A factory manufactures a metal piece in 32 minutes. New technology allowed the
factory to cut that time by 8%. Then another improvement cut the time by 5%.
How long does it take to manufacture the piece now? Round your answer to
the nearest minute.

[tex]3.5b + 4.5 + 0.5b - 0.5 - 1.5b[/tex]

Combine Like Terms:

[tex](3.5b+0.5b-1.5b)+(4.5-0.5)[/tex]

[tex]\boxed{2.5b+4}[/tex]

The 40th customer who gets the t-shirt and water bottle.

If the sporting goods store has 100 gifts each in stock, then the number of customers who get t-shirts and drinking bottles are 2 customers, namely the 40th customer and the 80th customer.

In finding the LCM, we also use prime factorization, namely multiplying all the factor numbers and if there are the same, take the largest value, if both are the same, then take one of them.

For example, determine the LCM of 30 and 48

30 = 2 x 3 x 5

48 = 2 x 2 x 2 x 2 x 3 = 2⁴ x 3

The LCM of 30 and 48 is 2⁴ x 3 x 5 = 240

The above Question can be solved with the concept of LCM

where the 8th customer gets a T-shirt and the 10th customer gets a water bottle. To find out which customer gets the two gifts, then look for LCM from 8 and 10

LCM(8, 10) =2×2×2×5=40

LCM of 8 and 10 is 40.

So the 40th customer who gets the t-shirt and water bottle.

If the store has 100 gifts each in stock, then the number of customers who get t-shirts and drinking bottles are 2 customers, namely the 40th customer and the 80th customer.

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Answer:

d= -1/8

Step-by-step explanation:

8d+d+3d+2+4d= 16d+2

16d= -2

d= -1/8

A total of 250 packets of  4g cremora will make 1kg cremora box.

A function is a elation between a dependent and independent variable.

Given are 4g cremora sachets.

We can write the total number of cremora sachets that will make 1kg cremora box as -

{n} = 1000/4

{n} = 250

Therefore, a total of 250 packets of  4g cremora will make 1kg cremora box.

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Triangle rst is congruent to triangle wxy. If the area of triangle wxy is 20 square inches, then the area of triangle rst is 20 square inches.

When two triangles are congruent, it means that they are exactly the same in every aspect, including their size and shape. This means that their corresponding sides and angles are equal in length and measure, respectively.

In terms of area, if two triangles have the same shape and size, then they will have the same area. This is because the area of a triangle is determined by the length of its sides and the angles between them, and if two triangles are congruent, then their sides and angles are equal.

Therefore, if the area of triangle WXY is 20 square inches, then the area of triangle RST must also be 20 square inches. This is because triangle RST has the same size and shape as triangle WXY, and therefore must have the same area.

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Answer: Let's represent the cost of one roll of plain wrapping paper as x, and the cost of one roll of holiday wrapping paper as y. We can write two equations based on the information given:

2x + 11y = 208

11x + 9y = 320

We can use these equations to find the values of x and y. Solving the first equation for y:

y = (208 - 2x) / 11

We can substitute this expression for y into the second equation to eliminate y:

11x + 9((208 - 2x) / 11) = 320

11x + 208 - 18x / 11 = 320

11x - 18x / 11 = 320 - 208

-7x / 11 = 112 / 11

-7x = 112

x = -16

So one roll of plain wrapping paper costs -16 dollars, which is not possible. This means there is no solution for this system of equations, and therefore the problem has no solution.

Step-by-step explanation:

The ACT Math section tests a wide range of mathematical concepts and skills, so there are many formulas and concepts that you should be familiar with.

Here are some of the most important ACT math formulas that you should know:

1. Basic operations: addition, subtraction, multiplication, and division.

2. Exponents and roots: [tex]a^n[/tex] means a multiplied by itself n times; the nth root of a is the number that, when raised to the nth power, gives a.

3. Order of operations: parentheses, exponents, multiplication/division (from left to right), and addition/subtraction (from left to right).

4. Fractions: converting between fractions, decimals, and percents; adding, subtracting, multiplying, and dividing fractions.

5. Algebra: solving equations and inequalities; simplifying algebraic expressions; factoring quadratics; understanding linear and quadratic functions.

6. Geometry: properties of lines, angles, and polygons; Pythagorean theorem; trigonometric functions; volume and surface area of 3D shapes.

7. Probability and statistics: calculating probabilities; mean, median, and mode; standard deviation.

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The product of the rational expression shown above include the following: B. x² - 36/(x² - 9).

In Mathematics, a rational expression simply refers to a type of expression  which is expressed as a fraction. This ultimately implies that, a rational expression is composed of two (2) main parts and these include the following:

In this exercise, we would determine the product of the numerator for this rational expression and the product of the denominator for this rational expression as follows;

Product of numerator = (x + 6)(x - 6)

Product of numerator = x² + 6x - 6x - 36

Product of numerator = x² - 36

For the denominator, we have the following:

Product of denominator = (x + 3) × (x - 3)

Product of denominator = x² - 3x + 3x - 9

Product of denominator = x² - 9

Therefor, the product of the rational expression is given by x² - 36/(x² - 9).

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The probability of getting: A. a five-card hand that has three Jacks and two Queens is 0.000009, or 0.000923% and B. a "four of a kind" is 0.00024, or 0.02401%.

A. The probability of getting a five-card hand that has three Jacks and two Queens can be calculated by using the formula:
P(3 Jacks and 2 Queens) = C(4,3) x C(4,2) / C(52,5)
Where C(n,k) is the combination of n items taken k at a time.

= (4 x 6) / 2598960
= 24 / 2598960
= 0.00000923

Therefore, the probability of getting a five-card hand that has three Jacks and two Queens is 0.000009, or 0.000923% when rounded to six decimal places.

B. The probability of getting a "four of a kind" can be calculated by using the formula:
P(four of a kind) = (C(13,1) x C(4,4) x C(12,1) x C(4,1)) / C(52,5)

= (13 x 1 x 12 x 4) / 2598960

= 624 / 2598960
= 0.00024010

Therefore, the probability of getting a "four of a kind" is 0.00024, or 0.02401% when rounded to five decimal places.

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Answer:

Step-by-step explanation:

The ratio of a change in a quantity (dL) to the original quantity (L) is given by:

dL/L

This ratio can also be expressed as a percentage change, which is calculated by multiplying the ratio by 100:

(dL/L) * 100 = percent change

In general, the ratio of dL/L represents the fractional change in the quantity L and is used to quantify the effect of small changes in a system or process. For example, if L is the length of an object and dL is a small change in length, then dL/L represents the fractional change in length due to this change.

The graph is a linear function with a growth factor of 4

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The graph has the shape of a straight line, so it is linear.

The graph starts at point (0, 0). It passes through point (1, 4).

slope = 4/1 = 4

The slope is 4. Growth factor is the same as slope for a linear function.

Hence, the graph is a linear function with a growth factor of 4

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Answer:

2:1

2:5

4:3

Step-by-step explanation:

In these examples the comparison words "per", "to", "for every" is the colon.

Then just put the numbers in the same order they are in in the problem

1. Two cookies per student. __:__

Means 2 cookies per 1 student

We're writing the ratio

cookies:students

2:1

2. The odds of the horse winning the race are 2 to 5. __:__

The "to" is the colon

2:5

3. Colorado State University, there are 4 female students for every 3 male students. __:__

We are comparing

female:male

4:3

The number of sunglasses that will fail the quality inspection are 7.

What is a ratio?

A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six.

We are given that, A company produced 9,800 pairs of sunglasses

in one week, and 49 of the sunglasses failed a quality inspection.

And based on this data we are asked to find the number of sunglasses which will fail the quality inspection If the company produces

1,400 pairs of sunglasses in one day

Let the number of sunglasses failing the quality inspection be x

hence the ratio becomes

9800/49 = 1400/x

x= 1400*49/9800

x= 7

The number of sunglasses that will fail the quality inspection are 7.

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Answer:

quadrilaterals

ok I only guss it

Answer:

The diameter is 8.3cm.

Step-by-step explanation:

The circumference is the distance all the way around a circle. To find circumference, multiply pi times diameter:

C = pi • d

Fill in given circumference.

26 = pi • d

Divide both sides by pi (you should use a calculator) in this question it doesn't happen to matter if you use a pi button or 3.14 for pi.

26/3.14 = d

8.276057 = d if you use the pi button.

or,

8.28025 = d if you use 3.14

Both of these round to 8.3, since the question asked for one decimal place (1dp)

The diameter is 8.3cm.

Answer :

x = -2

-8 + -4 + 12 = 3(-6 + 6)

Im not sure

Tn = 6Tn-1 is the recursive form of the sequence

A geometric sequence is determined by its common ratio. The standard recursive formula is expressed as:

Tn = rTn-1

Determine the common ratio of the sequence

r = 6/1 = 36/6

r = 6

Substitute the common ratio into the formula to have:

Tn = 6Tn-1

Hence the recursive form of the sequence above is Tn = 6Tn-1

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The function that models the growth of the Bacillus Megaterium over each generation is B. P (n) = 12 + 2n.

Answer:

Veronica is correct

Step-by-step explanation:

1/2 x 5/2 = 5/4

1/2 + 5/2 = 6/4

Penelope has, 52quarters, 104 dimes, 416 nickels, and 162 pennies.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

From the given information let, 'x' be the number of quarters,

Therefore, Dimes is 2x, Nickels is 8x and Pennies is 3x.

So, x + 2x + 8x + 4x = 780.

15x = 780.

x = 52, The number of quarters.

2×52 = 104, The number of Dimes.

8×52 = 416 Nickels.

3×52 = 162 Pennies.

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The measure of side RS is 7.6 units .

A quadrilateral's interior angles add up to 360 degrees. Two quadrilaterals are said to be identical when two adjacent sides have the same ratio and all three matching angles are equal (the fourth angle automatically becomes equal because the internal angle sum equals 360 degrees).

The corresponding angles of similar quadrilaterals should be equal in accordance with the similarity of quadrilaterals. Since we know that every angle in a square is 90 degrees, every matching angle in any two squares will be the same.

In the given question ,

Quadrilateral MNOP is similar to quadrilateral QRST .

[tex]\frac{ON}{NM} =\frac{RS}{RQ} \\\\\frac{2}{4} = \frac{RS}{15.2} \\\\\frac{1}{2} =\frac{RS}{15.2} \\\\RS=\frac{15.2}{2} \\\\RS=7.6units[/tex]

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The value of the variable r  when t = 5h and d = 240m is 48m/h

Algebraic expressions are described as expressions that are composed of terms, variables, factors, coefficients and constants.

They are also made up of mathematical operations like subtraction. division, addition, multiplication, floor division, etc

From the information given, we have the equation;

d = rt

Make 'r' the subject of formula

r = d/t

Now, substitute the values into the equation, we get

r = 240/5

Divide the values

r = 48m/h

Hence, the value is 48m/h

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The inverse of the given function f(x) = -5x-3, is f⁻¹(x) = -x/5-3/5

An inverse function is a function that undoes the action of the another function. A function g is the inverse of a function f if whenever y=f(x) then x=g(y).

Given that a finction f(x) = -5x-3, we need to find the inverse of the function,

We can write,

y = -5x-3,

Interplace, x and y,

x = -5y-3

-5y = x+3

y = -(x+3)/5

y = -x/5-3/5

f⁻¹(x) = -x/5-3/5

Hence, the inverse of the given function f(x) = -5x-3, is f⁻¹(x) = -x/5-3/5

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The amount of each deposit that Abbie made was $8

The amount of each deposit that Abbie made can be found by dividing the total amount she put into her savings account by the number of deposits she made.

In this case, we can use the formula: Amount of each deposit =

Total amount / Number of deposits

Substituting the given values into the formula, we get:

Amount of each deposit = $40 / 5

Amount of each deposit = $8

Therefore, the amount of each deposit that Abbie made was $8. In conclusion, if Abbie has put $40 into her savings account and has made 5 deposits of the same amount, then the amount of each deposit is $8.

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The graph of the equation -3x+y=6 is linear and is attached with the answer below.

A linear equation is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

The given linear equation is -3x+y=6. When we plot the linear equation -3x+y=6 on the graph it will be a straight line and the x and y-intercepts are -2 and 6 respectively.

The graph of the linear equation is attached with the answer below.

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The angle measure of the missing angle is  630 - 11x.

Angles inside a polygon are referred to as interior angles. A triangle, for instance, has three internal angles. Interior angles are sometimes defined as "angles confined in the interior area of two parallel lines when they are crossed by a transversal."

Given:
A non-regular hexagon.

The sum of all the interior angles of the hexagon is,

= (6 - 2) 180

= 4(180)

= 720

Now, the angle measure of the missing angle,

= 720 - 2x - 3x - 2x - 4x - 90

= 630 - 11x

Therefore, 630 - 11x is the required expression.

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Answer:

45? I'm not 1000% sure tog

Step-by-step explanation:

the relation has the domain of -4> x> 4 and the given relation is continuous for the given range.

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

Given a graph,

The relation that defines the set of inputs to the set of outputs is called the functions. In function, each input in set X has exactly one output in set Y. Note: All functions are relations but all relations are not functions.

thus the given graph is a relation but not a function.

Given relation is continuous in the domain.

since the domain of the relation is The set which contains all the first elements of all the ordered pairs of relation R.

the given relation and has x values from -4 to 4 thus, the domain of the relations -4> x> 4.

Therefore, the relation has the domain of -4> x> 4 and the given relation is continuous for the given range.

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