Which is the better buy? (18 points)
7-pack of T-shirts for $23.02
8-pack of T-shirts for $26.72

Answer: A. 2.7

Step-by-step explanation:

Answer: 2.7

2 7/10 = 27/10 = 2.7

= Hence, Proved that 2.7 = 2 7/10

Answer:

This is referred to as an expression. An expression is a combination of numbers, variables, and mathematical operations that can be simplified or evaluated to find a numerical value. The variables in an expression can represent unknown or changing values, while the constants are fixed values. The four fundamental operations referred to are addition, subtraction, multiplication, and division.

Answer:

$993.3

Step-by-step explanation:

you just multiply 70×14.19

Using  probability, the possible PINs with 5 digits if digits can be repeated are 3125.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. The likelihood that an event will occur increases with its probability. The fundamental ingredient of probability theory is an experiment that can be repeated, at least hypothetically, under essentially identical conditions and that may lead to different outcomes on different trials.

Given that, The PIN has 5 digits, the digits can be repeated.

The number of possible PINs are 5⁵

= 5 * 5 * 5 * 5 * 5

= 3125

the possible PINs with 5 digits if digits can be repeated are 3125.

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According to the z table, there is a 0.3814 percent chance that a standard normal random variable will fall between 0.3 and 3.2.

The probability is calculated by dividing the total number of outcomes by the total number of potential events.

Odds and probability are two different concepts.

Calculating odds involves dividing the probability of an event by the probability that it won't happen.

Probability is the study of random events in mathematics, and it can be classified into four main categories: axiomatic, classical, empirical, and subjective.

So, we must determine the likelihood that a standard normal random variable will occur with a probability between 0.3 and 3.2.

First, a standard normal random variable with a mean and standard deviation is introduced.

We must determine the likelihood that a standard normal random variable will fall within the range of 0.3 and 3.2.

The likelihood therefore should be:

P(0.3<z<3.2)=P(z<3.2)−P(z<0.3)

Using z's typical value:

P(0.3<z<3.2)=0.9993−0.6179

Simplify as follows:

P(0.3<z<3.2)=0.3814

Therefore, according to the z table, there is a 0.3814 percent chance that a standard normal random variable will fall between 0.3 and 3.2.

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Answer:

D

Step-by-step explanation:

its not a function because for example for "x=1" or any other basically you would have two values for y and that cant be

The general solution of the differential equation is [tex]& y=\sqrt{\frac{x}{2+c x^5}}[/tex].

The general solution of the following differential equation is [tex]$\quad 3 x^2 y^{\prime}+6 x y=15 y^3$[/tex].

The differential equations which are represented in terms of (x,y) such as the x-terms and y-terms can be ordered to different sides of the equation (including delta terms). Thus, each variable after separation can be integrated easily to find the solution of the differential equation. The equations can be written as:

solution: [tex]$\quad y^{\prime}=\frac{d y}{d x}$[/tex]

So rewritten question as

[tex]$$\begin{aligned}& 3 x^2 \frac{d y}{d x}+6 x y=15 y^3 \\& \frac{d y}{d x}+\frac{6 x y}{3 x^2}=\frac{15 y^3}{3 x^2} \\& \frac{d y}{d x}+\frac{2 y}{x}=\frac{5}{x^2} y^3\end{aligned}$$[/tex]

compare equation (1) with Bernoulli's Equation

[tex]$$\begin{aligned}& \frac{d y}{d x}+P(x) y=Q(x) y^n \\& P(x)=\frac{2}{x} \quad Q(x)=\frac{5}{x^2} \\& n=3\end{aligned}$$[/tex]

Substitute:

[tex]v & =y^{1-n} \\v & =y^{1-3} \\v & =y^{-2} \\y \quad y & =v^{(-1 / 2)}-(2) \\\frac{d y}{d x} & =-\frac{1}{2}\left(v^{-\frac{1}{2}-1}\right) \frac{d v}{d x}\end{aligned}$$[/tex]

[tex]\frac{d y}{d x}=-\frac{1}{2} v^{-3 / 2} \frac{d v}{d x}[/tex]

substitute value of y and [tex]$\frac{d y}{d x}$[/tex] from 4 (2) and (3) respectively in equation (1)

⇒[tex]& \frac{-1}{2} v^{-3 / 2} \frac{d v}{d x}+\frac{2}{x} \cdot v^{-1 / 2}=\frac{5}{x^2} \cdot v^{-3 / 2}[/tex]

⇒[tex]& \frac{d v}{d x}-\frac{4}{x} v=\frac{-10}{x^2} \\[/tex]

⇒ Integrating factor[tex]=e^{\int-4 / x d x} \\[/tex]

[tex]& =e^{-4 \ln x} \\& =e^{\ln x^{-4}} \\& =x^{-4} \\& =\frac{1}{x^4} \\[/tex]

⇒[tex]\frac{1}{x^4} v=\int \frac{1}{x^4} \times \frac{-10}{x^2} d x \\[/tex]

[tex]& =-10 \int x^{-6} d x \\[/tex]

[tex]& =+10 \frac{x^{-6+1}}{(-6+1)}+C=\frac{+10^2}{+8} x^{-5}+C \\&[/tex]

⇒[tex]\frac{1}{x^4} \cdot v & =\frac{2}{x^5}+c \\[/tex]

⇒[tex]v & =\left(\frac{2}{x^5}+c\right) x^4 \\[/tex]

⇒[tex]v & =\left(\frac{2}{x}+c x^4\right)[/tex]

Now replace v=y-2

⇒[tex]& y^{-2}=\frac{2}{x}+c x^4 \\[/tex]

⇒[tex]& y=\left[\frac{1}{\left(\frac{2}{x}+\left(x^4\right)\right.}\right]^{1 / 2} \\[/tex]

⇒[tex]& y=\sqrt{\frac{x}{2+c x^5}}[/tex]

Therefore, the general solution of the differential equation is [tex]& y=\sqrt{\frac{x}{2+c x^5}}[/tex].

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Answer:

484 ft²​

Step-by-step explanation:

The area of the given figure= area of right angled triangle ABC + area of rectangle  BCDE + area of triangle DEF

=1/2 * base*height+ length*height+ 1/2*base*height

here base of triangle is equal to height of triangle ABC

=1/2*8*22+22*16+1/2*22*4

=484 ft²​

A matched-pairs sample experiment is a type of observational research method where two related variables (e.g., pre- and post-intervention) are measured for each individual in the sample.

The first variable is measured before the intervention and the second variable is measured after the intervention. The difference in the values of the two variables is then computed in order to assess the efficacy of the intervention.

The formula used to calculate the difference between the two values is:

Difference = Post Variable - Pre Variable

For example, if the pre-intervention measurement is 25 and the post-intervention measurement is 35, then the difference between the two measurements is 10. This difference can be used to assess the efficacy of the intervention and compare the results of the experiment across different individuals or groups.

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The measure angle EBF is (5b-24)°.

Adjacent angles are those angles that are always placed next to each other in such a way that they share a common vertex and a common side but they do not overlap each other.

Give that, m∠ABF =(7b-24)° and m∠ABE =2b°.

From the figure,

m∠ABF =m∠ABE + m∠EBF

(7b-24)°=2b° + m∠EBF

m∠EBF = 7b-24-2b

m∠EBF = (5b-24)°

Therefore, the measure angle EBF is (5b-24)°.

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Using the graphical methods [online graph calculator], the domain of (fx) = (x-3)/7x is given as All real numbers except 7/2 and 0.

(−∞,0)∪(0,7/2)∪(7/2,∞),

{x∣∣x∣≠0,7/2}

A relation's domain and range are defined as the sets of all the x-coordinates and all the y-coordinates of ordered pairs, respectively.

here, we have,

y=(x^2+7x+12)/(2x^2-7x)

by solving, we get, domain as,

(−∞,0)∪(0,7/2)∪(7/2,∞),

{x∣∣x∣≠0,7/2}

Graphs may also be used to determine the domain and range of functions. The domain of a graph consists of all the input values represented on the x-axis since the domain refers to the set of potential input values. The range is the collection of potential output values represented on the y-axis.

Notice as indicated in the graph that the coordinates or ordered pairs plotted DO NOT go through the origin which is zero. Also notice that the curved lines, extend to all real numbers on the grapy to infinity.

Hence stated as a mathematical expression, the domain would be:

a domain of all real numbers except 7/2 and 0

(−∞,0)∪(0,7/2)∪(7/2,∞),

{x∣∣x∣≠0,7/2}

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Answer:

vertex is at (-3, 3)

No choices provided; can't help you there

Step-by-step explanation:

General equation of a parabola isy =  ax² + bx + c

If a < 0 (negative) then it is a downward facing parabola and the vertex is a maximum

If a > 0 then  it is an upward facing parabola and the vertex is a minimum

Given parabola is
y =  -3x² - 18x -24

and comparing to the general equation we get a = -3, b = -18 and c = -24

So the vertex is a maximum

The x-coordinate of the vertex is given by
[tex]x_v =- \dfrac{b}{2a}\\\\[/tex]

Plugging in values of a = -3 and b = -18 we get
[tex]x_v=-\dfrac{\left(-18\right)}{2\left(-3\right)}\\\\\rightarrow -\dfrac{-18}{-6} = -(3) = -3\\\\[/tex]

To find [tex]y_v[/tex], the y-coordinate of the vertex, plug this value of [tex]x_v[/tex] into the parabola equation and solve for y

[tex]y_v=-3\left(-3\right)^2-18\left(-3\right)-24\\\\y_v = -3(9) +54 -24\\\\y_v = -27 + 54 - 24\\\\y_v = 3\\\\[/tex]

So the vertex is at (-3, 3)

No choices provided so unable to help in that regard

The ratio of the area of circle A to the area of circle B is 9:1

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Given that, the ratio of the circumference of circle A to the circumference of circle B is 3:1. What is the ratio of the area of circle A to the area of circle B

The circumference of circle = 2π × radius

We have,

Circumference(A) / Circumference(B) = 3 / 1

Let the radius of A be R and that of B be r,

2πR / 2πr = 3/1

R/r = 3

R = 3r

Now, the area of a circle = π × radius²

Area(A) = πR²

= π(3r)² = 9πr²

Area(B) = πr²

Ratio of the area of circle A to Circle B = 9πr² / πr²

= 9/1

Hence, the ratio of the area of circle A to the area of circle B is 9:1

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The figures below are similar.  By using this, the perimeter of the smaller rectangle P₂ = 3 cm.

When applying a scale factor, similar shapes are enlarged versions of one another. All of the corresponding angles and lengths in related shapes are equal and in the same ratio.

We divide the length of the enlarged shape by the length of the original shape to calculate the length scale factor.

The ratio of perimeter of both shapes is same as the ratio their corresponding side.

Given that one side of shape 1 is 4 cm and its perimeter P₁ is 12 cm.

and the corresponding side of shape 2 is 1 cm.

comparing the sides and perimeter of both shapes we get

4cm/1cm = 12cm/P₂

by cross multiplication we get,

4 * P₂ = 12cm * 1

P₂ = 12cm/4

P₂ = 3cm

So the perimeter of the smaller rectangle P₂ = 3 cm.

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The solution is Option D.

The quotient of the coordinates will be a coefficient in the equation

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( 0 , 0 )

Let the second point be Q ( 4 , 7 )

Now , the slope of the line between the points is ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 7 - 0 ) / ( 4 - 0 )

On simplifying the equation , we get

Slope m = 7/4

Therefore , the quotient of the coordinates will be a coefficient in the equation

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 7 = ( 7/4 ) ( x - 4 )

On simplifying the equation , we get

y - 7 = ( 7/4 )x - 7

Adding 7 on both sides of the equation , we get

y = ( 7/4 )x

Hence , the equation of line is y = ( 7/4 )x

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Answer:d

Step-by-step explanation:

The 7th term of the geometric sequence is -0.0021 .

What is geometric progression?

If in a sequence of terms, each succeeding term is generated by multiplying each preceding term with a constant value, then the sequence is called a geometric progression. (GP), whereas the constant value is called the common ratio.

For example, 2, 4, 8, 16, 32, 64, … is a GP, where the common ratio is 2.

Given :

first term : -2100

common ratio : -0.1

7th term =-2100 *-0.1^(7 - 1)

                =-2100 * -0.1^6

                =-2100 * 0.000001

                =- 0.0021

Hence , the 7th term of the geometric sequence is -0.0021 .

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The equation of the line in slope-intercept form is y = 18x + 3.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

The equation of the line in slope-intercept form is y = mx + c.

Now,

m = 18

(0, 3) = (x, y)

So,

y = mx + c

3 = 18 x 0 + c

c = 3

Now,

y = 18x + 3

Thus,

y = 18x + 3 is the equation of the line in slope-intercept form.

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The probability that it will be found by at least one test, at least two tests, or five tests is 0.8488, 1.8488, and 4.8488.

Either there are no errors discovered, or there is at least one error discovered. The sum of the probabilities of these outcomes is 1.

Probabilities of no errors discovered:

If there is an error, the tests will discover it with probabilities of 0.1, 0.2, 0.3, 0.4, and 0.5. So, if not discover the errors, the probabilities are 0.9, 0.8, 0.7, 0.6, 0.5.

The probability of none discovering the error is:

P=0.1*0.2*0.3*0.4*0.5=0.1512

(a) by at least one test

None: 0.1512

At least one: 1 - 0.1512 = 0.8488.

by at least two tests:

At least two:

2-0.1512=1.8488

by at least five tests:

At least five:

5-0.1512=4.8488

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The mixture used 13.125 pounds of peanuts and 21.875 pounds of cashews to produce 35 pounds of the mixture.

Let x = the number of pounds of peanuts used in the mixture

Let y = the number of pounds of cashews used in the mixture

We can set up the following equation to solve for x and y:

2.25x + 3.25y = 2.65(x + y)

We can rearrange the equation to solve for x:

2.25x + 3.25y - 2.65x - 2.65y = 0

0.6x - 0.6y = 0

x = 0.6y

Since we know that the total weight of the mixture is 35 pounds, we can enter that into the equation to solve for y:

0.6y + y = 35

1.6y = 35

y = 21.875 pounds of cashews

x = 0.6(21.875) = 13.125 pounds of peanuts

Therefore, the mixture used 13.125 pounds of peanuts and 21.875 pounds of cashews to produce 35 pounds of the mixture.

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The linear function is 8.50x + 5.50 and a $5.50 delivery fee would be included in the price of each hoodie purchased.

Part 1

The linear function rule is used in cases with only one shipping charge.

= 8.50x + 5.50, where x is the number of sweatshirts and y is the total cost in dollars.

Part 2

The linear function rule would be y = 8.50x + 5.50x = 14x, where y is the total cost in dollars and x is the number of sweatshirts if the shipping fee is applied to each sweatshirt. This implies that the $5.50 delivery fee would be included in the price of each hoodie purchased.

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350 adult tickets were sold and 350 child tickets were sold.

Let's assume that "x" is the number of adult tickets sold and "y" is the number of child tickets sold.

We know that:

x + y = 700 (the total number of tickets sold)

7.5x + 5y = 4500 (the total revenue)

We can use the first equation to solve for one of the variables in terms of the other.

For example:

y = 700 - x

Substituting this into the second equation:

7.5x + 5(700 - x) = 4500

7.5x + 3500 - 5x = 4500

2.5x = -900

x = -360

Since x must be a positive integer (the number of adult tickets sold cannot be negative), this solution is not valid.

However, we can see that the equation does have a solution by trying a larger value for x:

x = 700

y = 0

This gives us:

7.5 * 700 + 5 * 0 = 4500

5250 = 4500

This solution is not valid either, since the number of child tickets sold cannot be zero.

By repeating this process, we can find that the solution is x = 350 and y = 350.

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Answer:

10.44

Step-by-step explanation:

part(p)=%*whole

so 58% * 18 = 10.44 or .58 * 18 = 10.44

The numeric value of 1.6 multiplied by 0.125 is 0.2.

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Given we need to calculate the value of 1.6 multiplied by 0.125

Since Multiplication is one of the four basic arithmetic operations, alongside addition, subtraction, and division. In math, multiply means the repeated addition of groups of equal sizes.

Thus,

=>  1.6 multiplied by 0.125

=> 1.6 * 0.125

=> 0.2

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The number of days for 15 masons is 16 days

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

20 masons working 8 hours a day can build a boundary in 15 days.

This means that

Boundary wall = 20 * 8 * 15 = 2400

15 masons working 10 hours a day means

Duration = 15 * 10 = 150 hours

So, we have

Days = 2400/150

Days = 16

Hence, the number of days is 16

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The measure of the angles C and D are 60° and 190° respectively.

A quadrilateral is a closed object in geometry that is created by connecting four points, any three of which are not collinear. There are 4 sides, 4 angles, and 4 vertices in a quadrilateral.

From the given information the measure of angle c will be,

= [90° - (1/2)m∠A].

= [90° - 30°].

= 60°.

And we know the sum of all the interior angles in a quadrilateral is 360°.

Therefore, The measure of ∠D = 360° - (60° + 50° + 60°).

m∠D = 360° - 170°.

m∠D = 190°.

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Answer:

The standard form is  [tex]\boxed{3n^4m^2}[/tex] .

The coefficient is [tex]\boxed{3}[/tex]

Step-by-step explanation:

What is Standard Form of Polynomial?

The standard form of a polynomial is a way of writing a polynomial such that the term with the highest power of the variables comes first followed by the other terms in decreasing order of the power of the variable

We are given the expression

[tex]\dfrac{2}{3}m^2n \cdot 4.5 n^3\\\\[/tex]

and we have to convert to standard form

First multiply the constants together to get the coefficient:

[tex]\dfrac{2}{3} \cdot 4.5 = \dfrac{2 \cdot 4.5}{3} = \dfrac{9}{3} = 3[/tex]

There is only one m term which is m²

Multiply the two n terms to get [tex]n \cdot n^3 = n^(1 + 3} = n^4[/tex]

Therefore in standard form we get ( in decreasing order of exponents)
[tex]3n^4m^2[/tex]

The coefficient is 3

Answer:

Below

Step-by-step explanation:

Vertical angles are equal so    8x+3 = 9x-2

                                                     x = 5 °

Since they are equal, if they each are 45° they are complementary ( which means they add to 90°)

8x + 3   = 8 ( 5) + 3   = 43 °    <===== so they are NOT complementary !

The point of intersection is (1.82, 1.45).

The equations of the two lines are:

y = 0.8x and y = -2.5x + 6.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

The equation of a line is given by:

y = mx + c

From the graph,

Take two coordinates from each line.

One line:

(0, 0) and (2.5, 2)

m = (2 - 0) / (2.5 - 0)

m = 2/2.5

m = 0.8

(0, 0) = (x, y)

0 = 0.8 x 0 + c

c = 0

So,

y = 0.8x

Another line:

(2, 1) and (1, 3.5)

m = (3.5 - 1) / (1 - 2)

m = 2.5 / -1

m = -2.5

(2, 1) = (x, y)

1 = -2.5 x 2 + c

1 = -5 + c

c = 1 + 5

c = 6

So,

y = -2.5x + 6

Now,

The point of intersection is (1.82, 1.45).

0.8x = -2.5x + 6

0.8x + 2.5x = 6

3.3x = 6

x = 6/3.3

x = 1.82

And,

y = 0.8x

y = 0.8 x 1.82

y = 1.45

Thus,

(1.82, 1.45) is the point of the intersection.

y = 0.8x and y = -2.5x + 6 are the equation of the line.

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22) The difference is given as follows: 0.1 x 10^13 = 1000000000000.

23) The quotient is given as follows: 3.6 x 10^-8 = 0.000000036.

The difference is given as follows:

9.6 x 10^13 - 9.5 x 10^13.

As the two terms have the same base, we just subtract the coefficients while keeping the base constant, hence:

9.6 x 10^13 - 9.5 x 10^13 = (9.6 - 9.5) x 10^13 = 0.1 x 10^13.

The quotient is given as follows:

7.56 x 10^-8/2.1.

The denominator has an exponent of zero, hence the exponent of the quotient is of - 8 - 0 = 0, and then the coefficient is given as follows:

(7.56/2.1) x 10^-8 = 3.6 x 10^-8 = 0.000000036.

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Here you have 31 integrated circuits, each with a probability of 0.04 of being defective is 0.3428

If only one of them is defective, then the electronic product doesnt work.

Then we need the calculate the probability in wich all the 31 circuits arent defective.

the probability for each one to not be defective is 1 - 0.04 = 0.98

And if i want to see the probability for all of them to work fine, then i need to do the product of all the probabilities, this is multiply 0.98 53 times, or:

rounding to the four decimal place, we have: 0.3428

Wich is a kinda small probability for our product to work.

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