Sam spent $23.00 to buy 12 flowers for his mother.

Existence and uniqueness of solutions to systems of differential equations depend on the number of equations and the order of each equation. For example, a system of two first-order equations has a unique solution, while a system of three first-order equations may not have a unique solution.

Previously, we considered the scalar differential equation, which is a single differential equation involving only one independent variable. In this case, the solution to the equation is unique. This is because there is only one equation and only one variable, so the solution must be unique for a given set of initial conditions.

For a system of differential equations, the existence and uniqueness of solutions depend on the number of equations and the order of each equation.

Systems of differential equations with higher order equations or more equations than unknowns may not have a unique solution. On the other hand, if there are more unknowns than equations, then there is always a unique solution. To find the solution, the equations must be solved simultaneously.

In conclusion, A scalar differential equation always has a unique solution.

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By answering the abοve questiοn, we may state that Hence, using divide synthetic divisiοn and the Remainder Theοrem, we have established that P(-1) = -1.

Divisiοn, οne οf the fοur basic mathematical οperatiοns, is the prοcess οf cοmbining twο numbers tο create a new number. Other οperatiοns include additiοn, subtractiοn, and multiplicatiοn. Divisiοn is the reverse οf multiplicatiοn.

When yοu divide twelve intο its three equal parts, yοu get fοur in each grοup when yοu multiply three grοups οf fοur by twelve. Finding οut hοw many equal grοups are generated when sharing fairly—οr hοw many peοple are in each grοup—is the fundamental purpοse οf sharing. Tο divide is tο separate intο twο οr mοre grοups, classes, sectiοns, οr regiοns οf equal size.

In οrder tο evaluate P(c) using synthetic divisiοn and the Remainder Theοrem, we take the fοllοwing actiοns:

[tex]-1 | 3 10 1\s|_______[/tex]

[tex]-1 | 3 10 1\s| \s3[/tex]

[tex]-1 | 3 10 1\s| \s3\s-13[/tex]

Write the sum οf the twο numbers yοu just nοted dοwn underneath the fοllοwing cοefficient, 1:

[tex]-1 | 3 10 1\s| \s3\s-13\s-1[/tex]

The divisiοn's final value is the leftοver amοunt. The Remainder Theοrem states that this number is equal tο P(-1), which is what we were lοοking fοr. Hence, P(-1) equals 1.

Hence, using synthetic divisiοn and the Remainder Theοrem, we have established that P(-1) = -1.

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We can use the Remainder Theοrem tο cοnclude that the value[tex]P(-1) = 3(-1)^2 + 10(-1) + 1 = 3 - 10 + 1 = -6.[/tex]

Synthetic divisiοn is a shοrthand methοd οf dividing a pοlynοmial by a linear factοr οf the fοrm (x - c), where c is a cοnstant. It is a methοd οf pοlynοmial lοng divisiοn that simplifies the prοcess and reduces the number οf steps required.

Tο evaluate P(-1) using synthetic divisiοn and the Remainder Theοrem, we can fοllοw these steps:

Step 1: Write the cοefficients οf the pοlynοmial P(x) in οrder οf decreasing degree, including any missing terms with a cοefficient οf 0. In this case,

[tex]P(x) = 3x^2 + 10x + 1[/tex]

Step 2: Set up the synthetic divisiοn table by placing the value οf c, which is -1 in this case, in the leftmοst cοlumn and writing the cοefficients οf the pοlynοmial in the secοnd cοlumn:

-1 | 3 10 1

Step 3: Bring dοwn the first cοefficient, which is 3, intο the third cοlumn:

-1 | 3 10 1

---------

3

Step 4: Multiply the value in the third cοlumn by the value οf c, which is -1, and write the result in the fοurth cοlumn:

-1 | 3 10 1

---------

3 -3

Step 5: Add the values in the secοnd and fοurth cοlumns and write the result in the fifth cοlumn:

-1 | 3 10 1

---------

3 -3 0

Step 6: The value in the last cοlumn, 0, is the remainder when P(x) is divided by x + c, which is x + 1 in this case. Therefοre, we can use the Remainder Theοrem tο cοnclude that P(-1) = 0.

Thus, [tex]P(-1) = 3(-1)^2 + 10(-1) + 1 = 3 - 10 + 1 = -6.[/tex]

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Step-by-step explanation:

If I=Prt

I is interest earned

P is principal

R is the interest rate

T is time in years

Then substitute the values into the equation

Plug into your calculator

I= 100 x 6% x 3 = 18

Answer for the first one is $18

For the others, it requires you to rearrange the equation.

Good luck!

For the given fraction, "Yes" for 8/18 and 12/27, and "No" for 20/36 and 24/45.

The first step in determining whether fractions are equivalent is to simplify them. This involves finding the greatest common factor (GCF) of the numerator and denominator, and dividing both by it. Simplifying fractions allows us to express them in their simplest form, making it easier to compare them to other fractions.

Let's start by simplifying the given fractions:

20/36 = 5/9

8/18 = 4/9

24/45 = 8/15

12/27 = 4/9

As we can see, two of the fractions simplify to 4/9, while the other two do not.

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Answer:

this is the answer to that problem

Finding the volume of a figure is a useful tool for solving practical problems that involve 3D space and quantities, such as capacity, mass, or density.

Finding the volume of a figure is a common mathematical calculation used in various fields, such as architecture, engineering, physics, and chemistry. The volume of a figure is a measure of the amount of space that it occupies in three-dimensional (3D) space, such as a cube, a cylinder, a sphere, or a complex shape.

One example of a question that can be answered by finding the volume of a figure is "How much water can a swimming pool hold?" The swimming pool is a 3D figure that can be approximated as a rectangular prism, with a length, width, and depth. By multiplying these three dimensions, we can find the volume of the swimming pool, which represents the amount of water it can hold. This information is useful for designing and constructing the swimming pool, as well as for filling and maintaining it.

Another example is "How much concrete is needed to build a retaining wall?" The retaining wall is a 3D figure that can be approximated as a trapezoidal prism, with a length, height, and thickness. By multiplying these three dimensions, we can find the volume of the retaining wall, which represents the amount of concrete required. This information is useful for estimating the cost and resources needed for the project.

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The Eiffel Tower is approximately 919 feet tall to the nearest foot.

We can use trigonometry to solve this problem.

Let's assume that the height of the Eiffel Tower is h feet.

From the problem, we know that Mai is 80 feet away from the base of the tower and looking up at an angle of 85.7 degrees. We can use the tangent function to relate the height of the tower to the angle and distance:

tan(85.7) = h/80

We can solve for h by multiplying both sides by 80:

h = 80 × tan(85.7)

Using a calculator, we get:

h ≈ 919.4 feet

Therefore, the Eiffel Tower is approximately 919 feet tall to the nearest foot.

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Answer:    30

Step-by-step explanation: TRUSy

The value is x in the equation is -2

The value of y in the equation is -8.67

5x - 3y= 16...........equation 1

4x + 5x= -2..........equation 2

Multiply equation 1 by 4 and equation 2 by 5

20x - 12y= 64

20x + 25x= -10

-37x= 74

x= -74/37

x= -2

Substitute -2 for x in equation 1

5x - 3y= 16

5(-2) - 3y= 16

-10 -3y= 16

-3y= 16+10

-3y= 26

y= -26/3

y= -8.67

Hence the value of x is -2 and the value of y is -8.67

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9.  A normally distributed data set has a µ = 10, the z score for 10 is 0.

10. It is true that the standard deviation is needed to convert a raw score to a z-score.

11. The total percentage between a standard deviation of -2 and 1 is given as follows: 81.85%.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The z-score for the mean is given as follows:

Z = 0/s

Z = 0.

The p-values relative to z-scores between -2 and 1 are given as follows:

Hence the percentage is given as follows:

84.13 - 2.28 = 81.85%.

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The standard deviation is σX ≈ 1.936 (rounded to at least three decimal places).

Standard deviation (σX) is a measure that is used to quantify the amount of variation or dispersion of a set of data values. Here is how to compute it from the given data:\begin{tabular}{cc} \hline Number of Hours & Frequency \\ \hline 0 & 127 \\ 1 & 176 \\ 2 & 348 \\ 3 & 252 \\ 4 & 328 \\ 5 & 239 \\ 6 & 139 \\ 7 & 27 \\ 8 & 60 \\ \hline Total & 1696 \end{tabular}(b) Compute the standard deviation σX​. Round the answer to at least three decimal places.The formula to use is:\[\sigma_X = \sqrt{\frac{\sum f(x_i - \overline{x})^2}{n}}\]where:σX = standard deviation∑ = sum off = frequencyxi = value of i-th datan = total number of data\[\overline{x} = \frac{\sum fx}{n}\]is the sample mean, which we must calculate first.\[\overline{x} = \frac{\sum fx}{n} = \frac{0\cdot127 + 1\cdot176 + 2\cdot348 + 3\cdot252 + 4\cdot328 + 5\cdot239 + 6\cdot139 + 7\cdot27 + 8\cdot60}{1696} \approx 2.7875\]Substituting into the standard deviation formula:\[\sigma_X = \sqrt{\frac{\sum f(x_i - \overline{x})^2}{n}} = \sqrt{\frac{0\cdot(127 - 2.7875)^2 + 1\cdot(176 - 2.7875)^2 + 2\cdot(348 - 2.7875)^2 + 3\cdot(252 - 2.7875)^2 + 4\cdot(328 - 2.7875)^2 + 5\cdot(239 - 2.7875)^2 + 6\cdot(139 - 2.7875)^2 + 7\cdot(27 - 2.7875)^2 + 8\cdot(60 - 2.7875)^2}{1696}} \approx 1.936\]Therefore, the standard deviation is σX ≈ 1.936 (rounded to at least three decimal places).

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Answer: First 2 questions are 12.5% and the third is 25%

Step-by-step explanation: Add up all the possibilities then take the desired possibility and divide by the total possibilities then multiply by 100  

The perimeter of the triangle is  72 √5 / 3 units.

The perimeter of a triangle is the sum of the whole three sides of the triangle. The triangle above is an equilateral triangle.

An equilateral triangle has all it sides and angles congruent to each other.

Therefore, the perimeter of the triangle can be found as follows:

Let's find the side of the triangle using trigonometric ratios,

sin 60 = opposite / hypotenuse

sin 60 = 4√15 / h

cross multiply

h = 4√15 ÷ √3 / 2

h = 4√15 × 2 / √3

h = 8√15 / √3

Hence,

hypotenuse side = 8√45 / 3

perimeter of the triangle = 8√45 / 3 + 8√45 / 3 + 8√45 / 3

perimeter of the triangle = 8√45 + 8√45 + 8√45 / 3

perimeter of the triangle = 24√45 / 3

perimeter of the triangle = 72 √5 / 3 units

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Answer:

-7.9,   -7.881,   -7.88,   0.07,   7.03

Step-by-step explanation:

Numbers provided: 0.07, -7.88, -7.9, 7.03, -7.881

Answer:

What does the circled part of the picture represent?

A)  a point

B)  a line

C)  line segment

D)  ray

Step-by-step explanation:

it is a btw

[tex]36 cm^3[/tex] of pure alcoh ol must be added to the [tex]10 cm^3[/tex] of the 8% solution to obtain [tex]10 + 36 = 46 cm^3[/tex] of an 80% solution.

What is Algebraic expression ?

Algebraic expression can be defined as combination οf variables and constants

Let's first calculate the amount  of pure alcohol in the 8% solution:

Amount of pure alcohol = 8%  of [tex]10 cm^3 = 0.08 x 10 cm^3 = 0.8 cm^3[/tex]

N ow, let's  assume [tex]x cm^3[/tex]of pure alcohol must be added to the 10 cm^3 of the 8% solution to obtain a total volume of [tex]10 + x cm^3[/tex] of an 80% solution. The amount of pure alcohol in the final solution would be:

ο[tex](10 + x) cm^3 = 0.8 (10 + x) cm^3[/tex]

Since we started with [tex]0.8 cm^3[/tex]of pure alcohol and we want to end up with  

[tex]0.8 (10 + x) cm^3[/tex], we can set up the following equation:

[tex]0.8 + x = 0.8 (10 + x)[/tex]ο

Simplifying and solving for x, we get:

[tex]0.8 + x = 8 + 0.8x[/tex]

[tex]0.2x = 7.2[/tex]

[tex]x = 36[/tex]

Therefore, [tex]36 cm^3[/tex] of pure alcohol must be added to the [tex]10 cm^3[/tex]of the 8% solution to obtain [tex]10 + 36 = 46 cm^3[/tex] of an 80% solution.

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Answer:

36cm^3

Step-by-step explanation:

[tex] \bf Question :- \\ [/tex]

what is the value of expression

when g=4 and h=2

[tex] \bf Solution :- \\ [/tex]

[tex] \longrightarrow \: \: \frac{1}{4} (16 + g) - h \\ \\ \longrightarrow \: \: \frac{1}{4} (16 + 4) - 2 \\ \\ \longrightarrow \: \: \frac{1}{{ \cancel{4} }} \times( \cancel{ 20)} - 2 \\ \\ \longrightarrow \: \: 1 \times 5 - 2 \\ \\ \longrightarrow \: \: 1 \times 3 \\ \\ \longrightarrow \: \: 3 \\ [/tex]

Henceforth, Option c is the required answer.

Answer:   [tex]\frac{10}{100}[/tex]× 100

Step-by-step explanation:

Answer:

10/100 = 10%

Step-by-step explanation:

10/100 = 0.1

0.1 * 100 = 10%

If a large diamond with a mass of 4289.6 grams was recently discovered in a mine and the density of the diamond is 3.51 grams over centimeters cubed, the volume is 1221.9 cm³.

To find the volume of the diamond, we need to use its mass and density. The density of the diamond is given as 3.51 grams per cubic centimeter. This means that every cubic centimeter of diamond has a mass of 3.51 grams.

We can use this information to find the volume of the diamond by dividing its mass by its density. Plugging in the given values, we get:

Volume = Mass / Density

Volume = 4289.6 g / 3.51 g/cm³

Volume = 1221.86 cm³

This means that the diamond has a volume of 1221.86 cubic centimeters. However, the question asks us to round the answer to the nearest hundredth, so we round this value to: Volume = 1221.9 cm³

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Answer:

90$

Step-by-step explanation:

We need to find 15% of the number 600:

[tex] \frac{600 \times 15\%}{100\%} = 90 [/tex]

So, the answer is 90$

The graph of the function has zeros of 0 and 3, two distinct real zeros, and no complex zeros.

What is a function?

It is defined as a special type of relationship and they have a predefined domain and range according to the function.

We have a function:

y= x²(x² - 6x + 9)

We can write it as a:

y=x²(x-3)²

To find the zeros equate to the function with the zero.

y = 0

x²(x-3)² =0



First, take  x²=0  we get:

x = 0

Now

(x - 3)² =0

x - 3 = 0

x = 3

Thus, the graph of the function has zeros of 0 and 3, two distinct real zeros, and no complex zeros.

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The exact value of sin−1(cos(1013​π)) is sin−1(1 / (2sin(1013π) - cos(1013π) + 1)).

To find the exact value of sin−1(cos(1013​π)), we need to use the identity sin^2(x) + cos^2(x) = 1. Since sin−1(cos(1013​π)) is an angle whose sine is cos(1013​π), we can let that angle be x: sin(x) = cos(1013π).Let's find the sine of x using the identity sin^2(x) + cos^2(x) = 1:sin^2(x) + cos^2(x) = 1sin^2(x) + (cos(1013π))^2 = 1sin^2(x) + cos^2(1013π) = 1sin^2(x) + sin^2(π/2 - 1013π) = 1Now we need to simplify sin^2(π/2 - 1013π):sin^2(π/2 - 1013π) = sin^2(π/2)cos^2(1013π) - 2sin(π/2)cos(1013π)sin(1013π/2) + sin^2(1013π/2)= 1(cos(1013π))^2 - 2sin(1013π/2)cos(1013π) + 0= cos^2(1013π) - 2sin(1013π)cos(1013π)= cos(1013π)(cos(1013π) - 2sin(1013π))Using the identity sin^2(x) + cos^2(x) = 1, we can rewrite sin^2(x) as 1 - cos^2(x):sin^2(x) + cos^2(x) = 11 - cos^2(x) + cos^2(1013π) = 11 - cos(1013π)(cos(1013π) - 2sin(1013π)) + cos^2(1013π) = 1cos(1013π) - cos(1013π)^2 + 2sin(1013π)cos(1013π) = 1cos(1013π) + cos(1013π)(2sin(1013π) - cos(1013π)) = 1cos(1013π)(2sin(1013π) - cos(1013π) + 1) = 1cos(1013π) = 1 / (2sin(1013π) - cos(1013π) + 1)Therefore, the exact value of sin−1(cos(1013​π)) is sin−1(1 / (2sin(1013π) - cos(1013π) + 1)).

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The null hypothesis and alternative hypothesis for the population mean µ are identified for the given research hypotheses.

The null hypothesis and alternative hypothesis for the population mean µ are as follows:a) H0: µ ≥ 14; H1: µ < 14b) H0: µ ≤ $4.50; H1: µ > $4.50c) H0: µ ≥ $5000; H1: µ < $5000d) H0: µ = 60; H1: µ ≠ 60 Research hypotheses that are to be substantiated by sample data are as follows:a) The mean time a health insurance company takes to pay claims is less than 14 working days.Null hypothesis H0: µ ≥ 14 Alternative hypothesis H1: µ < 14b) The average person watching a movie at a local multiplex theater send over $4.50 on refreshments.

Null hypothesis H0: µ ≤ $4.50 Alternative hypothesis H1: µ > $4.50c) The mean hospital bill for birth in the city is less than $5000.Null hypothesis H0: µ ≥ $5000 Alternative hypothesis H1: µ < $5000d) The mean time between purchases of a brand of mouthwash by loyal customers is different from 60 days.Null hypothesis H0: µ = 60 Alternative hypothesis H1: µ ≠ 60 Hence, the null hypothesis and alternative hypothesis for the population mean µ are identified for the given research hypotheses.

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Answer:

hey will you be my friend

I yes then text me

The equation of the function that is graphed as line b is,

⇒ y = - 2x - 1

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line b are (- 1, 1) and (- 2, 3).

Now,

Since, The equation of line passes through the points ( (- 1, 1) and (- 2, 3).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (3 - 1)) / (- 2 + 1)

m = 2 / - 1

m = - 2

Thus, The equation of line with slope - 2 is,

⇒ y - 1 = - 2 (x + 1)

⇒ y - 1 = - 2x - 2

⇒ y = - 2x - 1

Therefore, The equation of the function that is graphed as line b is,

⇒ y = - 2x - 1

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Answer:

10. To find the area of rhombus ABCD, we can use the formula:

Area = (diagonal 1 x diagonal 2) / 2

We need to find the length of both diagonals. Since the diagonals of a rhombus are perpendicular and bisect each other, we can use the Pythagorean theorem to find the length of each diagonal.

AC is one diagonal, AB is a side of the rhombus, and BD is the other diagonal divided by 2 (since BD bisects AC):

BD = AC/2 = 10/2 = 5 cm

Using the Pythagorean theorem with AC and BD:

AC^2 = AB^2 + BD^2

AC^2 = 13^2 + 5^2

AC^2 = 169 + 25

AC^2 = 194

AC = sqrt(194) ≈ 13.93 cm

Now that we have the lengths of both diagonals:

Area = (AC x BD) / 2

    = (13.93 x 5) / 2

    ≈ 34.83 cm^2

Therefore, the area of rhombus ABCD is approximately 34.83 cm^2.

11. We know that the area of rhombus ABCD is 96 cm^2, and that BD is 8 cm. To find the length of AC, we can use the formula:

Area = (diagonal 1 x diagonal 2) / 2

Solving for diagonal 1 (AC):

AC = (2 x Area) / BD

  = (2 x 96) / 8

  = 24 cm

Therefore, the length of AC is 24 cm.

12. We know that AB is a side of the rhombus and that AB = 16 m. We also know that mZABD = 60 degrees. We can use trigonometry to find the length of the diagonals.

First, we can find the length of AD using the law of cosines:

AD^2 = AB^2 + BD^2 - 2(AB)(BD)cos(mZABD)

AD^2 = 16^2 + (2x)^2 - 2(16)(2x)cos(60)

AD^2 = 256 + 4 - 32x

AD^2 = 260 - 32x

AD = sqrt(260 - 32x)

Then, we can find the length of AC using the law of sines:

AC / sin(mZBAD) = AD / sin(mZABD)

AC / sin(120) = AD / sin(60)

AC = (AD x sin(120)) / sin(60)

AC = (sqrt(260 - 32x) x sqrt(3)) / 2

Now that we have the lengths of both diagonals:

Area = (AC x BD) / 2

    = [(sqrt(260 - 32x) x sqrt(3)) / 2] x 8 / 2

    = 2(sqrt(260 - 32x) x sqrt(3))

    ≈ 67.29 m^2

Therefore, the area of rhombus ABCD is approximately 67.29 square meters.

13. We know that the perimeter of the rhombus is 20 mm, so each side is 5 mm. We also know that AC is one of the diagonals. To find the length of the other diagonal, we can use the Pythagorean theorem.

Let x be half the length of the other diagonal:

AC^2 = (2x)^2 + 5^2

x^2 = (AC^2 - 25) / 4

x = sqrt((AC^2 - 25) / 4)

Now that we have the lengths of both diagonals:

Area = (AC x BD) / 2

    = (AC x 2x) / 2

    = xAC

    = sqrt((AC^2 - 25) / 4) x AC

    ≈ 19.80 mm^2

Therefore, the area of rhombus ABCD is approximately 19.80 square millimeters.

The customer will pay R108 for the screwdriver set.The trader bought a screwdriver set for R90 and added 20% to the cost price for profit and expenses. To calculate the amount a customer will pay for the screwdriver set, we need to add the profit and expenses to the cost price.

First, let's calculate the profit and expenses added by the trader. Since the trader added 20% to the cost price, the profit and expenses will be:

20% of R90 = 0.2 x R90 = R18

Now, we can calculate the selling price of the screwdriver set by adding the cost price and the profit and expenses:

Cost price = R90

Profit and expenses = R18

Selling price = Cost price + Profit and expenses = R90 + R18 = R108

Therefore, the customer will pay R108 for the screwdriver set.

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Kayla would ultimately spend $210.91 + $14.76 = $225.67 for all the clothing items, including sales tax.

To determine if Kayla's budget will be enough to purchase all the clothing items listed after sales tax is applied, we need to calculate the total cost of the items first.

The cost of 2 T-shirts would be 2 x $9.98 = $19.96.

The cost of 3 dresses would be 3 x $24.99 = $74.97.

The cost of 1 pair of pants would be $25.99.

The cost of 1 pair of shoes would be $89.99.

Therefore, the total cost of the clothing items is $19.96 + $74.97 + $25.99 + $89.99 = $210.91.

Next, we need to add the sales tax rate of 7% to the total cost to find the final price that Kayla would pay.

7% of $210.91 = $14.76

Therefore, the final price that Kayla would pay for all the clothing items, including sales tax, is $210.91 + $14.76 = $225.67.

Since Kayla's budget is $200, she would not have enough money to purchase all of the clothing items listed after sales tax is applied.

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The expression is always positive Philip's statement is always true.

The expression -p + 5 + p can be written as -p + 5 + p = -p + p + 5,

which simplifies to 5, no matter what the value of p is.

An expression is a mathematical phrase that can contain numbers, variables, and operations such as addition, subtraction, multiplication, and division. Expressions may or may not have an equal sign. Expressions can be evaluated by replacing any variables with specific values and then simplifying the resulting expression using the order of operations.

Therefore, the expression is always positive and Philip's statement is correct.

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