a) Work out the mean income to 2 DP.
b) Deva was given a large bonus for 30 years service.
Excluding Deva's income, what was the mean income for the remaining 6 workers to 2 DP?

Answer: 133,827 lb/ft^3

Step-by-step explanation:

V = (4/3) (3.14)(8^3) = 133,827

Explanation

To answer this given question, we will make use of the Empirical rule of normal distribution

The Empirical Rule states that 99.7% of data observed following a normal distribution lies within 3 standard deviations of the mean. Under this rule, 68% of the data falls within one standard deviation, 95% percent within two standard deviations, and 99.7% within three standard deviations from the mean.

The image below helps gives a clearer understanding

So in our case, since the mean is 189 mg/dL and the standard deviation is 23

Then we will have the following values at

Answer:

you were awake for 4.5 hours and the battery was at 90% when you woke up.

Step-by-step explanation:

just look at the x and y intercepts. the x intercept is how long you were awake and the y-inter is what the charge was when you woke up.

Answer:

The answer for the Area of the shape is

1357in²

Step-by-step explanation:

cut the shape into rectangle and another rectangle

then,Area of the shape =Area of small rectangle +Area of big Rectangle)

A=L×B+L×B

A=25×1015×75

A=250+1125

A=1357in²

Answer:

gzhausiaoa

Step-by-step explanation:

hshshsshhehehehehhdhdhdhdhhdhdhdfhfh

Answer:

D

Step-by-step explanation:

4x²= 32

x²= 32 ÷4 (÷4 on both sides)

x²= 8

x= ±√8 (square root bith sides)

☆ A '±' symbol has to be added whenever we introduce a square root as the square of any number, positive or negative, would result in a positive number.

Answer:

P'(10, - 5 )

Step-by-step explanation:

Under a counterclockwise rotation about the origin of 90°

a point (x, y ) → (- y, x ) , then

P(- 5, - 10 ) → P'(10, - 5 )

Answer:

75.4

Step-by-step explanation:

calculator

Answer:

75.36

Step-by-step explanation:

circumference = C = 2πr

π = 3.14

3.14 x 2 = 6.28

r = 12

12 x 6.28 = 75. 36

An ordered pair is a solution of an equation in two variables if replacing the variables by the coordinates of the ordered pair results in a true statement.

In mathematics, an equation in two variables represents a relationship between two quantities. An ordered pair consists of two values, typically denoted as (x, y), that represent the coordinates of a point in a two-dimensional plane.

When these values are substituted into the equation, if the equation holds true, then the ordered pair is considered a solution or a solution set to the equation. This means that the relationship described by the equation is satisfied by the values of the ordered pair. In other words, the equation is true when evaluated with the values of the ordered pair.

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Answer:

paso a paso

Step-by-step explanation:

tienes que saber cuanto bale o la equivalencia de cm 10 haci que

tienes que multiplicar 5 x10 igual con los de mas si te sirvio apoyame plsssss

To write the expression with a rationalized denominator, you need to eliminate the square root from the denominator. Here's the expression you provided: (3√2) / (3√4). Let's rationalize the denominator step by step:

1. Evaluate the square root in the denominator: √4 = 2.
  So, the expression becomes: (3√2) / (3 * 2).

2. Simplify the denominator: 3 * 2 = 6.
  The expression now is: (3√2) / 6.

3. Since there is no square root in the denominator, it is already rationalized.

So, the expression with a rationalized denominator is (3√2) / 6.

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Answer:

don't know bro

sry

don't mind

<>

Answer:

0.0625

Step-by-step explanation:

Answer:

1/3

Step-by-step explanation:

The coordinates of the unit vector, having positive first coordinate and orthogonal to the plane through a given point P(3, -4, 4) = \((\frac{\sqrt{2} }{2}, \frac{-\sqrt{2} }{2},0)\)

Let the coordinates of Q be (6 , -1 , 7) and R be (6, -1 ,9).

Then coordinates of vector(PQ) = < 6 - 3, -1 - (-4), 7 - 4 > = (3, 3, 3)

And coordinates of vector(PR) = < 6 - 3, -1 - (-4), 9 - 4 > = (3, 3, 5)

Thus, vector (n) = vector (PQ) x vector (PR)

=> vector (n) =  \(\left[\begin{array}{ccc}3&3&3\\3&3&5\end{array}\right]\)

Solving for the determinant, we get the coordinates of vector (n)

= (6, -6, 0).

Magnitude of vector (n) = \(\sqrt{6^{2}+{(-6)^{2}+{0^{2} }\) = \(6\sqrt{2}\)

Thus, the unit vector (n) = \(\frac{Coordinates Of Vector (n)}{Magnitude Of Vector(n)}\)

=> Unit vector (n) = \(\frac{(6,-6,0)}{6\sqrt{2} }\) = \((\frac{\sqrt{2} }{2},\frac{-\sqrt{2} }{2},0)\)

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COMPLETE QUESTION:

Find a unit vector with positive first coordinate that is orthogonal to the plane through the points P (3,-4,4).

So on solving the provided question, we can say that fraction we have are  \(4\frac{2a}{3} + \frac{1a}{4} - \frac{1a}{a} (b - 7)\)   = 14/6

Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.

here the fraction we have are

\(4\frac{2a}{3} + \frac{1a}{4} - \frac{1a}{a} (b - 7)\)

12/3 + 12/4 + 15/2

14/6

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By using the rule of 3, we will see that the percentage of money that she spent is the 40%.

Here we define $200 as the 100%, then we can write the relation:

$200 = 100%

We know that Sofia spent $80, this represents a percentage X, then we can write:

$80 = X

So we have two equations:

$80 = X

$200 = 100%

Taking the quotient between the two we get the rule of 3:

$80/$200 = X/100%

Solving for X, we get:

($80/$200)*100% = X = 40%

She spent 40% of the money.

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Answer:

D is your answer

Step-by-step explanation:

(2y-7) (y+6) that is my answer and it matches with D promise 100%

The possible dimensions of the pool are the factors of the trinomial, which are:

2y - 7 and y + 6

The correct answer is (D).

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

To find the possible dimensions of the pool, we need to factor the trinomial 2y² + 5y - 42.

We can start by looking for two numbers that multiply to -84 (the product of the first and last coefficients of the trinomial) and add up to 5 (the middle coefficient of the trinomial).

Those numbers are 12 and -7, because 12 x -7 = -84 and 12 + (-7) = 5.

Using these numbers, we can rewrite the trinomial as:

2y² + 12y - 7y - 42

Now we can factor by grouping:

(2y² + 12y) - (7y + 42)

2y(y + 6) - 7(y + 6)

(2y - 7)(y + 6)

So the possible dimensions of the pool are the factors of the trinomial, which are:

2y - 7 and y + 6

Therefore,

The possible dimensions of the pool are the factors of the trinomial, which are:

2y - 7 and y + 6

The correct answer is (D) 2y - 7 and y + 6.

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Answer: True, because the negative numbers are located to the left of zero on the number line.

Answer:

True

Step-by-step explanation:

-2,-1,0,1,2

Negative—|—Positive

The amount that must be saved by him during each of the next 10 years (end-of-year deposits) to meet his retirement goal is $5,280.33 (rounded to the nearest cent).

From the question above, Required retirement income at the time of his retirement = $50,000

Annual inflation rate = 5%

Expected period of receiving payments after retirement = 25 years

Number of annual payments after retirement = 24

The number of years before he retires = 10

Total present value of the annuity = 50,000 / (1 + 0.05)²⁵= $15,144.16

The future value of the annuity at the end of the 25 years period= $15,144.16 x (1 + 0.05)²⁵= $50,000.00

Therefore, the annual payment (PMT) that will allow the present value of the annuity to be $15,144.16 is:

PMT = (0.08)($15,144.16) / (1 - (1 + 0.08)-24)= $1,131.38

Therefore, the total amount that he should save for the next 10 years can be calculated using the Future Value (FV) formula.

FV = PV x (1 + r)n + PMT × [(1 + r)n - 1] / r

Where, PV = the present value of the savings

PMT = the annual payment

r = the interest rate per year (same as the expected annual return on his savings) = 8%

n = the number of years

The total amount of savings required would be:

FV = $0 (he doesn't have any savings now)

PV = -$15,144.16 (since he will need to pay this amount at retirement)

PMT = -$1,131.38r = 8%n = 10 years

FV = 0, PV = -15,144.16, PMT = -1,131.38, r = 8%, n = 10 years

Therefore, the end-of-year deposit (PMT) that he needs to make for the next 10 years to meet his retirement goal is $5,280.33.

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The linear equation of the relationship is L = -8t + 40.

The amount Austin paid back each week is: $8.

A linear equation is straight line graph, which can be expressed as y = mx + b, in slope-intercept form. In the slope-intercept form, we have:

Slope = change in y / change in x.

Using two pairs of values from the table given, (1, 32) and (2, 24):

Slope (m) = (32 - 24) / (1 - 2)

m = 8/-1

m = -8.

Find the y-intercept (b) by substituting m = -8 and (x, y) = (1, 32) into y = mx + b:

32 = -8(1) + b

32 = -8 + b

32 + 8 = b

40 = b

b = 40

Substitute b = 40 and m = -8 into L = mt + b:

L = -8t + 40

Using the linear equation, the amount Austin paid back each week is: $8.

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In the survey conducted in a city with a population of one million (10^6) people, a sample size of 1000 is collected. The sampling method used is random sampling with replacement and equal probabilities for everyone in the city.

Random sampling with replacement means that after selecting an individual for the sample, they are placed back into the population, and it is possible for them to be selected again for subsequent samples. This method allows each individual in the population to have an equal chance of being selected each time, as the selection process is independent for each sample.

By collecting a sample of size 1000 from a population of one million, the aim is to obtain a representative subset of the population that can provide insights and make inferences about the entire population. Random sampling helps ensure that the sample is unbiased and minimizes selection bias.

With the sample size of 1000, the survey can provide valuable information about the city's population, allowing for statistical analysis and generalizations to be made about the population as a whole. The sample size is large enough to provide a reasonable level of confidence in the survey results, assuming that the sample was selected randomly and with equal probabilities for everyone in the city.

By conducting a survey using random sampling with replacement and a sample size of 1000 in a city with a population of one million people, the researchers aim to gather representative data and make informed conclusions about the entire population based on the characteristics observed in the sample.

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The graph of an equation is the collection of all of its solution points.

Consider the function y=f(x). All the ordered pair ( a, b) such that b=f(a) is called the graph of the equation.

The solution set consists of all points whose y-coordinate is greater than or equal to 1.

These points are contained in the shaded region in the graph below. This kind of region is called a half-plane because it is one of two parts of the plane into which a boundary line divides it.

Therefore, the set of all solution points of an equation is the graph of the equation.

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The third variable is the type of hiking boots the hiker wears. Option C

We know that when we talk about a positive correlation, what we are saying is that the the increase in none of the variables does affect the other variable and causes it to increase also or vice versa.

In this case, we have been told that An outdoor reporter finds a positive correlation between the number of granola bars a hiker eats on a trip and the number of bug bites the hiker receives.

Hence, the third variable must be the type of hiking boots the hiker wears.

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The equation of the inverse function is given as n(t) = (t+3)/4

Given the function that is represented as;

\(t(n)=8\cdot\frac{n+3}{2}\)

This is further simplified to have:

t(n) = 4(n + 3)

Replace t with t(n)

t = 4n - 3

Make n the subject of the formula

4n = t+3

n = (t+3)/4

Hence the equation of the inverse function is given as n(t) = (t+3)/4

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Answer: See explanation

Step-by-step explanation:

Do you mean the greatest common factor (GCF), or the lowest common multiple (LCM).

If you mean GCF, then it is 1 because 7 is a prime number and has two facotrs (1 and itself) and since 9 isn’t divisible by 7, the GCF must be 1.

If you mean the LCM, the answer is 63. Using prime factorisation, we find the lowest prime factor of both numbers:

9 = 3^3

7= 7^1

Then, we multiply these together to give 63.

You cannot have a GCM, because you can’t find a greatest common multiple as numbers go on forever.

I hope this helps!

Answer:

B) f(x) = 3x^2+5x-2 and D) f(x)=x^3 -8x^2

Step-by-step explanation:

the degree of the polynomial function below is 5 and the leading coefficient of this polynomial function is -3 :)

Answer:

Which polynomial functions are written in standard form? Select all that apply.

B. f(x) = –3x5 + 5x – 2

D. f(x) = x3 – 8x2

Step-by-step explanation:

The degree of the polynomial function below is  5.

 f(x) = –3x5 +4x – 2

The leading coefficient of this polynomial function is  

✔ –3

Answer:

The correct option is;

(2·x - y = -2 and 22·x + 10·y = 7)

2 x minus y = negative 2 and 22 x + 10 y = 7

Step-by-step explanation:

2x - y = -2.........(1)

3x + 2y = 5.......(2)

4x - y = 2..........(3)

22x + 10y = 7...(4)

Given that the solution of the system of equation is (-0.3, 1.4), we have;

The system of equations consist of those equations that pass through the point (-0.3, 1.4)

We check as follows;

Equation (1)

2×(-0.3) - 1.4 = -2

Therefore, equation (1) passes through the point (-0.3, 1.4) and is one of the equations

Equation (2)

3×(-0.3) + 2×1.4 = 1.9 ≠ 5

Equation (2) is not part of the system of equations

Equation (3)

4×(-0.3) - 1.4 = -2.6 ≠2

Equation (3) is not part of the system of equations

Equation (4)

22×(-0.3) + 10×1.4 = 7.4 ≈ 7

Therefore, equation (4) approximately passes through the point (-0.3, 1.4) and is one of the equations

The correct option is A. \(2x - y = -2\ and 22x + 10y = 7.\)

Given equations,

\(2x - y = -2.........(1)\)

\(3x + 2y = 5.......(2)\)

\(4x - y = 2..........(3)\)

\(22x + 10y = 7...(4)\)

Since the solution of the system of equation is \((-0.3, 1.4),\)  Hence the system of equation satisfy the above point.

Now check all the equations,

Equation (1),

\(2\times(-0.3) - 1.4 = -2\\-0.6-1.4=-2\\-2.0=-2\)

Hence, equation (1) passes through the point\((-0.3, 1.4)\)  and is one of the equations.

Similarly, Equation (2)

\(3\times (-0.3) + 2\times1.4 = 5\\-0.9+2.8=5\\1.9=5\\\)

Hence the above equation does not satisfy the solution, so it is not the other system of equation.

Now, Equation (3)

\(4\times(-0.3) - 1.4 = -2.6 \neq 2\)

Hence Equation (3) is not part of the system of equations.

Now, Equation (4)

\(22\times (-0.3) + 10\times1.4 = 7.4\)

Hence the above equation approximately passes through the solution\(.(-0.3, 1.4)\) and is one of the equations.

Hence the required system of equation is  \(2x - y = -2\) and \(22x + 10y = 7\).

Therefore the correct option is A.

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Answer:

175 %

Step-by-step explanation:

x % of 4 = 7

\(\dfrac{x}{100}*4 = 7\\\\\\x = 7*\dfrac{100}{4}\\\\x = 7*25\\\\x = 175\)

Answer:

35b is the answers for the question

Step-by-step explanation:

please give me brainlest