Caysen and Kyle are selling T-shirts and sweatshirts with the school logo. Caysen sells 6 T-shirts and 4 sweatshirts for $212. Kyle sells 3 T-shirts and 5 sweatshirts for $202. Part A Write a system of equations to represent the situation. Using x for the price of t-shirts and y for the price of sweatshirts. Caysen: 6x+4y=212 Kyle: 3x+5y=202 Part B Solve the system of equations using elimination or substitution. Show your work. x = y = Part C What does the solution of the system mean in this situation?

The window on the train will be 48 times wider than a window on the model .

In the question ,

it is given that ,

the length of the model train is = 18 inches   and

the length of the exact train is = 72 feet ,

on comparison , we need to convert it into inches .

we know that 1 feet is = 12 inches ,

So , 72 feet is = 72×12 inches = 864 inches

So , the length of the original train is = 864/18 = 48 times the model train .

the ratio will remain same for the width of the window .

So , the window on the train is 48 times wider than a window on the model .

Therefore , the window of the train is 48 times wider.

The given question is incomplete , the complete question is

Your model train is 18 inches long. It is an exact model of a train that is 72 feet long. A window on the train is how many time wider than a window on the model ?

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The interquartile range of the given data set is  2.16.

When a group of values is sorted from smallest to greatest, the median is the number in the middle of the range.

The given set of data,

2.35, 1.56, 1.77, 2.45, 6.92, 4.38, 2.77, 5.23, 2.22, 3.26

To find the interquartile, range of the given data set,

First find median of the set,

Arrange the given date in lowest to highest order,

1.56, 1.77, 2.22, 2.35, 2.45, 2.77, 3.26, 4.38, 5.23, 6.92.

There are 10 terms in the set,

The median will be middle term,

median = (2.45 + 2.77) / 2 = 2.61

The lower half of the set = 1.56, 1.77, 2.22, 2.35, 2.45.

The upper half of the set = 2.77, 3.26, 4.38, 5.23, 6.92.

Here, Q₁ = Middle term of the lower half = 2.22

And Q₂ = Middle term of the upper half = 4.38

The interquartile range = Q₂ - Q₁ = 4.38 - 2.22 = 2.16

The interquartile range of the data set is 2.16

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Answer:

a.  It increases by 4

b. It stays the same.

Mean is the average of a set of values. It is calculated by adding up all the values in the set and dividing by the number of values in the set.

Median is the middle value of a set of values. It is calculated by arranging all the values from smallest to largest and then finding the middle value in the set. Mean and median are used to measure the center of a set of values. Mean and median are often used to identify trends and patterns in data sets, as they are useful in describing the “average” or “typical” value of a set of data. They are also used in hypothesis testing and various statistical tests.

Formula for mean:

Mean = (Sum of all values) / (Number of values)

Formula for median:

Median = (Middle value of sorted set)

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The required simplified value of the function at x = 2 is -23.

An expression, [tex]f(x) = x^4-8x^3+4x^2+6x-3,[/tex] solution of the expression at x = 2 is to be determined.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,

In order to simplify the given expression association of the terms that have equal value in the exponent.
[tex]f(x) = x^4-8x^3+4x^2+6x-3,[/tex]

Put x = 2
[tex]f(2) = 2^4-8*2^3+42^2+6*2-3,[/tex]
f(2) = -23

Thus, the required simplified value of the function at x = 2 is -23.

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The percentage  growth rate would the population show in the absence of constraints is 22%

A logistic model is modeled by the function

N = K/1+be^rt

where, the constant k represents carrying capacity,

the constant b is formed by b = k/n(o) - 1

the value of r will be the intrinsic exponential growth rate and t represent time.

⇒ If there is no limiting factors, then the logistic model would be exponential according to formula:

N = N(0)e^rt

Since the corresponding growth factor for this exponential function is a = e^r

so the variable r can be obtained from a using :

r = ln a

a = e^r

given r= 0.2

a = ?

a = e°·²

a = 1.221

a = 1.22

⇒ 1.22 -  1 = 0.22

0.22×100 = 22%

Hence we get the percentage growth as 22%.

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Answer:

Step-by-step explanation:

the sum of the dice is at least 5

one die is showing a 2

2 and 3

2 and 4

2 and 5

2 and 6

4 out of 36 ways to get the sum at least 5 and one die is always 2

Probability = 4/36 = 1/9

If it is known that one die is showing a 2, then the probability that the sum of the dice is at least 5, is the probability that the other die shows 3 or 4 or 5 or 6, i. e. 4/6=2/3=0.666.

The value of h(f(3)) is 348.

What is simplification?

The method of simplifying something so that it is simpler to carry out or understand, or the product of such a method.

Here, we have

Given functions: f(x) = x³ + 8x, g(x) = √2x, h(x) = 7x-9

First, we will find f(3)

f(x) =  x³ + 8x

By simplification, we put x = 3 and get

f(3) = 27 + 24

f(3) = 51

Now, we find h(f(3)) and we get

h(x) = 7x-9

h(f(3)) = 7(51)-9

h(f(3)) = 357 - 9

h(f(3)) = 348

Hence, the value of h(f(3)) is 348.

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Within the third step of the control process, management by exception is a principle that states that managers should be informed of a situation only if data show a significant deviation from standards.

The third step of the process of controlling is to compare the actual performance of the organization with the established standards. By comparing the actual performance with the standards, an organization can determine the deviation between them.

The final step of the control process is the correction of deviations to improve the performance so that in the future it matches with the plan. Establishing standards and methods for measuring performance. Measuring performance. Determine if performance is up to par. take corrective action. The marginal rate of return reduction is set to reduce the factor's marginal rate of return.

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Answer:

[tex]\frac{8b-33}{12}[/tex]

Step-by-step explanation:

Sorry the answer is 8b-33/12

By solving a linear equation, it can be calculated that

The integers are 5 and 6

What is linear equation?

At first it is important to know about linear equation

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Here, a linear equation needs to be solved

Let the integers be x, x + 1

Three times the greater integer is 7 less than than 5 times the lesser integer

By the problem,

The linear equation is

3(x + 1) = 5x - 7

3x + 3 - 5x = -7

-2x = -7 - 3

-2x = -10

x = [tex]\frac{-10}{-2}[/tex]

x = 5

The other integer is 5 + 1 = 6

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If [tex]$\tan \theta=\frac{a}{b}$[/tex], then [tex]$\frac{a \sin \theta+b \cos \theta}{a \sin \theta-b \cos \theta}$[/tex] is equal to the [tex]\frac{a^2+b^2}{a^2-b^2}[/tex].

What is Hypotenuse?

The longest side of a right-angled triangle, or the side opposite the right angle, is known as the hypotenuse in geometry. The Pythagorean theorem, which asserts that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides, may be used to determine the length of the hypotenuse.

Given: [tex]$\tan \theta=\frac{a}{b}$[/tex]

We have to find the value of following expression in terms of a and b

We know that: [tex]$\tan \theta=\frac{\text { Perpendicular }}{\text { Base }}$[/tex]

[tex]$\Rightarrow$[/tex] Base [tex]$=b$[/tex]

[tex]$\Rightarrow$[/tex] Perpendicular[tex]$=a$[/tex]

[tex]$\Rightarrow$[/tex] Hypotenuse [tex]$=\sqrt{(\text { Perpendicular })^{2}+(\text { Base })^{2}}$[/tex]

[tex]$\Rightarrow$[/tex] Hypotenuse[tex]$=\sqrt{a^{2}+b^{2}}$[/tex]

Now we find,

[tex]$\frac{a \sin \theta+b \cos \theta}{a \sin \theta-b \cos \theta}=\frac{a\left(\frac{a}{a^{2}+b^{2}}\right)+b\left(\frac{b}{a^{2}+b^{2}}\right)}{a\left(\frac{a}{a^{2}+b^{2}}\right)-b\left(\frac{b}{a^{2}+b^{2}}\right)}$[/tex]

[tex]$=\frac{\frac{a^{2}+b^{2}}{a^{2}+b^{2}}}{\frac{a^{2}-b^{2}}{a^{2}+b^{2}}}$[/tex]

[tex]$=\frac{a^{2}+b^{2}}{a^{2}-b^{2}}$[/tex]

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Step-by-step explanation:

i can't read acruse please some one help me I am trying to answer it

The decreased amount of oranges will be equal to $1.4.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that the price of oranges at the farmers' market was 1.75 pounds the price was decreased by 20%.

The decreased price of the oranges will be calculated as,

Decreased price = 1.75 x (1 - 0.2)

Decreased price = 1.75 x 0.8

Decreased price = $1.4

The reduced number of oranges will equal $1.4.

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The expanded form of the given exponential expression -z³ is -(z×z×z).

Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.

The given expression is -z³.

Here, -z raised to 3, so multiply -z times itsef

-z³=(-z)×(-z)×(-z)

= -(z×z×z)

Therefore, the expanded form of the given exponential expression -z³ is -(z×z×z).

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Step-by-step explanation:

The equation of a parabola with focus at (h, k) and the directrix y = p is given by the following formula:

(y - k)^2 = 4 * f * (x - h)

In this case, the focus is at the origin (0, 0) and the directrix is the line y = -1.3, so the equation representing the cross section of the reflector is:

y^2 = 4 * f * x

  = 4 * (-1.3) * x

  = -5.2x

The depth of the reflector is the distance from the vertex to the directrix. In this case, the vertex is at the origin, so the depth is simply the distance from the origin to the line y = -1.3. Since the directrix is a horizontal line, this distance is simply the absolute value of the y-coordinate of the line, which is 1.3 inches. Therefore, the depth of the reflector is approximately 1.3 inches.

To find the cost of one pie, we need to divide the total cost by the number of pies. In this case, that would be $75.80 / 4 = $<<75.8/4=18.95>>18.95. Therefore, each pie cost $18.95.

The measure of angle U is 74 degrees

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

△PQR ≅ △STU

. If m ∠P = 62 degrees and m ∠Q = 45 degrees

The above parameters mean that

P  = S Q = T and R = U

So, we have

U = R = 180 - P - Q -- by the angles in a triangle theorem

So, we have

U = 180 - 61 - 45

Evaluate

U = 74

Hence, the value of m ∠U is 74 degrees

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the sum of all positive rational numbers that are less than 10 and that have a denominator 30 is 400.

What is Rational Number?

Numbers that may be expressed in the form p/q, where p and q are integers and q0, are considered rational numbers. Because fractions cannot have a negative numerator or denominator, they differ from rational numbers in this respect. Because of this, the numerator and denominator of a fraction are whole numbers (denominator 0), unlike in the case of rational numbers, when they are both integers.

So to convert a fractional to reduce form we have to divide by 10 to power how many digits thereafter decimal point, and make sure that the numerator or denominator doesn't have commonly divisible.

As a small addition, you get 4+12+20+…+76, which is an arithmetic sequence. There are ten terms, so you can use

So the sum will be 10(4+76)/2 = 400

Hence the sum of all positive rational numbers that are less than 10 and that have a denominator 30 is 400.

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Answer:

Vertex = (5,0)

Axis of symmetry = x = 5

Explanation:

Y = 3(x-5)^2

Equal 3(x-5) to 0

y = 3 = 0

x-5 = 0

x = 5

Vertex = (5,0)

Formula for Axis of symmetry: x = -b/2a

Write 3(x-5)^2 in standard form

Y = 3x^2 - 30x + 75

x = -b/2a

x = -(-30)/2(3)

x = 30/6

x = 5

The weight in ounces of paint which left after painting the wall is 114 ounces.

1 ounce is equivalent to 437.5 grains or 28.349 grams Abbreviation: oz. a unit of weight equivalent to one twelfth of a Troy or Pharmacists' pound; 1 ounce is equivalent to 480 grains or 31.103 grams. short for liquid ounce. a little part or sum.

Let x be how much paint in a strip. The aggregate sum of paint is 130+164+188=482. In the wake of painting the wall, the aggregate sum of paint is 482-4x. Since the aggregate sum in each tone is similar in the wake of getting done.

Then equation can be written as,

482 - 4x/3 = 130 -x

482 - 4x = 390 - 3x

x = 92

so, the paint left = 482-4x = 482 - 4(92) = 114.

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Answer: 1/2, or half of something, is 0.5.

Step-by-step explanation: 1/2 means half, as you are halfway to 2 and to a whole number. This means the value of 1/2 is 0.5.

Raw data can be calculated by using mathematical operations such as addition, subtraction, multiplication, and division.

This can be done manually or by using a calculator or a computer program .Additionally, statistical methods such as mean, median, mode, and standard deviation can be used to calculate raw data.Raw data can also be manipulated in various ways. For example, data can be sorted, filtered, and organized into categories or hierarchies. Data can also be visualized in graphs, charts, and diagrams to make patterns and trends easier to identify. Statistical methods such as correlation and regression can also be used to analyze and interpret raw data. Additionally, data can be combined with other data sets to create new insights and relationships. Finally, machine learning and predictive analytics can be used to make predictions about future outcomes based on existing data.

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From the production set, we can choose 8.803884057 × 10¹⁵² different samples.

Given,

The total microchips in a production run = 60

Number of microchips are defective in 60 = 3

Sample selected to check the defect = 5

We have to find the number of different samples of 5 can be chosen from the production run of 60;

Here,

Combinations formula:

According to the following formula, Cₙ, ₓ is the quantity of distinct combinations of x objects from a group of n members.

Cₙ, ₓ = n! / x! (n - x)!

Number of samples we can choose;

We are choosing 5 microchips from a set of 60.

Then,

C₆₀,₅ = 60! / 5! (60 - 5)! = 8.803884057 × 10¹⁵²

So,

We can choose 8.803884057 × 10¹⁵² different samples from the production set.

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The equation that relates the volume of water and the total ingredient volume is the one in option C, it is written as:

t = 4*w

So we know that the volume of water before mixing is 25% of the total ingredient volume.

So if we define the variables:

Then we know that w is equal to the 25% of t.

Then the relation can be written as:

w = (25%/100%)*t

Where we divide the percentage by 100% so we write a decimal number instead of a percentage.

Now we can simply it so we get:

w =  (25%/100%)*t

w = 0.25*t

Now we can isolate t to get:

t = (1/0.25)*w

t = 4*w

So the correct option is C.

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Answer: 0

Step-by-step explanation:

Simplifying

6x2[(3x + -4) + (4x + 2)] = 0

Reorder the terms:

6x2[(-4 + 3x) + (4x + 2)] = 0

Remove parenthesis around (-4 + 3x)

6x2[-4 + 3x + (4x + 2)] = 0

Reorder the terms:

6x2[-4 + 3x + (2 + 4x)] = 0

Remove parenthesis around (2 + 4x)

6x2[-4 + 3x + 2 + 4x] = 0

Reorder the terms:

6x2[-4 + 2 + 3x + 4x] = 0

Combine like terms: -4 + 2 = -2

6x2[-2 + 3x + 4x] = 0

Combine like terms: 3x + 4x = 7x

6x2[-2 + 7x] = 0

[-2 * 6x2 + 7x * 6x2] = 0

[-12x2 + 42x3] = 0

Solving

-12x2 + 42x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6x2'.

6x2(-2 + 7x) = 0

Ignore the factor 6.

The face value of a 10-year term insurance policy on a 24-year-old male will be $75,000 based on the amount paid per $1,000 of face value.

A contract for insurance provides protection from losses resulting from particular calamities or risks on the part of the insurer. It assists in against financial loss for the insured person or their family. The most prevalent types of insurance are life, health, homeowners, and auto.

Face value of the insurance policy

The formula use to calculate face amount is

= 1,000 x (Annual premium paid / Amount paid for $1,000 of coverage for a male 24 year old for a 10 year insurance)

How to solve:

= 1,000 x (359.25 / 4.79)

= 1,000 x 75

= $75,000

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Answer:

5 if your doing subtraction or Percent Change from 28 to 23 ≈ -17.86%

Step-by-step explanation:

Here's a explanation for % of change.

1) Find the difference between 28 and 23 as a number.

2) Divide the result from Step 1 by the starting number 28.

3) Multiply the result from Step 2 by 100 to get it in terms of percent.

I hope this helped.

Answer:

The correct expression to solve for z is z = 8 tan 22°. This expression uses the tangent function and the angle measure in degrees to find the value of z. The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side in a right triangle, and the angle measure must be in degrees in order to use the tangent function. The other answer choices do not use the tangent function or the angle measure in degrees, so they are not correct.

Step-by-step explanation: