Write a function that models each variation.

x=0. 2 and y=3 when z=2 , and z varies jointly with x and y.

The cost of 5 pounds of bananas in 1939 would have been $2.709.

According to the US Bureau of Labor Statistics, the cost of 1 pound of bananas is $0.63/lb. In 1939, the cost of bananas was 14% lower. Therefore, to find the cost of bananas in 1939, we need to calculate 14% of $0.63/lb and then subtract it from $0.63/lb.

Calculate 14% of $0.63/lb
0.14 * $0.63/lb = $0.0882/lb

Subtract $0.0882/lb from $0.63/lb to get the cost of bananas in 1939
$0.63/lb - $0.0882/lb = $0.5418/lb

Multiply the cost of bananas in 1939 by the number of pounds Pam buys
$0.5418/lb * 5 lb = $2.709

Therefore, the cost of 5 pounds of bananas in 1939 would have been $2.709.

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The expression in the form [tex]y^n[/tex]is [tex]y^9[/tex].

What is expression?

In mathematics, an expression is a combination of numbers, symbols, and/or variables that are arranged in a particular way. Expressions can represent various mathematical operations, such as addition, subtraction, multiplication, division, and exponentiation, and can be used to calculate a value or to represent a relationship between quantities.

The given expression is:

[tex]y^6 * y^3[/tex]

We can simplify this expression by adding the exponents of y:

[tex]y^6 * y^3 = y^(6+3) = y^9[/tex]

Therefore, the expression in the form [tex]y^n[/tex]is [tex]y^9[/tex].

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The perimeter of a regular octagon, we use the expression 8s, where s represents side length. The perimeter of a regular octagon with side length 1.5 feet is equals to the 12 feet.

Regular octagon is a polygon with eight sides. The perimeter of a polygon is equals to the sum of all its sides. All eight sides of regular octagon are same measure. So, in other words the perimeter of Regular octagon is equal to eight times the length its side. Here,

Side length of a regular octagon

= 1.5 feet

=> Perimeter = 8 × 1.5 feet [An octagon has 8 sides]

=> Perimeter = 12 feet

Hence, required perimeter is 12 feet.

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The zeros of the function are: x = 1, x = -3, and the other two zeros may be irrational or complex.

A function is a mathematical rule that assigns a unique output value for each input value. It is a set of ordered pairs where the first element is the input and the second element is the output.

Using the Rational Root Theorem, the possible rational roots of the polynomial function F(x) = x⁴ - 2x³ - 6x² + 22x - 15 are:

±1, ±3, ±5, ±15

Using synthetic division, we can find that x = 1 and x = -3 are zeros of the function. Therefore, the zeros of the function are:

x = 1, x = -3, and the other two zeros may be irrational or complex.

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The base and height of the parallelogram is B = 16 cm and H = 48 cm

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure

The four types are parallelograms, squares, rectangles, and rhombuses

Properties of Parallelogram

Opposite sides are parallel

Opposite sides are congruent

Opposite angles are congruent.

Same-Side interior angles (consecutive angles) are supplementary

Each diagonal of a parallelogram separates it into two congruent triangles

The diagonals of a parallelogram bisect each other

Given data ,

Let the area of the parallelogram be represented as A

Now , area of parallelogram A = bh

And , base of a parallelogram is one third its height

So , B = ( 1/3 )H

And , area of parallelogram is A = 768 cm²

On simplifying , we get

768 = ( 1/3 )H²

Multiply by 3 on both sides , we get

H² = 2304

Taking square roots on both sides , we get

H = 48 cm

So , the height of the parallelogram is 48 cm

And , the base of the parallelogram is 16 cm

Hence , the base and height of the parallelogram are 16 cm and 48 cm respectively

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Step-by-step explanation:

for % questions always find 100% and/or 1%.

everything else can be easily calculated out of these 2.

the original price of $210 = 100%, as we want to know how many % the new price is different from that.

100% = $210

1% = 100%/100 = 210/100 = $2.10

the new price is $300.

the difference is 300 - 210 = $90

how many % are $90 compared to the original price ?

well, as many as the times 2.1 (1%) fits into 90 :

90/2.1 = 42.85714286...%

that increase from $210 to $300 was 42.85714286...%.

an additional $50 baggage fee ?

we have to add this to the $300 and get $350 as new price.

that difference is now 350 - 210 = $140.

how many % are $140 compared to the original price ?

140/2.1 = 66.66666666...%

that increase from $210 to $350 was 66.66666666...%.

The fraction of all the sandwiches that are ham sandwiches on rye bread is 4⁄15.

To find the fraction of all the sandwiches that are ham sandwiches on rye bread, we need to multiply the fraction of sandwiches that use rye bread by the fraction of those that are ham sandwiches.

Here's how we can do that:

1. Start with the fraction of sandwiches that use rye bread: (4)/(5)
2. Multiply that by the fraction of those that are ham sandwiches: (1)/(3)
3. Multiply the numerators together: 4 x 1 = 4
4. Multiply the denominators together: 5 x 3 = 15
5. Put the new numerator and denominator together to get the fraction: (4)/(15)

So, the fraction of all the sandwiches that are ham sandwiches on rye bread is (4)/(15).

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Answer:

x would be 8 and y is 10

so (8,10)

Step-by-step explanation:

hope it helps

David will need to fill the measuring cup 15 times in order to fill the 5 bottles.

An object or event's attributes are quantified through measurement so that they can be compared to those of other things or events. Measurement, then, is the process of establishing how big or small a physical quantity is in relation to a fundamental reference quantity of the same kind.

Each bottle holds 3/4 of a quart, and his measuring cup holds 1/4 of a quart.

David will have to fill his measuring cup 3 times in order to fill 1 bottle of capacity 3/4 quarts.

For 5 bottles, it will be 3*5 times which results in 15 times.

Thus, David will need to fill the measuring cup 15 times in order to fill the 5 bottles.

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The given statement [tex]x = \frac76[/tex] can be proved by using the given equation.

Algebra, a discipline of mathematics where abstract symbols rather than concrete numbers are subjected to arithmetic operations and formal transformations. The idea that there is such a separate branch of mathematics, as well as the term algebra to identify it, came about gradually through time. tries to find solutions to equations that contain one or more unknown quantities. Although early mathematicians would not have been familiar with such a concept, the word "equation" is frequently employed to conveniently represent these operations when discussing the early history of algebra.

As per the given data:

[tex]\frac{2x+6}{5} = 4x -3[/tex]

Simplifying to evaluate the expression:

[tex]\frac{2x+6}{5} = 4x -3[/tex]

[tex]= 2x+6 = 5(4x -3)\\= 2x + 6 = 20x - 15\\= 18x = 21\\= x = \frac{21}{18}\\\\= x = \frac76[/tex]

Hence, the given statement [tex]x = \frac76[/tex] can be proved by using the given equation.

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By answering the above question, we may infer that So Kendra's water equation bottle holds 64 fluid ounces.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

The volume of a quart is 32 fluid ounces. Kendra's water bottle, which holds 2 quarts of water, therefore has:

64 fluid ounces are equal to 2 quarts when each is 32 fluid ounces.

So Kendra's water bottle holds 64 fluid ounces.

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Graph of g(x) will be wider than f(x) is false.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The graph of f(x)=x² was transformed to create g(x)=2/3x².

The transformation applied to f(x) to create g(x) is a vertical compression by a factor of 2/3.

This means that the graph of g(x) will be narrower than the graph of f(x), not wider.

Specifically, the parabola of g(x) will be compressed vertically towards the x-axis by a factor of 2/3, making it more pointy than the original graph of f(x).

Hence,  graph of g(x) will be wider than f(x) is false.

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Answer: g(g(1)) = 4 and g(g(g(1))) = 5 1/2

Step-by-step explanation:

We will first find g(1). To do so, we plug 1 in for x.

g(1) = (1) + 3/2 = 5/2 = 2 1/2

To find g(g(1)) we will plug in 5/2 for x.

g(g(1)) = (5/2) + 3/2 = 8/2 = 4

To find g(g(g(1))) we will plug in 4 for x.

g(g(g(1))) = (4) + 3/2 = 11/2 = 5 1/2

Hope this helps!

The inverse of a function, denoted f^-1(x), is a function that "undoes" the original function. In other words, if f(x) = y, then f^-1(y) = x.

To find the inverse of a function from a table of values, we simply switch the x and y values. So, for the given table of values:
x | 1 | 2 | 3 | 4 | 5 | 6
---|---|---|---|---|---|---
f(x) | 7 | 9 | 3 | 0 | 4 | 1
The inverse function f^-1(x) would have the table of values:

x | 7 | 9 | 3 | 0 | 4 | 1
---|---|---|---|---|---|---
f^-1(x) | 1 | 2 | 3 | 4 | 5 | 6
Now, to find f^-1(0), we simply look for the value of x that corresponds to f^-1(x) = 0. From the table, we can see that f^-1(0) = 4.

Therefore, the answer is f^-1(0) = 4.

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The greatest common factor of these three expressions, 28w, 8w⁵, and 20w⁴, is 4w.

The greatest common factor (GCF) of three univariate monomials is the largest factor that divides all three expressions. To find the GCF of 28w, 8w⁵, and 20w⁴, we need to find the largest factor that is common to all three expressions.

First, we need to find the GCF of the coefficients of the three expressions. The GCF of 28, 8, and 20 is 4.

Next, we need to find the GCF of the variables of the three expressions. The GCF of w, w⁵, and w⁴ is w, since it is the lowest power of w that is common to all three expressions.

Therefore, the GCF of 28w, 8w⁵, and 20w⁴ is 4w.

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Rounded to the nearest whole number, the international company has approximately 86,026.2 employees in total.

We must first divide the value by the whole sum, and then multiply the result by 100 to get the percentage.

Let's use algebra to solve the problem.

If 19,700 employees represent 22.9% of the company's total number of employees, we can write:

0.229 = 19,700 / Total number of employees

To find the total number of employees, we can isolate the variable on one side of the equation:

Total number of employees = 19,700 / 0.229

Using a calculator, we get:

Total number of employees = 86,026.2

Rounded to the nearest whole number, the international company has approximately 86,026.2 employees in total.

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The value of the variable x for the similar triangles is equal to 3

The triangles PTQ and STR are similar, this implies that the length ST of the smaller triangle is similar to the length PT of the larger triangle

and the length RT of the smaller triangle is similar to the length QT of the larger triangle

so;

5/(2x + 9) = 7/(3x + 12)

5(3x + 12) = 7(2x + 9) {cross multiplication}

15x + 60 = 14x + 63

15x - 14x = 63 - 60 {collect like terms}

x = 3.

Therefore, the value of the variable x for the similar triangles is equal to 3

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Answer:

When you make 3x + y = -8 into a slope intercept equation it will become the same question

3x + y = -8

-3x      |       -3x

y = -3x - 8

Answer:

$109+$281=x when x=391

so that means a laptop equals $391 dollars

Based on the histograms, it appears that Machine B is doing a better job of dispensing the correct amount of liquid.

The most common graph for displaying frequency distributions is a histogram.

To begin, Machine B's histogram is more symmetrically distributed around the 5.5-ounce mark, which is the target fill level.

Machine A's histogram, on the other hand, is skewed to the right, indicating that it is more likely to dispense more than 5.5 ounces.

Second, Machine B's histogram has a narrower spread, with most measurements falling between 5.4 and 5.6 ounces.

This indicates that the machine fills the bottles consistently within a narrow range of the target fill level.

Thus, the histogram for Machine A, on the other hand, has a wider range, with some measurements falling below 5.4 ounces and others exceeding 5.6 ounces, indicating a less consistent performance.

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Your question seems incomplete, the probable complete question is:

ln(144) can be written in terms of ln(3) and ln(4) as:

ln(144) = 4 ln(2) + 2 ln(3) ≈ 4 ln(1.386) + 2 ln(3) ≈ 2.7726 + 2 ln(3)

We can use the logarithmic property that states that ln(a * b) = ln(a) + ln(b) to rewrite ln(144) in terms of ln(3) and ln(4).

First, we can find the prime factorization of 144:

[tex]144 = 2^4 * 3^2[/tex]

Using the property above, we can rewrite ln(144) as:

[tex]ln(144) = ln(2^4 * 3^2) = ln(2^4) + ln(3^2)[/tex]

Now, we can use another logarithmic property that states that ln(aᵇ) = b * ln(a) to simplify ln(2⁴) and ln(3²):

ln(144) = 4 ln(2) + 2 ln(3)

Therefore, ln(144) can be written in terms of ln(3) and ln(4) as:

ln(144) = 4 ln(2) + 2 ln(3) ≈ 4 ln(1.386) + 2 ln(3) ≈ 2.7726 + 2 ln(3)

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Answer: Option B is the correct answer

Step-by-step explanation:

Area of lateral surface = 3 x Area of rectangle

The rectangle is of  5 inches wide and 14 inches long.

Area of rectangle =  5 x 14 = 70 square inches

Area of lateral surface = 3 x Area of rectangle

Area of lateral surface = 3 x 70 = 210 square inches

Option B is the correct answer.

Answer:

The distributive property is used when finding the product of two polynomials by distributing one polynomial to each term of the other polynomial. For example, if we wanted to multiply (3x - 4)(2x + 5), we would use the distributive property by first multiplying 3x(-4) and 2x(5) and then adding the results together.

Polynomials are closed under multiplication, meaning that when two polynomials are multiplied together, the result is always another polynomial. This is true because a polynomial is a combination of constants and variables raised to non-negative integer powers, and when two polynomials are multiplied, the result is a combination of constants and variables raised to non-negative integer powers, which is a polynomial.

Answer:

Step-by-step explanation:

A=[tex]\frac{1}{2}[/tex]bh

  =[tex]\frac{1}{2}[/tex]×34×14

  =238 in²

Answer:

Yes, the ratios 3:6 and 2:4 are equivalent because they represent the same proportion. To confirm, we can simplify both ratios to their simplest form:

3:6 can be simplified by dividing both terms by 3: 3/3 : 6/3 -> 1:2

2:4 can be simplified by dividing both terms by 2: 2/2 : 4/2 -> 1:2

Since both ratios simplify to the same ratio, 1:2, they are equivalent.

Answer: yes !!

Step-by-step explanation: 3:6 and 2:4 are equivalent b/c of their common factors.

The probability a firm will have a stock price of at least $40 is 0.1112. There should be 40.50 stock price have to be to put a firm in the top 10%.  The correct answer is e) None of the answers are correct.

(i) To find the probability that a firm will have a stock price of at least $40, we need to find the z-score for $40 and use the standard normal table to find the corresponding probability. The z-score is calculated as (x - μ)/σ, where x is the value we are interested in, μ is the mean, and σ is the standard deviation.

In this case, the z-score for $40 is (40 - 30)/8.20 = 1.22. Using the standard normal table, we find that the probability of a z-score less than 1.22 is 0.8888. Therefore, the probability of a stock price of at least $40 is 1 - 0.8888 = 0.1112.

(ii) To find the stock price that puts a firm in the top 10%, we need to find the z-score that corresponds to the 90th percentile in the standard normal table. The z-score for the 90th percentile is 1.28. We can then use the formula x = μ + zσ to find the stock price that corresponds to this z-score. In this case, the stock price is 30 + 1.28(8.20) = 40.50.

Therefore, the correct answer is (i) 0.1112 and (ii) 40.50.

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Percentage error is 17.30%, it can be said that the answer given by student is correct.

The percent error is the distinction between the estimated value and the actual value in relation to the actual value.

Estimated number of balls in each bag = 86

Real number of balls in the bag = 104

Percentage error = | ( estimated value - real value / real value ) | * 100

Percentage error = | ( 86 - 104 / 104 ) | * 100

Percentage error = | ( -18 / 104 ) | * 100

Percentage error = | - 17.30 | * 100

Percentage error = 17.30%

Thus, it can be said that the answer given by student is correct.

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The mass of the P₂O₅ formed from 3.4 moles of O₂ gas is equal to 386.1 g.

A mole can be described as a unit for measurement of a huge number of quantities of atoms, molecules, ions, or other particles. The atomic mass can be expressed as the one mole of any element.

The number of particles present in one mole was to be equal to 6.023 × 10 ²³ which is Avogadro’s constant.

Given, the number of moles of O₂ gas = 3.4 moles

The balanced chemical reaction of phosphorous and oxygen gas can be given as:

4 P  +  5 O₂   →   2 P₂O₅

5 mol of Oxygen reacts with moles of P₂O₅ = 2 mol

3.4 mol of O₂ gas reacts with moles of P₂O₅ = (2/5) × 3.4 = 1.36 mol

The mass of the 1.36 mol of P₂O₅ = 1.36 × 283.89 = 386.1 g

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The possible values of x are 2 and 17

The complete question is added as an attachment

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

Similar triangles

In the triangles, we have the following possible equations

15/18 = 10/(10 + x)

10/18 = 15/(10 + x)

Solving the equations, we have

15/18 = 10/(10 + x)

150 + 15x = 180

15x = 30

x = 2

10/18 = 15/(10 + x)

100 + 10x = 270

10x = 170

x =17

Hence, the values of x are 2 and 17

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Complete Question

The two triangles in the diagram are similar there are 2 possible values for x

See attachment for image of the triangle

For Part 1 of 2 (a): The exact distance between the points (2,73) and (-22,3) is 74.
For Part 2 of 2 (b): The midpoint of the line segment whose endpoints are the given points is (−10,38).

(a) The exact distance between the points is found using the distance formula:

d = √[(x2 - x1)² + (y2 - y1)²]

Where (x1, y1) and (x2, y2) are the coordinates of the given points. Plugging in the values from the given points:

d = √[(-22 - 2)² + (3 - 73)²]

Simplifying:

d = √[(-24)² + (-70)²]

d = √[576 + 4900]

d = √[5476]

d = 74

Therefore, the exact distance between the points is 74.


(b) The midpoint of the line segment whose endpoints are the given points is found using the midpoint formula:

M = [(x1 + x2)/2, (y1 + y2)/2]

Where (x1, y1) and (x2, y2) are the coordinates of the given points. Plugging in the values from the given points:

M = [(2 + (-22))/2, (73 + 3)/2]

Simplifying:

M = [(-20)/2, (76)/2]

M = [-10, 38]

Therefore, the midpoint is (-10, 38).

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