Allister’s father is 120% of Allister’s height. If his father measures 180 cm, then how many centimeters tall is Allister?

Answer:

Length = 14cm

Breadth ( AKA Width) = 9cm

Step-by-step explanation:

1) Address the facts

(L)Length = b + 5

(W)Width = b

(P)Perimeter = 46cm

= 2(b + 5 +b)

= 2(2b + 5) 2)Simplify the equation

3) Make b the SOTF (subject of the formula)

46 = 2(2b + 5)

46 = 4b + 10 3a) Simplify further

36 = 4b 3b) Minus 10 on both sides

9 = b

\____ 3c) Divide by 4 on both sides to get JUST b

4) Substitute aka replace the letters with numbers

L = b + 5

= 9 + 5

= 14cm

W = b = 9cm

Therefore the breadth(/width) is 9cm and the length is 14cm :)

On average, a customer spends approximately 1.16 minutes waiting time on hold before they can start speaking to a representative.

To find the average waiting time for a customer on hold before they can start speaking to a representative, we need to consider both the arrival rate of calls and the average service time of the staff members.

Given:

9 staff members taking calls.

On average, one call arrives every 5 minutes (standard deviation of 5 minutes).

Each staff member spends on average 18 minutes with each customer (with a standard deviation of 27 minutes).

To calculate the average waiting time, we need to use queuing theory, specifically the M/M/c queuing model. In this model:

"M" stands for Markovian or memoryless arrival and service times.

"c" represents the number of servers.

In our case, we have an M/M/9 queuing model since we have 9 staff members.

The average waiting time for a customer on hold is given by the following formula:

Waiting time = (1 / (c * (μ - λ))) * (ρ / (1 - ρ))

Where:

c = number of servers (staff members) = 9

μ = average service rate (1 / average service time)

λ = average arrival rate (1 / average interarrival time)

ρ = λ / (c * μ)

First, let's calculate the average arrival rate (λ):

λ = 1 / (average interarrival time) = 1 / 5 minutes = 0.2 calls per minute

Next, calculate the average service rate (μ):

μ = 1 / (average service time) = 1 / 18 minutes = 0.0556 customers per minute

Now, calculate ρ:

ρ = λ / (c * μ) = 0.2 / (9 * 0.0556) ≈ 0.407

Finally, calculate the waiting time:

Waiting time = (1 / (c * (μ - λ))) * (ρ / (1 - ρ))

= (1 / (9 * (0.0556 - 0.2))) * (0.407 / (1 - 0.407))

≈ 1.16 minutes

Therefore, on average, a customer spends approximately 1.16 minutes waiting on hold before they can start speaking to a representative.

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Answer:

jajajaja que risa la mejor respuesta del mundo me jajaj mira como me río

Answer:

70

Step-by-step explanation:

you just have to divide the 6300 checks by 90

6300÷90=70

Answer:

15

Step-by-step explanation:

Just substitute the x for 5
In this case:

Original function: f(x) = \(x^{2}\) - 2x

Substitute function: f(5) = \((5)^{2}\) - 2(5)

Now solve for the substitute function

\((5)^{2}\) - 2(5)

25 - 10

15

Therefore, f(5) is equal to 15

If the side length is greater than 11.11 cm then it will not overflow.

Otherwise, it will overflow.

If Joe tips the bucket of water in a cuboid container and the water is not overflowing then the cuboid container must be of volume greater than 1370 cm³.

We find the cube root of 1370 cm³.

\(\sqrt[3]{1370} \approx11.11\)

Then the cuboid container should have a side of length greater than 11.11 cm.

Here the statement  "If I tip my bucket of water in the cuboid container, it will never overflow" is correct or wrong based on the information that the container has a side length lesser or greater than 11.11 cm.

If the side length is greater than 11.11 cm then it will not overflow.

Otherwise, it will overflow.

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Answer:

x = -9

I'm not sure if you were looking for a solution to x but I hope this helps :)

The experimental probability that Kyle's next toss will be a hit is 11/18 or approximately 0.61.

The experimental probability of Kyle's next toss being a hit can be calculated by dividing the number of hits by the total number of tosses. In this case, the total number of tosses is the sum of hits and misses, which is 22 + 14 = 36. Therefore, the experimental probability of Kyle's next toss being a hit is 11/18 or approximately 0.61.
To find the experimental probability of Kyle's next toss being a hit, you need to consider the number of hits and total tosses so far.
Hits: 22
Misses: 14
Total tosses: 22 hits + 14 misses = 36 tosses
Now, calculate the experimental probability by dividing the number of hits by the total number of tosses:
Experimental probability = Hits / Total tosses = 22 / 36
Simplify the fraction:
Experimental probability = 11/18
So, the experimental probability that Kyle's next toss will be a hit is 11/18.

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Answer:

11/18

Step-by-step explanation:

Answer:

They are 12, 13, 14 and 15.

Step-by-step explanation:

If the least integer is x, then:

x + x + 1 + x + 2 + x + 3 = 54

4x + 6 = 54

4x = 48

x = 12.

The width in simplest form is \(2\frac{7}{12}\).

Given data;

The width of the vegetable garden is 1/3 times the length \(7\frac{3}{4}\) .

What is the width?

The simplest form of an improper fraction,

\(7\frac{3}{4}\) ⇒ 31/4

Now multiplying the above fractions we get the width,

⇒ 1/3 * 31/4

⇒ 31/12

The simplest form is \(2\frac{7}{12}\).

Therefore, the width in simplest form is \(2\frac{7}{12}\).

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Answer:

6

Step-by-step explanation:

JK+KL=JL

2x + x + 3 = 4x

3x + 3 = 4x

-4x -4x

-x + 3 = 0

-3 -3

-x = -3

-x/-1 = -3/-1

x = 3

Plug in value of x to find KL:

JL = 4(3) = 12

it’s 6 because on the line it’s half; between JK and KL.

final answer:

KL = 6

The numerical length of KL is 6 units.

Given that, point K is on line segment JL, JK=2x, KL=x+3, and JL=4x.

We need to determine the numerical length of KL.

In geometry, a line segment is a part of a line that is bounded by two distinct end points and contains every point on the line that is between its endpoints.

Now, JK+KL=JL

⇒2x + x + 3 = 4x

⇒3x + 3 = 4x

Subtract 3x on both sides of the equation.

That is, 3x + 3-3x= 4x-3x

⇒x=3

Now, substitute the value of x to find KL.

That is, KL = x+3= 6

Therefore, the numerical length of KL is 6 units.

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Answer:

3

Step-by-step explanation:

6x+3

6+6+6=18

or 6 divided by 2 which is 3

The statement that describes Jaden's error is; Jaiden should have added

zeros to each of the shorter decimals to get 2.615, 2.650, 2.700, and 2.623, then he should have compared them using place values.

What is error?

Actions that are inaccurate or incorrect are considered errors. An error is the same as a mistake in some contexts. The word 'errare,' which means 'to stray,' is where the etymology originates from. In statistics, the term "error" describes the discrepancy between the computed value and the correct value.

The place value indicates the multiple of 10 by which the digit is multiplied. The given numbers have the same values in the ones place value, the difference are in the numbers to the right of the decimal point.

The given numbers are;

2.615

2.65

2.7

2.623

The steps to order the numbers from least to greatest;

Add zeros to the shorter decimals such that each number have the same number of digits after the decimal point; 2.615, 2.650, 2.700 2.623

Then

Select the number with the lowest ones; Which gives all the numbers

Then

From the above list, select the number with the lowest tenth, and move them to the left of the list; Which gives the numbers, 2.615, 2.650, 2.623, 2.700

Next

From the above list, select the number with the lowest hundredth, and move them to the left of the list, in increasing order of the hundredth; Which gives the numbers, 2.615, 2.623, 2.650, 2.700

The numbers 2.615, 2.623,2.650, 2.700,  are in the order from least to

greatest.

Hence, Jaiden's error is that Jaiden should have added zeros to each of the shorter decimals to get 2.615, 2.650, 2.700, and 2.623, then he should have compared them using place values.

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Complete question:

Jaiden is ordering 2.615, 2.65, 2.7, and 2.623 from least to greatest. Here are his steps: (1) Compare and order 2.7 and 2.65 because they have the fewest digits. (2) Compare each digit of the numbers 2.615 and 2.623. * The units digits are equal. * The tenths digits are equal. * 1 < 2 in the hundredths place so 2.615 < 2.623. (3) Combine the two lists into one: 2.7, 2.65, 2.615, 2.623. Which statement describes Jaiden’s error?

(1) The numbers are listed from greatest to list

(2) The two numbers with the most digits should have been compared first

(3) Zeros should have been added to the numbers to get, 2.615, 2.065, 2.007, and 2.623. Then the numbers should be compared using place value

(4) He should have added zeros to each of the shorter decimals to get 2.615, 2.650, 2.700, and 2.623, then he should have compared them using place values.

Answer:

7. x = 23

Step-by-step explanation:

They are angles on transversals intersecting parallel lines. Also vertical angels are equal to each other.

So for example question 7 you need to use these two things to realize that 4x is the same angle as (3x + 23) so you have to put them in an equation like this

4x = 3x + 23 and then solve it algebraically

Answer:

90

Step-by-step explanation:

Given,

t = 300

Replace,

Multiply -0.01*300 = 3

Apply exponent rule,

Simplify, 4^3=64

Answer: B = 1 / 64

The measure of ∠C using sine rule formula and as shown in the triangle is 39.8°.

The sine rule formula gives the ratio of the sides and angles of a triangle. The sine rule can be explained using the expression, a/sinA = b/sinB = c/sinC,

From the diagram, to calculate the measure of the ∠C, we use the sine rule formula.

From the diagram,

Given:

Substitute these values into equation 1 and solve for angle C

Hence, ∠C is 39.8°.

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60 degrees is the measure of arc BC from the figure

The given diagram is a circle with several arc angles

arcAWB = 120 degrees

The line AC is a diameter

Since the sum of angles on a straight line is 180 degrees, hence:

arc AWB + arcBC = 180

arcBC = 180 - arc ZWX

arcBC = 180 - 120

arcBC = 60 degrees

Hence the measure of the arc BC from the diagram is 60 degrees

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Answer:

x = 8

Step-by-step explanation:

Answer:

-15

Step-by-step explanation:

Answer:

-15

Step-by-step explanation:

This because the additive inverse is the opposite number. If you where to use a number line, you would have the same amount of spaces from zero as 15. that is an additive inverse.

The scatter plot has been attached

Answer:

Options C, D & E are true

Step-by-step explanation:

Option A is wrong because from the scatter plot, only four athletes were faster in the second race than in the first one.

Option B is wrong because only 1 athlete had his second race time differing from the first race time by exactly 2 seconds.

Option C is true because exactly 9 of the times for the first race were at least 16 seconds

Option D is true because there are exactly 3 athletes who had the same time in both races

Option E is true because 8 of the times for the second race were less than 17 seconds

The angle between a tangent and a radius is 90°. ... Tangents which meet at the same point are equal in length.

Told to walk in first week = 5km

Told to walk in second week = 8km

Told to walk in third week = 11km

It is forming a pattern,

5km      8km      11km       ..........

     +3       +3        +3

5km      8km     11km     14km     17km     20km    23km     26km   29km     32km

    +3       +3        +3       +3        +3        +3        +3         +3      +3  

The patient has to walk 32km in the 10th week.

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Answer:

It should be 1/2 sorry if i"m wrong

See attachment for math work and answer.

The measure of ∠RSV is 31°.

Given that, SV bisects ∠RST=62°.

We need to find the value of m∠RSV.

The angle bisector in geometry is the ray, line, or segment which divides a given angle into two equal parts. For example, an angle bisector of a 60-degree angle will divide it into two angles of 30 degrees each. In other words, it divides an angle into two smaller congruent angles.

Since SV bisects ∠RST into equal parts.

That is, ∠RSV=∠TSV

So, ∠RST=∠RSV+∠TSV

⇒∠RST=2∠RSV

⇒62°=2∠RSV

⇒∠RSV=31°

Therefore, the measure of ∠RSV is 31°.

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Due to the fact that they are both increased to the same power, the two functions are exponential. Both functions have distinct constants and rates.

A unit of code known as a function carries out a particular task. A function in mathematics is a relationship between a set of allowable inputs and outputs, having the condition that each input is connected to exactly one output.

As illustrated in the graphic that represents the posed question, the two functions that we are considering are all such that we can see that they are exponential in nature.

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The last blue colored square on a 1x100 board with alternating color pattern every increasing number is 97th box.

In an 1x100 board, the boxes are numbered from 1 to 100. The boxes are painted with three colors from left to right in the following way: the first box is blue, then 2 red boxes, then 3 green boxes, then 4 blue boxes, 5 red boxes, and so on, painting one more box each time. What number is the last blue painted box? Explain how you found it.

To solve the problem, we need to find the pattern in the way the boxes are painted. We can notice that the colors repeat after every three boxes, so we need to find the remainder when 100 is divided by 3.

100 ÷ 3 gives a quotient of 33 and a remainder of 1.

This means that after painting 99 boxes, the next box would be the first blue box again. Therefore, the last blue painted box is the 97th box, which is two boxes before the first blue box on the board.

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Let a be the first, b be second and c be the third whole number.

Since the sum of these three numbers is 100.

So, \(a+b+c=100\) (equation 1)

Since, The first number is a multiple of 15

Therefore, \(a = 15n\)

And, the second number is ten times the third number.

\(b = 10c\)

Substituting the values of 'a' and 'b' in equation 1

So, \(15n+10c+c=100\)

\(15n+11c=100\)

\(11c=100-15n\)

\(c=\dfrac{100-15n}{11}\)

Therefore, \(100-15n\) should be exactly divisible by 11.

So, by taking \(n= 1\) and 2, \(100-15n\) is not divisible by 11

Let \(n =3\)

\(c=\dfrac{100-15\times3}{11}\)

\(c= 5\)

Now, second number (b) \(= 10c = 10\times5=50\)

As, \(a+b+c=100\)

\(a+50+5=100\)

\(a+55=100\)

\(a=45\)

Therefore, the three whole numbers are 45, 50, 5.

For n ≥ 459, Algorithm A is better than Algorithm B when B uses n√n operations.

To determine the value of n₀ for which Algorithm A is better than Algorithm B when B uses n√n operations, we need to find the point at which the number of operations for Algorithm A is less than the number of operations for Algorithm B.

Algorithm A: 10n log n operations

Algorithm B: n√n operations

Let's set up the inequality and solve for n₀:

10n log n < n√n

Dividing both sides by n gives:

10 log n < √n

Squaring both sides to eliminate the square root gives:

100 (log n)² < n

To solve this inequality, we can use trial and error or graph the functions to find the intersection point. After calculating, we find that n₀ is approximately 459. Therefore, For n ≥ 459, Algorithm A is better than Algorithm B when B uses n√n operations.

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R-1.3: For \($n \geq 14$\), Algorithm A is better than Algorithm B when B uses \($n^2$\) operations.

R-1.4: Algorithm A is always better than Algorithm B when B uses \($n\sqrt{n}$\) operations.

R-1.3:

Algorithm A: \($10n \log n$\) operations

Algorithm B: \($n^2$\) operations

We want to determine the value of \($n_0$\) such that Algorithm A is better than Algorithm B for \($n \geq n_0$\).

We need to compare the growth rates:

\($10n \log n < n^2$\)

\($10 \log n < n$\)

\($\log n < \frac{n}{10}$\)

To solve this inequality, we can plot the graphs of \($y = \log n$\) and \($y = \frac{n}{10}$\) and find the point of intersection.

By observing the graphs, we can see that the two functions intersect at \($n \approx 14$\). Therefore, for \($n \geq 14$\), Algorithm A is better than Algorithm B.

R-1.4:

Algorithm A: \($10n \log n$\) operations

Algorithm B: \($n\sqrt{n}$\) operations

We want to determine the value of \($n_0$\) such that Algorithm A is better than Algorithm B for \($n \geq n_0$\).

We need to compare the growth rates:

\($10n \log n < n\sqrt{n}$\)

\($10 \log n < \sqrt{n}$\)

\($(10 \log n)^2 < n$\)

\($100 \log^2 n < n$\)

To solve this inequality, we can use numerical methods or make an approximation. By observing the inequality, we can see that the left-hand side \($(100 \log^2 n)$\) grows much slower than the right-hand side \($(n)$\) for large values of \($n$\).

Therefore, we can approximate that:

\($100 \log^2 n < n$\)

For large values of \($n$\), the left-hand side is negligible compared to the right-hand side. Hence, for \($n \geq 1$\), Algorithm A is better than Algorithm B when B uses \($n\sqrt{n}$\) operations.

So, for R-1.4, the value of \($n_0$\) is 1, meaning Algorithm A is always better than Algorithm B when B uses \($n\sqrt{n}$\) operations.

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