we found earlier, we get b = 4.

Therefore, the values of a and b that satisfy the conditions are a=1/6 and b=24.

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a)  The period interest rate on the mortgage with a 4.8% APR compounded semi-annually is 2.4%.

b) the maximum mortgage amount they can afford with a monthly payment of $1,340.00, an APR of 5.25%, and a 20-year amortization period is approximately $245,724.03.

c) the Lees will have paid approximately $279,841.68 in total interest over the 20-year mortgage period.

d) The family will save $43,208.75 in total interest by making the $25,000 extra payment at the end of the 4th year of the mortgage.

a)
To calculate the period interest rate on a mortgage with a 4.8% APR compounded semi-annually, we need to divide the annual percentage rate (APR) by the number of compounding periods per year. In this case, since the mortgage is compounded semi-annually, there are two compounding periods per year.

So, the period interest rate (r) can be calculated as:

r = APR / (2 * 100)

Substituting the given values:

r = 4.8% / (2 * 100)

r = 0.024 or 2.4%

Therefore, the period interest rate on the mortgage with a 4.8% APR compounded semi-annually is 2.4%.



b)

Using the given information, we can use the financial formula to calculate the maximum mortgage amount they can afford. The formula is:

PV = PMT * ((1 - (1 + I%)^(-N*P/Y))) / (I%/P/Y)

where:

PV = Present Value or the maximum mortgage amount they can afford

PMT = Monthly mortgage payment they can afford = $1,340.00

N = Number of payments or the total number of months they will pay = 20 years * 12 months/year = 240 months

I% = Annual percentage rate (APR) = 5.25%

P/Y = Number of payment periods per year = 12 (compounded monthly)

C/Y = Number of compounding periods per year = 12 (compounded monthly)

Substituting the given values into the formula:

PV = $1,340.00 * ((1 - (1 + 5.25%/12)^(-240*12/12))) / (5.25%/12)

PV ≈ $245,724.03

Therefore, the maximum mortgage amount they can afford with a monthly payment of $1,340.00, an APR of 5.25%, and a 20-year amortization period is approximately $245,724.03.

c)

Using the given information, we can calculate the total interest paid over the 20-year mortgage period using the financial formula for the total interest paid:

Total Interest = (PMT * N) - PV

First, we need to calculate the monthly mortgage payment, which can be done using the financial formula for mortgage payments:

PMT = (PV * I%/P/Y) / (1 - (1 + I%/P/Y)^(-N*P/Y))

where PV, I%, P/Y, and C/Y are the same as before, and N is the number of payments.

Substituting the given values:

PV = $360,000 - $50,000 = $310,000

I% = 5.25%

P/Y = 12

C/Y = 12

N = 20 years * 12 months/year = 240 months

PMT = ($310,000 * 5.25%/12) / (1 - (1 + 5.25%/12)^(-240)) ≈ $1,999.27

Now, we can use the formula for total interest paid:

Total Interest = (PMT * N) - PV

Total Interest = ($1,999.27 * 240) - $310,000 ≈ $279,841.68

Therefore, the Lees will have paid approximately $279,841.68 in total interest over the 20-year mortgage period.


d)
To determine how much interest the family will save by making a $25,000 extra payment at the end of the 4th year of the mortgage, we need to compare the total interest paid over the remaining period of the mortgage with and without the extra payment.

First, let's calculate the total interest paid without the extra payment using the given information.

Using the financial formula for the total interest paid:

Total Interest = (PMT * N) - PV

PV = $295,000

PMT = $1,639.71

I% = 4.5%

P/Y = 12

C/Y = 12

N = (25 - 4) * 12 = 252 months

Total Interest = ($1,639.71 * 252) - $295,000 = $198,059.92

Now, let's calculate the total interest paid with the extra payment.

The extra payment will reduce the remaining mortgage balance, and we need to recalculate the monthly payment to ensure the mortgage is still amortized over 25 years. We can use the financial formula for mortgage payments to do this:

PMT = (PV * I%/P/Y) / (1 - (1 + I%/P/Y)^(-N*P/Y))

where PV, I%, P/Y, and C/Y are the same as before, and N is the number of payments.

PV = $295,000 - $25,000 = $270,000

I% = 4.5%

P/Y = 12

C/Y = 12

N = (25 - 4) * 12 = 252 months

PMT = ($270,000 * 4.5%/12) / (1 - (1 + 4.5%/12)^(-252)) ≈ $1,529.54

Now, we can calculate the total interest paid with the extra payment using the same formula as before:

Total Interest = (PMT * N) - PV

PV = $270,000

PMT = $1,529.54

I% = 4.5%

P/Y = 12

C/Y = 12

N = 21 * 12 = 252 months

Total Interest = ($1,529.54 * 252) - $270,000 = $154,851.17

Therefore, the family will save $198,059.92 - $154,851.17 = $43,208.75 in total interest by making the $25,000 extra payment at the end of the 4th year of the mortgage.

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f(-4) = 2

since the line passes through the point (- 4 ; 2)

point ( x ; f(x) )

The linear equation that shows a proportional relationship is y = 5x/6, the correct option is C.

A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0. A proportional relationship is one where two variables are related in such a way that when one variable changes, the other changes by a constant factor. In other words, the ratio of the two variables remains constant.

We are given that;

Linear equations to chose from

Now,

when x increases by a certain amount, y increases by a corresponding amount that is exactly 5/6 times as much. In other words, the ratio of y to x is always 5/6, which means that the two variables are proportional to each other.

Therefore, the linear equation will be y = 5x/6.

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50,400 different anagrams can be made from the letters in the word statistics.

Given word : STATISTICS

Anagrams are words formed by jumbling the positions of the letters given in the word.

For such problems we do factorial of number of words and divide by the repeated letters factorials.

Total number of letters = 10

They can be permutated among themselves in 10! ways.

Some letters are repeated in word STATISTICS

Since, there are 3 S's and 3 T's and 2 I's

So, Number of anagrams = \(\frac{10!}{3!.3!.2!}\)

= \(\frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3!}{3! \times 3 \times 2 \times 1 \times 2 \times 1}\)

= \(\frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4}{3 \times 2 \times 2}\)

= 10 × 9 × 8 × 7 × 2 × 5

= 50,400

50,400 different anagrams can be made from the letters in the word statistics.

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part one of this would be x=6;

2x6 is 30

30+5 is 35

part two of this would be x=20;

20x4 is 80

80-7 is 73

Answer:

x = 15 and x = 20

Step-by-step explanation:

(2)

35 = 2x + 5 ( subtract 5 from both sides )

30 = 2x ( divide both sides by 2 )

15 = x

(3)

4x - 7 = 73 ( add 7 to both sides )

4x = 80 ( divide both sides by 4 )

x = 20

The value of the expression a^3 is 3 3/8

The given parameters can be represented as

If a = 3, then 5a = 15.

Also, we have the value of the variable a to be

a = 1 1/2

Express the value of the variable a as an improper fraction

So, we have

a = 3/2

When a = 1 1/2 or a = 3/2, the value of a³ is calculated using the following formula

a³ = (1 1/2)³ = (3/2)³

Rewrite the formula as

a³ = (3/2)³

Evaluate the exponent in the above equation

So, we have

a³ = (27/8)³

Evaluate the quotient in the above equation

So, we have

a³ = 3 3/8

Hence, the value of the expression a³ is 3 3/8

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The shaded area between the two hexagons is 128√3 square feet.

A regular polygon is a two-dimensional shape with straight sides, where all sides are of equal length and all angles between the sides are of equal measure.

The center-to-vertex distance of the small hexagon is given as 4 ft. This means that the side length of the small hexagon is 4 ft/√3 or (4√3)/3 ft.

The distance between the small and larger hexagons is also given as 4 ft. This means that the radius of the circle circumscribing the larger hexagon is (4√3)/3 + 4 ft.

The formula for the area of a regular hexagon is:

Area = (3√3 / 2) × (side length)²

For the smaller hexagon, the side length is (4√3)/3 ft, so its area is:

Area of smaller hexagon = (3√3 / 2) × [(4√3)/3]²= 16√3 ft²

For the larger hexagon, the side length is the distance from the center to a vertex, which is the radius of the circle circumscribing the hexagon. So the area of the larger hexagon is:

Area of larger hexagon = (3√3 / 2) × [(4√3)/3 + 4]² = 144√3 ft²

Therefore, the area between the two hexagons is:

Area = Area of larger hexagon - Area of smaller hexagon

Area = 144√3 - 16√3

Area = 128√3 square feet

So the area between the two hexagons is 128√3 square feet.

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Answer:

y = \(-\frac{1}{5}x\) - 3

OR

y = \(-\frac{x}{5}\) - 3

Step-by-step explanation:

x + 5y = -15

5y = -x - 15

y = \(-\frac{1}{5}x\) - 3

or

(it's the same thing)

y = \(-\frac{x}{5}\) - 3

They are the same because x by itself has an invisible 1 in front of it.

1x = x

\(-\frac{x}{5}\) = \(-\frac{1x}{5}\) = \(-\frac{1}{5}x\)

Answer:

CA=6x-24 and BD = 2x+8

Find CE

CA=BD => 6x-24=2x+8 => x=8

CE=1/2(CA) or 1/2(BD) => 1/2(6x-24)=12

CE=12

CA=24

BD=24

Step-by-step explanation:

If the value of the 2022 Jeep Wrangler Rubicon depreciates at a rate of 9.7% per year, then its value after t years can be modeled by:

V(t) = 67,035(1 - 0.097)^t

Simplifying the right side:

V(t) = 67,035(0.903)^t

Therefore, the function that models the car's value, V, t years since 2022 is V(t) = 67,035(0.903)^t.

Answer:

Quadrilateral DEFG has one set of opposite sides that are both congruent and parallel.

Quadrilateral DEFG has two sets of consecutive angles that are supplementary.

Step-by-step explanation:

Took the test

Answer:

Quadrilateral DEFG has one set of opposite sides that are both congruent and parallel.

Quadrilateral DEFG has opposite angles that are congruent.

Step-by-step explanation:

Verified correct with test results!

The plane EFG  in the rectangular prism is parallel to plane ABC.

In this question, we have been given the rectangular prism ABCDEFGH

We need to find the plane which is parallel to plane ABC.

We can observe that in given rectangular prism,

plane ABH is parallel to the plane CDF

plane BCE is parallel to the plane AGF

plane EFG is parallel to plane ABC.

Therefore, the plane EFG  in the rectangular prism is parallel to plane ABC.

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To find the volume of the solid generated by revolving the plane region about the line x using the shell method, we need more specific information about the given plane region and the boundaries of integration.

The shell method is a technique used to calculate volumes of solids of revolution. It involves integrating cylindrical shells along the axis of rotation. However, in order to apply the shell method, we require additional details regarding the given plane region and the boundaries of integration.

Typically, the plane region is defined by a function or an equation. For example, if the plane region is bounded by the curves y = f(x), y = g(x), and the line x = a, x = b (where f(x) > g(x) for all x in the interval [a,b]), we can proceed with the shell method.

To calculate the volume using the shell method, we integrate the circumference of each cylindrical shell multiplied by its height. The differential height is given by Δh = f(x) - g(x), and the differential circumference is 2πx.

The integral expression for calculating the volume using the shell method is:

V = ∫[a,b] 2πx * (f(x) - g(x)) dx

By evaluating this integral over the appropriate interval [a,b], we obtain the volume of the solid generated by revolving the given plane region about the line x.

However, without specific information about the plane region, the equations or functions defining it, and the boundaries of integration, it is not possible to provide a numerical value for the volume. If you can provide more details or specify the plane region, I would be happy to assist you further in using the shell method to determine the volume.

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Answer: 260 m

Step-by-step explanation:

Let's say the length of NR is x m, using the similarity rule, we get the equation

175/130 = (175+175)/x

x = 260

So NR is 260 m