F(x)=(3x+5)^2-10
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If knitting club sold 40 scarves and hats at a winter festival and made $700 from sales and charged $18 for each scarf and $14 for each hat , then the system of equations which represents the constraints in this situation is  s + h = 40 and 18s + 14h = 700    .

let the number of hats sold be = "h"  ;

and let number of scarves sold be = "s" ;

the total number of scarves and hats sold are 40 ;

the situation is represented as : h + s = 40  ...equation(1) ;

the per unit cost for each scarf is = $18  ;

the per unit cost for each hat is = $14  ;

the amount for which the items are sold is = $700 ;

this situation is represented as  : 18s + 14h = 700 ...equation(2) .

From equation(1) and equation(2)  , we can conclude that ;

the system of equation to represent the situation is , s + h = 40 and 18s + 14h = 700  .

The given question is incomplete , the complete question is

The knitting club sold 40 scarves and hats at a winter festival and made $700 from the sales. They charged $18 for each scarf and $14 for each hat. If s represents the number of scarves sold and h represents the number of hats sold, write system of equations which represents the constraints in this situation ? ​

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After evaluation of these value we get:

a) |5| = 5

b)|-5| = 5

c) -(5) = -5

d) -(-5) = 5

What is Integer?

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. The set of integers is frequently represented in mathematical notation by the boldface Z or blackboard bold mathbb Z.

What is Modulus?

A modulus function is a function that determines a number or variable's absolute value. It generates the size of the variable count. A function with absolute values is another name for it. No matter what input was provided to this function, the outcome is always favorable.

We are given some values to evaluate;

a) |5| = 5 (This is positve number so does not changes are made into it.)

b) |- 5| = 5 (Modulus has the property that it change every negative integer into positive integer)

c) - (5) = -5 (This number is multiplies by negative sign that's why it become negative integer.)

d) -(-5) = 5 (a negative integer multiplies with again negative sign so it become postive [- * -  = +])

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Answer: A) 10√2

Step-by-step explanation:

You can find the value of x by using the Pythagorean Theorem.

a = 10

b = 10

c = x

a^2 + b^2 = c^2

(10)^2 + (10)^2 = c^2

100 + 100 = c^2

200 = c^2

Square root both sides.

c = √200

Simplify the square root. 100 x 2 is 200, and 100 is a perfect square.

√200 = √100√2

√100 can be simplified to 10. √2 can not be simplified.

The answer would be option A ) 10√2

The value of x in the given triangle is 10√2 units.

Pythagoras theorem states that in a right triangle the three sides are related by the formula, a²+b² = c², where c is the hypotenuse and a and b are the other two sides.

Given that, a triangle, we need to find the hypotenuse x,

Using the Pythagoras theorem,

10²+10² = x²

x² = 100 + 100

x² = 200

x = 10√2

Hence, the value of x in the given triangle is 10√2 units.

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The probabilities are :

a) 0.8

b) 1/45

Probability refers to potential. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events.

Total no. of electrical parts = 10

No. of defective parts = 2

No. of non-defective parts = 10 - 2

                                        = 8

a) The probability of choosing a non-defective part from the box is 8/10 or 0.8.

b) The probability of choosing two defective parts in a row without replacement is (2/10) * (1/9) = 2/90 = 1/45.

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The dimensions of the figure is 3.23 by 7.43

From the question, we have the following parameters that can be used in our computation:

Side lengths = x and x + 4

Area = 24.5 square inches

The area of a rectangle is

Area = Product of dimensions

substitute the known values in the above equation, so, we have the following representation

x (x + 4.2) = 24.5

Using a graphing calculator, we have

x = 3.23

This means that

Other length = 4.2 + 3.23 = 7.43

Hence, the dimension is 3.23 by 7.43

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The multiplication of the numbers is 50.547.

When given two or more numbers to be multiplied, it is expected to get the product of the numbers. Such that an answer i.e. the final value which can either be a whole number or a number with a decimal part is gotten.

Given that 5.81 is to be multiplied by 8.7, we have;

One way to do it is by expressing the numbers in a standard form, so that we have;

5.81 X 8.7 = (581 x 10^-2) x (87 x 10^-1)

multiplying the whole parts of the number, we have;

581 x 87 = 50547

and multiplying the exponential part, we have;

10^-2 x 10^-1 = 10^-3

So that;

581 x 10^-2 x 87 x 10^-1 = 50547 x 10^-3

                                       = 50.547

The multiplication gives 50.547.

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Bailee's annual income was deducted for FICA is approximately C. $2,164.95.

FICA, or the Federal Insurance Contributions Act, is a payroll tax that is used to fund Social Security and Medicare. The current FICA tax rate for Social Security is 6.2% and the current rate for Medicare is 1.45%.

To find out how much of Bailee's annual income was deducted for FICA, we can multiply her gross income during each pay period by the FICA tax rate and the number of pay periods in a year.

Since Bailee gets paid monthly, there are 12 pay periods in a year.

FICA = (Gross income * (6.2% + 1.45%)) *12

FICA = (2358.33 * (6.2/100 + 1.45/100)) * 12

FICA = (2358.33 * 0.0765) * 12

FICA = 179.95 * 12

FICA = $2159.4

So, $2159.4 of Bailee's annual income was deducted for FICA.

This closest answer to this is: C. $2,164.95

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The travel time x is 41.162 min such that 17.36% of the 60 days have a travel time that is at least x.

We have to determine the travel time such that 17.36% of the 60 days have a travel time that is at least.

Total work days to work = 60 days

The travel mean time = 35.6

Standard deviation = 10.3

For normal distribution,

P(X < A) = P(Z < (A - mean)/standard deviation)

P(X > x) = 0.2946

P(X < x) = 1 - 0.2946 = 0.7054

P(Z < (x - 35.6)/10.3) = 0.7054

Take the z value that corresponds to 0.7054 in the table of the standard normal distribution.

(x - 35.6)/10.3 = 0.54

x = 41.162 min

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Answer:

x = 2 , y = - 1

Step-by-step explanation:

2x + 6y = - 2 → (1)

- 6x - 8y = - 4 → (2)

multiplying (1) by 3 and adding to (2) will eliminate x

6x + 18y = - 6 → (3)

add (2) and (3) term by term to eliminate x

(- 6x + 6x) + (- 8y + 18y) = - 4 - 6

0 + 10y = - 10

10y = - 10 ( divide both sides by 10 )

y = - 1

substitute y = - 1 into either of the 2 equations and solve for x

substituting into (1)

2x + 6(- 1) = - 2

2x - 6 = - 2 ( add 6 to both sides )

2x = 4 ( divide both sides by 2 )

x = 2

The simplified expression is  (11/12)x^2 - (161/10)x + (1/3)

From the question, we have the following parameters that can be used in our computation:

(11/12x-5/6)(x-(2/5)

To simplify the expression (11/12x-5/6)(x-(2/5)) we need to use the distributive property

(11/12x-5/6)(x-(2/5)) = (11/12x)(x) - (11/12x)(2/5) - (5/6)(x) + (5/6)(2/5)

= (11/12)x^2 - (11/60)x - (5/6)x + (1/3)

= (11/12)x^2 - (161/10)x + (1/3)

So the simplified form of the expression is (11/12)x^2 - (161/10)x + (1/3)

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If the ratio of two quantities is constant, then the two quantities are either in direct proportion to one another or vary in direct proportion to one another.

If the ratio of two quantities is constant, then the two quantities are either in direct proportion to one another or vary in direct proportion to one another.

The direct variation equation is represented by the symbols y=kx or k=y/x, where k is the proportionality constant or variation constant.

A) The relationship between the distance traveled and the number of traveled hours is straightforward.

B ) The only distinction between x and y representing the length of a table is in units.As a result, it also differs directly.

The amount of money saved in C increases as more $1-off coupons are used, and vice versa.

If the speed is increased in D, it will take less time to travel 60 miles.As a result, there is no direct variation.

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Based on the investment amount, rate of interest and time, Rita earned more interest than Mita by $324.

Calculating simple interest in both the cases to find the earned interest. The formula for simple interest is as follows -

S.I. = PRT/100, where S.I. is simple interest, P is principal, R is rate of interest and T is time.

Interest earned by Rita -

S.I. = 6800 × 5 × 5/100

Performing multiplication and cancelling zero

S.I. = $1700

Interest earned by Mita -

S.I. = 8600 × 4 × 4/100

Performing multiplication and cancelling zero

S.I. = $1376

Difference in interest = Interest earned by Rita - Interest earned by Mita

Difference in interest = 1700 - 1376

Performing subtraction

Difference in interest = $324

The interest earned by Rita is more than the interest earned by Mita by $324.

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Answer:5x - 8

Step-by-step explanation:

8x−9−(3x−1)8−9−(3−1)

8x−9−3x+18−9−3+1

8x−8−3x8−8−3

Answer:

Step-by-step explanation:

(8x−9)−(3x−1)

To find the opposite of 3x−1, find the opposite of each term.

8x−9−3x−(−1)

The opposite of −1 is 1.

8x−9−3x+1

Combine 8x and −3x to get 5x.

5x−9+1

Add −9 and 1 to get −8.

5x−8

The length of diagonal BD from the parallelogram ABCD is 10.

E is the intersection of the diagonals BD and AC. The point of bisection is therefore designated E.

BE = DE (The diagonals of a parallelogram bisect each other) (The diagonals of a parallelogram bisect each other)

From the provided diagram:

BE = 5

DE = BE = 5

BD length equals BE plus DE

BD length equals (5 + 5) to 10.

ABCD is a parallelogram, what is the length of BD

Consequently, Diagonal BD is 10 in length.

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Answer:

To determine which of the given lines is parallel to the line y = 2/3x + 5, we need to compare their slopes. The slope of a line is the coefficient of the x variable, in this case 2/3.

The lines that are parallel have the same slope.

A.y=2/3x-4 is parallel to the line y = 2/3x +5 because the slope of 2/3 is the same.

B.y=2/3x-7 is parallel to the line y = 2/3x +5 because the slope of 2/3 is the same.

C.y=-2/3x+5 is not parallel to the line y = 2/3x +5 because the slope of -2/3 is different from the slope 2/3.

D.y=-2/3x+5 is not parallel to the line y = 2/3x +5 because the slope of -2/3 is different from the slope 2/3.

So the answer is A and B are parallel to the line y = 2/3x +5

The system of equations have no solution, the correct option is A.

For a solution to be solution to a system, it must satisfy all the equations of that system, and as all points satisfying an equation are in their graphs, so solution to a system is the intersection of all its equation at single point(as we need common point, which is going to be intersection of course)(this can be one or many, or sometimes none)

Given;

-1/2x+1/2y=-1   (1)

x-y=2   (2)

Now, multiplying equation 1 by 2

-x+y=-2

y=-2+x

Substituting the value of y in equation 2

x+2-x=2

Therefore, the equation have no solution.

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Answer: a) To find the mean and standard deviation of the difference of their times, we need to use the properties of normal distributions. When two independent normal random variables are subtracted, the mean and standard deviation of the difference can be found using the following formulas:

Mean of the difference = Mean of x - Mean of y

Standard deviation of the difference = √(Standard deviation of x^2 + Standard deviation of y^2)

Plugging in the given values:

Mean of the difference = Mean of Molesky - Mean of Liberty = 100 - 110 = -10

Standard deviation of the difference = √(8^2 + 10^2) = √(64 + 100) = √(164) = 12.8

So the mean of the difference of their times is -10 minutes and the standard deviation is 12.8 minutes.

b) To find the probability that Mr. Molesky will finish his game before Mr. Liberty on any given day, we need to find the probability that the difference of their times is less than 0. Since the difference of their times is normally distributed with a mean of -10 and a standard deviation of 12.8, we can use the standard normal distribution table to find this probability.

To calculate the probability, we will standardize the distribution of the difference by subtracting the mean and dividing by the standard deviation.

z = (x - mean) / standard deviation

z = (-10) / 12.8 = -0.78125

Using a standard normal table we can find that P(z<-0.78125) = 0.22 or 22%

So the probability that Mr. Molesky will finish his game before Mr. Liberty on any given day is 22%.

Step-by-step explanation: