A factory produces 270000 000 sweets every
week. How many sweets does the factory
produce in a year? Give your answer in
standard form

The probability that he or she will be happy with the travel reimbursement will be 0.705.

The number of people who requested more vacation time indicates that they are plainly dissatisfied.

400 employees are satisfied with the vacation allowance. - The number of workers that requested greater vacation time.

Employees who are satisfied with their vacation pay are represented by the numbers 400 - 118 = 282.

The likelihood that he or she will be happy with the vacation allowance =

Employees that are happy with their vacation pay / Total number of employees

= 282 / 400 = 0.705.

Therefore, the likelihood that he or she will be happy with the vacation allowance = 70.5%

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Using the concepts of probability, we got 0.5 is the probability of drawing the sum $20 or more when  two bills are drawn randomly without replacement.

We have an envelope contains 8 bills;

Two of $1 bills, Two of $5 bills, Two of $10 bills, Two of $20 bills.

When two bills are drawn randomly without replacement, we have to find the probability that their sum is $20 or more.

Total  outcomes = 2 x 2 x 2 x 2 = 16

Total possible outcomes, more than 20;

(1, 20), (20, 1), (5, 20), (20, 5), (10, 10), (20, 10), (10, 20), (20, 20) = 8 cases

That is,

The total possible outcomes is 8.

Now,

The probability of bill to be $20 or more = Possible outcome / Total outcome

Probability = 8/16 = 1/2=0.5

Hence, When two bills are drawn randomly without replacement,  the probability that their sum is $20 or more is 0.5.

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(Complete question)

an envelope contains eight bills: 2 ones, 2 fives, 2 tens, and 2 twenties. two bills are drawn at random without replacement. what is  the probability that their sum is $20 or more?

The percent of the variation in the amount of money earned can be explained by differences in the number of hours worked 20.8%.

Given that, the correlation coefficient (r) between the number of hours worked x and the amount of money earned y is 0.456.

The correlation coefficient describes how one variable moves in relation to another. A positive correlation indicates that the two move in the same direction, with a value of 1 denoting a perfect positive correlation. A value of -1 shows a perfect negative, or inverse, correlation, while zero means no linear correlation exists.

The percent of the variation in the dependent variable that can be explained by the independent variable is called coefficient of determination, which is r².

In this case, r = 0.456. So r² = 0.456² = 0.208

That means 20.8% of the variation in the amount of money earned can be explained by differences in the number of hours worked.

Therefore, the percent of the variation in the amount of money earned can be explained by differences in the number of hours worked 20.8%.

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The equation that represents the cost of the van rental is $598.74 = 136.20 + $0.39m .

The equation that would model the cost of the van rental is a linear equation. A linear equation is an equation that has one variable that is raised to the power of one.

The general form of linear equations is: y = a + bx

Where:

a = intercept

b = slope

The form of the equation that models the cost is:

Total cost = cost of renting the van + [cost per mile x (m - 120 miles)

$598.74 = $183 + [$0.39 x (m - 120)

$598.74 = $183 + $0.39m - 46.80

$598.74 = 136.20 + $0.39m

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The 6th term is -487 i.e, option(a)

What is a Sequence ?

A sequence is an ordered list of objects (or events). Like a set, it contains members (also called elements, or terms). The number of ordered elements (possibly infinite) is called the length of the sequence.

There are 4 types of sequence, arithmetic sequences, geometric sequences, quadratic sequences and special sequences.

Given, the 1st term = -3

According to question, we get the term by multiplying the previous term by 3 and then adding 2.

Now, calculate the other terms.

so, the 2nd term will be

-3 * 3 + 2 = -7

3rd term

-7 * 3 + 2 = -19

4th term

-19 * 3 + 2 = - 55

5th term

-55 * 3 + 2 =  -163

6th term

-163 * 3 + 2 = -487

Hence, the 6th term is -487 i.e, option(a)

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The original number from the given decimal number is  0.02.

For the given question;

Moving a decimal point 4 places towards the right corresponds to multiplying the given integer by 10,000 if it is x.

This results in:

10000x = 4.(1/x)

Simplifying.

x² = 4/10000

x > 0.

Taking square root of the number.

x = 2/100

x = 0.02

Thus, the original number from the given decimal number is  0.02.

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The equation in terms of x, which represents the amount of money left on the gift card of Aaliyah upon buying a cup of coffee is; A = 30 - 2x  dollars.

The original value of the gift card was $30.

Coffee costs $2 per cup.

Let 'x' be the number of cup of coffee purchased by Aaliyah.

Total cost be 'A' be paid by her.

Thus, the equation in terms of x, which represents the amount of money left on the gift card upon buying a cup of coffee is;

A = 30 - 2x  dollars.

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The number of solutions each polynomial has is 1, 5 and 3

In mathematics, a polynomial is an equation made up of coefficients and indeterminates, sometimes referred to as variables. Only addition, subtraction, multiplication, and powers of positive-integer variables may be used to solve it. An example of a polynomial with one undetermined x is x2 4x + 7.

Polynomials are often employed in both mathematics and science. In fundamental chemistry and physics, economics, and social science, for example, they are used to define polynomial functions. They are also employed in calculus and numerical analysis to approximate other functions. From straightforward word problems to intricate scientific conundrums, polynomial equations are utilized to represent a broad variety of topics. polynomials' usage in complex maths.

The number of solutions of a polynomial is equal to the highest degree of the polynomial.

So,

1) y = -6x -9

Has 1 solution as highest degree = 1

2) y = 2x⁵-x⁴ +2x³-6x²+2x+4

Has 5 solutions as highest  degree = 5

3) y = -4x³-10x² +7x+5

Has 3 solutions as highest  degree = 3

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The Pythagorean Theorem indicates the following relationship between the squares and triangles.

Part A

Part E

Pythagoras theorem can be stated as follows; The square of the length of the hypotenuse side of a right triangle is equal to the sum of the squares of the other two sides.

Part A

The possible squares in the question are the three squares arranged on the three sides of the triangle, and having a side length which is the same as the length of the side of the triangle to which the square is attached

The relationship between the three squares of side length a, b, and c according to Pythagorean theorem is; a² + b² = c²

Therefore, the area of the largest square that is located on the hypotenuse side of the triangle is equal to the sum of the areas of the other two squares.

Part E

The length of the sides of the triangles, obtained from a similar question on the site are; a, b, and c and a, b, and n

It was shown that c² = n²

Therefore;

c = n

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The required equation for the given condition is 50x + 100y = 1000.

What is an algebraic expression?

An expression constructed using integer constants, variables, and algebraic operations is known as an algebraic expression (addition, subtraction, multiplication, division, and exponentiation by an exponent that is a rational number).

Given, the charge for every birthday party =$50

number of birthday parties = x

So, the total charge for birthday parties = 50x

the charge for every wedding  = $100

the number of weddings = y

So, the total charge for the wedding = 100y

Then,

Total amount achieve = $1000

or, 50x + 100y = 1000

Hence, the required equation is 50x + 100y = 1000.

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The equation for Jayden's paycheck is,

$9.64h+ 82.35= $14.86h+ $17.10

How to construct an algebraic equation?

STEPS TO CONSTRUCT AN ALGEBRAIC EQUATION---

let the number of hours Jayden works be h hours.

so, Jayden has got the total from the jewelry store is,,$9.64h+ 82.35

Jayden has got the total from the sales bonuses is,  $14.86h+ $17.10

so, the total paycheck from the jewelry store is,,$9.64h+ 82.35

and from the sales bonuses is $14.86h+ $17.10.

as they are equal, the equation is, $9.64h+ 82.35= $14.86h+ $17.10

Hence, the equation is,$9.64h+ 82.35= $14.86h+ $17.10

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The point slope form of the equation is = P2 = (11, 2)

acc to our question-

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The equivalent equation for the expression y = 3x-6 is none.

Equivalent equation:

If the two equations are said to be equivalent when they have the same solution set. Then it is called as Equivalent equation.

Given,

Here we have the expression y = 3x-6

Now, we need to find the equivalent equation.

In order to find the equivalent equation, we have to take some sample values for x,

The sample value of x as 1, 2, 3

Now, we have to apply these values on the given expression first,

Then we get,

x = 1 => y = 3(1) - 6 = -3

x = 2 => y = 3(2) - 6 = 0

x = 3 => y = 3(3) -6 = 9

Now, we have to apply these to the given equation and which has the same value of the given expression,

x = 1 => 3(1) - 2y = 6 = -2y = 6 - 3 => y = -3/2

x = 2 => 3(2) - 2y = 6 = -2y = 6 - 6 => y = 0

x = 3 => 3(3) - 2y = 6 = -2y = 6 - 9 => y = 3/2

This is not equal one.

Move on to the second one,

x = 1 => 2(1) + 3y = -6 => 3y = -6 - 2 => y = -8/3

x = 2 =>  2(2) + 3y = -6 = 3y = -6 - 4 => y = -10/3

x = 3 =>  2(3) + 3y = -6 = 3y = -6 - 6 => y = -4

This is not a equivalent one.

Move on to the third expression,

x = 1 => 3(1) - 2y = 12 = -2y = 12 - 3 => y = -9/2

x = 2 => 3(2) - 2y = 12 = -2y = 12 - 6 => y = -3

x = 3 => 3(3) - 2y = 12 = -2y = 12 - 9 => y = -3/2

This is not a equivalent one.

Finally we have to use the last one, then  we get,

x = 1 => 2(1) - 3y = 18 => -3y = 18 - 2 => y = -16/3

x = 2 =>  2(2) - 3y = 18 => -3y = 18 - 4 => y = -14/3

x = 3 =>  2(3) - 3y = 18 => -3y = 18 - 6 => y = -4

Therefore, none of them are the equivalent one.

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The equation representing the elevation of the loon and the time of the dive is 3x-2y = 0, and the Loon has been diving for 14.67 seconds.

The red throated loon dived down to a distance of 12 feet under the water in 8 seconds.

We can assume that the loon is diving at a constant rate.

The relation between the elevation wise of the loan after 1 second into the dive can be represented by the linear equation which has the slope,

Slope = 12/8

Slope = 3/2

Now as we have the slope of the equation we can write the equation by using the point slope form, with the point, (8,12)

(y - 12)/(x - 8) = 3/2

2y - 24 = 3x - 24

3x - 2y = 0

This is the equation that represent the elevation y of the loan after x seconds.

When the elevation of The Loon is 22 feet,

We can put y = 22,

3x = 2(22)

x = 14.67 seconds.

So, the loon has been diving for 14.67 seconds.

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Answer:

7

Step-by-step explanation:

65x+9.45y=160.657 point 6 5 x plus 9 point 4 5 y is equal to 160 point 6 5

Answer:10.3

Step-by-step explanation:

16(5h-29)=360

80h-464=360

80h-464+464=360+464

80h/80=824/80

h=10.3

The equation of the given line written in the slope-intercept form is: y = 21x + 10.25.

The slope or gradient of a line in mathematics is a quantity that specifies both the direction and the steepness of the line.

Note that the general slope equation is:

y = mx + b

Where

m is the slope of the line and

b is the y-intercept.

In this specific instance, m is the change in the price of the ticket

b is the additional fee value that needs to be included for each ticket

Hence, the cost of the ticket (y) is given as:

y = (change rate of x) + added fee to every order

Where rate of change = 21; and

The fee added to each order is 10.25

Given the above, the general equation becomes:

y = 21x + 10.25

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Total savings after 7 weeks : $140

Total savings after w weeks : $(70 + 10w)

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is a phrase : Taub is saving up to buy a new bicycle. She already has $70 and can save an additional $10 per week using money from her after school job.

Taub will have a total of -

70 + 7 x 10 = $140

The expression that represents the amount of money Taub would have saved in [w] weeks is -

y = 70 + 10w

Therefore -

Total savings after 7 weeks : $140

Total savings after w weeks : $(70 + 10w)

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Answer:

[tex]-9 (9x -6) = 3 (4x+6) \\ - 9 \times 9x + 9 \times 6 = 3 \times 4x + 3 \times 6 \\ - 81x + 54 = 12x + 18 \\ -81x - 12x = - 54 + 18 \\ - 93x = - 36 \\ x = \frac{36}{93} \\ x = \frac{18}{46.5} \\ x = 0.3870967742[/tex]

The sample size required in this case is 71 pupils, which must be tested in order for the margin of error to be equal to 3 points.

When it comes to statistics, selecting a relatively small representative sample and conducting hypothesis testing on it typically makes it easier to analyze a large population. By boosting the sample size, the margin of error, which represents the sampling procedure's statistical precision, can be decreased.

From standard normal tables,

P( -2.326 < Z < 2.326) = 0.98 here

The sample size required here is computed as:

n = [(z * α) / МОЕ]² = [(2.326 * 18) / 5]² = 70.12

Therefore, the required sample size, in this case, is 71.

To ensure that the margin of error is equivalent to 3 points, 71 students must be assessed.

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COMPLETE QUESTION:

An IQ test is designed to have scores that have a standard deviation of a 10. A simple random sample of students at a torgo university will be given the test in order to construct a 95% confidence interval for the mean 10 of all students at the university. How many students must be tested so that the margin of error will be equal to 3 points? The sample size required for the desired margin of error is.(Round your answer to next whole number.)

By performing some simple mathematical operations, we know that Sophia earns $366 per hour.

So, to calculate how much Sophia earns in 1 hour:

Now, calculate earnings per hour:

Rounding off: $366

Therefore, by performing some simple mathematical operations, we know that Sophia earns $366 per hour.

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Complete question:

Two friends, Sophia and Ruby, took summer jobs. the equation y=23.9x represents ruby's earnings in dollars and cents, y, for working x hours. Sophia earned 1098.20 in 38 hours.

sophia earns $___ per hour

Answer: D

Step-by-step explanation:

Answer:   Choice D

[tex]x = \frac{-3\pm\sqrt{-19}}{2}\\\\[/tex]

==================================================

Explanation:

Compare the given equation x² + 3x + 7 = 0 to ax² + bx + c = 0 to find that,

Those values are plugged into the quadratic formula to get the following:

[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-3\pm\sqrt{(3)^2-4(1)(7)}}{2(1)}\\\\x = \frac{-3\pm\sqrt{-19}}{2}\\\\[/tex]

which points us to choice D being the final answer.

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

Side note:

The discriminant [tex]d = b^2 - 4ac = (3)^2-4(1)(7) = -19[/tex] is negative, so there are no real solutions. Instead, the two solutions are non-real complex numbers.

answer:

x = 18, 60.

step-by-step explanation:

evaulating (3x+6) = (4x-12) and solving for x gives us x = 18. you didn't include the angle, so i can't give you that. but

(3x+6) = 60

(4x-12) = 60

if those were your angles, you would have an equilalateral triangle (all sides/angles even) and your missing angle would also be 60.

The correct option d. when the standard deviation is much less than 10.

When a value is 10 points beyond the norm, it is said to be an extreme value or an outlier.

When a point deviates significantly from the mean in comparison to other points, it is referred to as an outlier. Z-scores can be used to establish this. Remember the z-score formula:

z = (x - μ) / σ

The outlier should have a very big magnitude z-score. We are aware that the score in this issue is 10 points just below mean, we can say:

A lesser value of would raise the magnitude of a z-score, increasing it to the maximum extent achievable.

Therefore, this point would be an outlier whether its standard deviation was drastically lower than 10.

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Answer: 76

Step-by-step explanation: simplify equation

60+16=x-16+16 (cancel out 16 and add 60+16)

76=x

60+16=x-16+16
76=x
x=76

The rate of change here represents the time in seconds it takes her to perform a certain number of skills task

The rate of change is defined as the rate at which one quantity is changing with respect to another quantity. Mathematically:

rate of change = change in y /  change in x

Given that: The x-coordinate is the skills task number and the y-coordinate is the time in seconds

Thus, rate of change = time in seconds / skills task number  

Therefore, the rate of change in this context represents the time in seconds it takes  to perform a certain number of skills task

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The recommended screen size for the television is 59.85 inches.

An expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

In this case, the expression for the size of the television is given as:

S = 0.228x² + 8.154x - 8.3

where x = 7 feet

S = 0.228x² + 8.154x - 8.3

S = 0.228(7)² + 8.154(7) - 8.3

S = 11.172 + 57.078 - 8.4

S = 59.85

The size is 59.85 inches.

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Answer:

the answer is £15

Step-by-step explanation:

Carly works 6 hours for four days 6x4= 24

so she worked for 24 hours we know that she makes  £360 per week.

so we divide 360 by 24 which gives us the total of

£15 per hour

The equation of the line in fully simplified slope - intercept form is 5x + 4y = 12 .

In the question ,

a graph of the line is given , we need to find the equation of the given line in the simplified slope - intercept form .

to find the equation , we need minimum two points ,

So , from the given graph ,

we can find that

when x [tex]=[/tex] 0 , the value of y [tex]=[/tex] 3 ,

the first point is (0 [tex],[/tex] 3) .

when x [tex]=[/tex] 4 , the value of y [tex]=[/tex] -2 ,

the second point is (4 [tex],[/tex] -2) .

the slope can be calculated by

slope = (-2-3)/(4-0)

= -5/4

So , the equation of the line passing through point (4,-2) with slope -5/4 ,  in the slope intercept form is

(y -(-2)) = (-5/4)(x-4)

y + 2 = (-5/4)x + 5

y = (-5/4)x + 5 - 2

y = (-5/4)x + 3

Simplifying further , we get

4y = -5x + 12

5x + 4y = 12

Therefore , The equation  line in fully simplified slope - intercept form is 5x + 4y = 12 .

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