Which expression is equivalent to 10k+17–7j-18-11k

A. -8jk-1
B. -7j-k-1
C. -7j+k+1
D. -8j-k

multiply 2x+y = 3 by 2

4x + 2y = 6

x - 2y = -1

add terms (be careful about signs!)

5x + 0 = 2

Answer:

5x=5

Step-by-step explanation:

1/4 = 1/8

times by 4 to find the whole song as 1/4 × 4 is 1

1 = 4/8

4/8 = 1/2 of a minute

Answer:

The contribution is $ [tex]16.92\\[/tex] per biweekly payment

Step-by-step explanation:

Salary received in each of the [tex]26 \\[/tex] pay is

[tex]\frac{2}{100} * \frac{22000}{26} \\= 16.92\\[/tex]

Final answer:

To take full advantage of your company's retirement match, contribute at least $16.92 from each bi-weekly paycheck to your retirement account, which is 2% of your annual salary divided by 26 pay periods.

Explanation:

To determine how much you should contribute to the retirement account each pay period to take full advantage of the company match, you need to calculate 2% of your annual salary and then divide that number by the number of pay periods in a year. Here's the step-by-step calculation:

To fully utilize the company's matching program, you should contribute at least $16.92 from each bi-weekly paycheck to your retirement account.

Answer:

-1/2

Step-by-step explanation:

Rise in X / Rise in Y

1 / 2 = 1/2

The answer to ur question is slope =-1/2

Buckets of Soil : Buckets of Peat Moss = 5 : 4

Since Mr Carver needs to use 324 buckets in all,

He needs to use 324 * 5/9 = 180 buckets of Soil and 324 * 4/9 = 144 buckets of Peat Moss.

Mr. Carver will use 180 buckets of soil and 144 buckets of peat moss to fill the planting bed, based on the given ratio of 5 buckets of soil to 4 buckets of peat moss.

The problem at hand revolves around ratios and proportions where Mr. Carver is using a mix of soil and peat moss in a specific ratio to fill a planting bed. Given the ratio of 5 buckets of soil to 4 buckets of peat moss, we need to find the total number of buckets for each that will sum up to 324 buckets. First, we'll find the total number of parts in the ratio by adding 5 (for soil) and 4 (for peat moss), which gives us 9 parts. Since we have the total amount of 324 buckets, we can find the value of one part by dividing 324 by 9, which gives us 36.

Once we have the value of one part, we multiply it by the number of parts for soil and peat moss to find their respective quantities:

Therefore, Mr. Carver will use 180 buckets of soil and 144 buckets of peat moss to fill the planting bed.

For this case we must express the number "423" in a radical way.

We have to, we can rewrite it as:

[tex]423 = 9 * 47 = 3 ^ 2 * 47[/tex]

So, we have to:

[tex]423 = \sqrt {3 ^ 2 * 47}[/tex]

By definition of properties of powers and roots we have:

[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]

So:

[tex]423 = \sqrt {3 ^ 2 * 47} = 3 \sqrt {47}[/tex]

Answer:

[tex]3 \sqrt {47}[/tex]

Answer:

3^√4^2

Step-by-step explanation:

y=×^2+23

Answer letter B

×=y-23

Answer:

The answer is circle; 2(x')² + 2(y')² - 5x' - (5√3)y' - 6 = 0 ⇒ answer (b)

Step-by-step explanation:

* At first lets talk about the general form of the conic equation

- Ax² + Bxy + Cy²  + Dx + Ey + F = 0

∵ B² - 4AC < 0 , if a conic exists, it will be either a circle or an ellipse.

∵ B² - 4AC = 0 , if a conic exists, it will be a parabola.

∵ B² - 4AC > 0 , if a conic exists, it will be a hyperbola.

* Now we will study our equation:

* x² - 5x + y² = 3

∵ A = 1 , B = 0 , C = 1

∴ B² - 4AC = (0) - 4(1)(1) = -4 < 0

∵ B² - 4AC < 0

∴  it will be either a circle or an ellipse

* Lets use this note to chose the correct figure

- If A and C are equal and nonzero and have the same sign,

 then the graph is a circle.

- If A and C are nonzero, have the same sign, and are not equal

 to each other, then the graph is an ellipse.

∵ A = 1 an d C = 1

∴ The graph is a circle.

* To find its center of the circle lets use

∵ h = -D/2A and k = -E/2A

∵ A = 1 and D = -5 , E = 0

∴ h = -(-5)/2(1) = 2.5 and k = 0

∴ The center of the circle is (2.5 , 0)

* Now lets talk about the equation of the circle and angle Ф

∵ Ф = π/3

- That means the graph of the circle will transformed by angle = π/3

- The point (x , y) will be (x' , y'), where

* x = x'cos(π/3) - y'sin(π/3) , y = x'sin(π/3) + y'cos(π/3)

∵ cos(π/3) = 1/2 and sin(π/3) = √3/2

∴ [tex]y=\frac{\sqrt{3}}{2}x'+\frac{1}{2}y'=(\frac{\sqrt{3}x'+y'}{2})[/tex]

∴ [tex]x=\frac{1}{2}x'-\frac{\sqrt{3}}{2}y'=(\frac{x'-\sqrt{3}y'}{2})[/tex]

* Lets substitute x and y in the equation x² - 5x + y² = 3

∵ [tex](\frac{x'-\sqrt{3}y'}{2})^{2}-5(\frac{x'-\sqrt{3}y'}{2})+(\frac{\sqrt{3}x'-y'}{2})^{2}=3[/tex]

* Lets use the foil method

∴ [tex]\frac{(x'^{2} -2\sqrt{3}x'y'+3y')}{4}-\frac{(5x'-5\sqrt{3}y')}{2}+\frac{(\sqrt{3}x'+2\sqrt{3}x'y'+y'^{2})}{4}[/tex]=3

* Make L.C.M

∴ [tex]\frac{(x'^{2}-2\sqrt{3}x'y'+3y'^{2})}{4}-\frac{(10x'-10\sqrt{3}y')}{4}+\frac{(3x'^{2}+2\sqrt{3}x'y'+y'^{2})}{4} =3[/tex]

* Open the brackets ∴[tex]\frac{x'^{2}-2\sqrt{3}x'y'+3y'^{2}-10x'+10\sqrt{3}y'+3x'^{2}+2\sqrt{3}x'y'+y'^{2}}{4}=3[/tex]

* Collect the like terms

∴ [tex]\frac{4x'^{2}+4y'^{2}-10x'+10\sqrt{3}y'}{4}=3[/tex]

* Multiply both sides by 4

∴ 4(x')² + 4(y')² - 10x' + (10√3)y' = 12

* Divide both sides by 2

∴ 2(x')² + 2(y')² - 5x' + (5√3)y' = 6

∵ h = -D/2A and k = E/2A

∵ A = 2 and D = -5 , E = 5√3

∴ h = -(-5)/2(2) = 5/4 =1.25

∵ k = (5√3)/2(2) = (5√3)/4 = 1.25√3

∴ The center of the circle is (1.25 , 1.25√3)

∵ The center of the first circle is (2.5 , 0)

∵ The center of the second circle is (1.25 , 1.25√3)

∴ The circle translated Left and up

* 2(x')² + 2(y')² - 5x' - (5√3)y' - 6 = 0

∴ The answer is circle; 2(x')² + 2(y')² - 5x' - (5√3)y' - 6 = 0

* Look to the graph

- the purple circle for the equation x² - 5x + y² = 3

- the black circle for the equation (x')² + (y')² - 5x' - 5√3y' - 6 = 0

Answer:

B

Step-by-step explanation:

edge

Answer:

x = 13.9

Step-by-step explanation:

With respect to the angle shown, we have the hypotenuse (the side opposite the 90 degree angle) and we have the adjacent side (which is the side labeled x). thus we can use the ratio "cosine" to solve this.

The ratio of cosine is defined as:

[tex]Cos\theta=\frac{Adjacent}{Hypotenuse}[/tex]

Where adjacent and hypotenuse are the respective sides and [tex]\theta[/tex] is the angle

Thus, we can now write:

[tex]Cos\theta=\frac{Adjacent}{Hypotenuse}\\Cos(35)=\frac{x}{17}\\Cos(35)*17=x\\x=13.9[/tex]

The first answer choice is right, x = 13.9

The value of X to the nearest tenth in the triangle is 13.9.  

We have the neighboring side, which is the side with the letter x, and the hypotenuse, which is the side across from the 90-degree angle, with regard to the angle displayed.

Therefore, the ratio "cosine" can be used to solve this.

The definition of the cosine ratio is:  [tex]Cos \theta[/tex] = Adjacent side / hypotenuse.

where the angle and the corresponding sides are called the hypotenuse and adjacent.

So that we may write now:

[tex]Cos(35)= \frac{x}{17}[/tex]

[tex]Cos(35) \times 17 = x[/tex]

Therefore 13.9 = x  .

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Answer:

Part A) Option B. [tex]-4n^{3}+24n^{2}-12n[/tex]

Part B) Option A. [tex]4n^{4}-24n^{3}+12n^{2}[/tex]

Step-by-step explanation:

Part A) we have

[tex](n^{2}-6n+3)(-4n)[/tex]

the product is equal to

[tex]=(n^{2})(-4n)-6n(-4n)+3(-4n)\\=-4n^{3}+24n^{2}-12n[/tex]

Part B) When this product is multiplied by -n, the result is

we have

[tex](-4n^{3}+24n^{2}-12n)(-n)[/tex]

[tex]=(-4n^{3})(-n)+24n^{2}(-n)-12n(-n)\\=4n^{4}-24n^{3}+12n^{2}[/tex]

Answer:

3x=$20

Step-by-step explanation:

well first you divide    3x/3=$20/3                      

3 can go into 20 6 times that                                                                                                          would 18 and then u would have a remainder of 2 dollars and 3 cant go into 2 so it would be .67 so x=6.67

Answer: Option D.

Step-by-step explanation:

The expressions of boths sides of the equation must have the same value Or, in other words, if we call the expresion on the left side of the equation A, and the expression on the right side of the equation B, then:

[tex]A=B[/tex]

Keeping the above on mind, you can see that 5 and 11 are not equal, then:

5≠11

The correct value of s is:

[tex]s-3=11\\s=11+3\\s=14[/tex]

Substituting:

[tex]14-3=11\\11=11[/tex]

Answer:

No, because the last line of the work is not true. 5 and 11 are not equal.

Step-by-step explanation:

Answer:

line B.)

Step-by-step explanation:

2x+5y=10

5y=-2x+20

(5y/5) (2x+10/5)

y= (-2/5)x +2

add payment history and total debt it gibes you 65%

This should help

3 * a - 2 = a + 10

Answer:First one is D

Step-by-step explanation:

The graph passses through the pints neccessary for it to decrease by 300

Answer:

128 ft / second.

Step-by-step explanation:

It's acceleration is due to gravity and is 32 ft s^-2.

To find the velocity when it hits the ground we use the equation of motion

v^2 = u^2 + 2gs    where  u = initial velocity, g = acceleration , s = distance.

v^2 = 0^2 + 2 * 32 * 256

v^2 = 16384

v =  128 ft s^-1.

The rock will strike the ground with a velocity of 128 ft/s and will experience an acceleration of 32 ft/s^2.

First, we need to calculate the time it takes for the rock to fall to the ground. We can use the equation h = (1/2)gt^2, where h is the height of the building (256 ft) and g is the acceleration due to gravity (32 ft/s^2). Solving for t, we find t = sqrt(2h/g) = sqrt(2(256)/32) = 4 seconds.

Next, we can calculate the velocity of the rock just before it hits the ground. We can use the equation v = gt, where g is the acceleration due to gravity and t is the time it takes to fall (4 seconds). Plugging in the values, we find v = (32 ft/s^2)(4s) = 128 ft/s.

Lastly, the acceleration of the rock is equal to the acceleration due to gravity, which is 32 ft/s^2.

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Answer:

The exact form of [tex]\tan(\frac{7\pi}{8})[/tex] is [tex]-\sqrt{2}+1[/tex]

Step-by-step explanation:

We need to find the exact value of [tex]\tan(\frac{7\pi}{8})[/tex] using half angle identity.

Since, [tex]\frac{7\pi}{8}[/tex]  is not an angle where the values of the six trigonometric functions are known, try using half-angle identities.

[tex]\frac{7\pi}{8}[/tex]  is not an exact angle.

First, rewrite the angle as the product of [tex]\frac{1}{2}[/tex] and an angle where the values of the six trigonometric functions are known. In this case,

[tex]\frac{7\pi}{8}[/tex] can be written as ;

[tex](\frac{1}{2})\frac{7\pi}{4}[/tex]

Use the half-angle identity for tangent to simplify the expression. The formula states that [tex] \tan \frac{\theta}{2}=\frac{\sin \theta}{1+ \cos \theta}[/tex]

[tex]=\frac{\sin(\frac{7\pi}{4})}{1+ \cos (\frac{7\pi}{4})}[/tex]

Simplify the numerator.

[tex]=\frac{\frac{-\sqrt{2}}{2}}{1+ \cos (\frac{7\pi}{4})}[/tex]

Simplify the denominator.

[tex]=\frac{\frac{-\sqrt{2}}{2}}{\frac{2+\sqrt{2}}{2}}[/tex]

Multiply the numerator by the reciprocal of the denominator.

[tex]\frac{-\sqrt{2}}{2}\times \frac{2}{2+\sqrt{2}}[/tex]

cancel the common factor of 2.

[tex]\frac{-\sqrt{2}}{1}\times \frac{1}{2+\sqrt{2}}[/tex]

Simplify,

[tex]\frac{-\sqrt{2}(2-\sqrt{2})}{2}[/tex]

[tex]\frac{-(2\sqrt{2}-\sqrt{2}\sqrt{2})}{2}[/tex]

[tex]\frac{-(2\sqrt{2}-2)}{2}[/tex]

simplify terms,

[tex]-\sqrt{2}+1[/tex]

Therefore, the exact form of [tex]\tan(\frac{7\pi}{8})[/tex] is [tex]-\sqrt{2}+1[/tex]

The exact value of [tex]\( \tan\left(\frac{7\pi}{8}\right) \)[/tex] is [tex]\( \frac{2 - \sqrt{2}}{\sqrt{2}} \)[/tex].

To find the exact value of [tex]\( \tan\left(\frac{7\pi}{8}\right) \)[/tex] using the half-angle identity, we proceed as follows:

1. Identify the appropriate half-angle identity:

  The tangent half-angle identity is given by:

  [tex]\[ \tan\left(\frac{\theta}{2}\right) = \frac{1 - \cos(\theta)}{\sin(\theta)} \][/tex]

2. Apply the identity for [tex]\( \theta = \frac{7\pi}{4} \)[/tex] :

  First, determine [tex]\( \theta = \frac{7\pi}{4} \)[/tex] , then find [tex]\( \frac{\theta}{2} \)[/tex].

3. Calculate [tex]\( \cos\left(\frac{7\pi}{4}\right) \)[/tex] and [tex]\( \sin\left(\frac{7\pi}{4}\right) \)[/tex]:

  [tex]\[ \cos\left(\frac{7\pi}{4}\right) = \cos\left(\frac{2\pi + \frac{\pi}{4}}{2}\right) = \cos\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2} \][/tex]

  [tex]\[ \sin\left(\frac{7\pi}{4}\right) = \sin\left(\frac{2\pi + \frac{\pi}{4}}{2}\right) = \sin\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2} \][/tex]

4. Apply the half-angle identity:

  [tex]\[ \tan\left(\frac{7\pi}{8}\right) = \frac{1 - \cos\left(\frac{7\pi}{4}\right)}{\sin\left(\frac{7\pi}{4}\right)} = \frac{1 - \frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} \][/tex]

5. Simplify:

  [tex]\[ \tan\left(\frac{7\pi}{8}\right) = \frac{2 - \sqrt{2}}{\sqrt{2}} \][/tex]

Therefore, [tex]\( \tan\left(\frac{7\pi}{8}\right) = \frac{2 - \sqrt{2}}{\sqrt{2}} \)[/tex].

Using the half-angle identity for tangent, we substituted [tex]\( \theta = \frac{7\pi}{4} \)[/tex] and calculated [tex]\( \cos\left(\frac{7\pi}{4}\right) \)[/tex] and [tex]\( \sin\left(\frac{7\pi}{4}\right) \)[/tex] to find [tex]\( \tan\left(\frac{7\pi}{8}\right) \)[/tex] in exact form.

Answer:

Land on round 4 times; land on square 4 times

Step-by-step explanation:

Answer:

The correct option is 4.

Step-by-step explanation:

In the graph orange region represents the ways Janelle can win the beanbag toss game.

From the given graph it is clear that the related line passes through the points (2,5) and (10,0).

If a line passes through two points, then the equation of line is

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

The equation of related line is

[tex]y-5=\frac{0-5}{10-2}(x-2)[/tex]

[tex]y-5=-\frac{5}{8}(x-2)[/tex]

Add 5 on both the sides.

[tex]y-5+5=-\frac{5}{8}(x)+\frac{5}{4}+5[/tex]

[tex]y=-\frac{5}{8}(x)+\frac{25}{4}[/tex]

The shaded region is above the line, so the sign of inequality is ≥.

The required inequality is

[tex]y\geq -\frac{5}{8}(x)+\frac{25}{4}[/tex]

Check the each point whether it satisfy the inequality of not.

In option (1), the given point is (7,1).

[tex]1\geq -\frac{5}{8}(7)+\frac{25}{4}[/tex]

[tex]1\geq 1.875[/tex]

This statement is false.

In option (2), the given point is (6,2).

[tex]2\geq -\frac{5}{8}(6)+\frac{25}{4}[/tex]

[tex]2\geq 2.5[/tex]

This statement is false.

In option (3), the given point is (5,3).

[tex]3\geq -\frac{5}{8}(5)+\frac{25}{4}[/tex]

[tex]3\geq 3.125[/tex]

This statement is false.

In option (4), the given point is (4,4).

[tex]4\geq -\frac{5}{8}(4)+\frac{25}{4}[/tex]

[tex]3\geq 3.75[/tex]

This statement is true. It means the point (4,4) describes a way Janelle can win the game. Therefore the correct option is 4.

By using elimination to subtract the second equation from the first, we solve for x and then substitute x back into one of the original equations to solve for y, finding the solution as the ordered pair (1, -1).

To solve the system using elimination, we look at the given equations:

1) 5x + 4y = 1
2) -3x + 4y = -7

The goal is to eliminate one variable to solve for the other. In this case, we can subtract the second equation from the first one since they both have the same coefficient for y, which will eliminate the y variable.

Now that we have found x, we can substitute x into one of the original equations to find y:

5(1) + 4y = 1

The solution to the system is (1, -1), which is an ordered pair representing the x and y values that satisfy both equations.

Answer:

Circumference

Step-by-step explanation:

The circumference is the distance around the circle. It relates the number of times the diameter will encircle the circumference as 3.14 or π. As a result, the formulas for the circumference of a circle are C = 2πr and C = πd.

The largest volume that the box can have is 2.25 ft^3, and it's obtained when x = 0.5 ft. This came from a mathematical analysis of the volume function V(x) = 4x^3 - 12x^2 + 9x.

Given that a square is cut from each corner of the cardboard to form an open box, we can come up with the following: The width of the base, represented by y, would be equal to the initial width of the cardboard (3 ft) minus two times the sides of the squares being cut out (2x), so y = 3 - 2x. Part c: will be the Volume of the box which is given by V = x * y^2, substituting for y from the relation obtained above we get. Part d: V = x * (3 - 2x)^2. Part e: is just the simplification of the equation obtained in part d: V(x) = 4x^3 - 12x^2 + 9x. Part f: To find the maximum volume, we need to find the critical points of the V(x) function, these are obtained by setting the derivative of the function equal to zero, solving for x will give x = 0.5 and x =1.5 but since x > 1.5 would give a negative y, the maximum volume is obtained at x = 0.5, substituting this x into the V(x) equation gives V = 2.25 ft^3.

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No, it is not the same because in option 1, the interest is calculated based on two different principal amounts and then added together. The principal amounts will be different every year because of the varying interest rates. Since one of the interest rates in option 1 is 7%, the principal will grow at a faster rate because the interest rate is applied to a greater and greater principal amount over time. In option 2, the interest is being calculated only on one principal  

Answer:

Step-by-step explanation:

No, they are not always the same - the only time that they will be the same is after the first year:

$4000*1.05 + $4000*1.07 = $8480 = $8000*1.06

From there on, they will diverge. For example after the second year:

$4000*1.05^2 + $4000*1.07^2 = $8989.6

$8000*1.06^2 = $8988.8

After the third year:

$4000*1.05^3 + $4000*1.07^3 = $9530.672

$8000*1.06^3 = $9528.128

After the nth year:

The first option gives $4000*(1.05^n + 1.07^n)

The second option gives $8000*(1.06^n)

= $4000*(2)*(1.06^n)

= $4000*(1.06^n + 1.06^n)

Because 1.07^n - 1.06^n > 1.06^n - 1.05^n for n>1, the first option will be a better investment.

Answer:

The answer is (b) moved right 3 units and moved down 3 units

Step-by-step explanation:

∵ f(x) = 4^x ⇒ red in the graph

∵ f(x) = 4^(x-3) - 3 ⇒ blue in the graph

∵ x  becomes x - 3 ⇒ means:

 The graph moved right 3 units

∵ f(x) = 4^x becomes 4^(x-3) - 3 ⇒ means:

  The graph moved down 3 units

∴ The answer is (b)

The graph of f(x) = 4ˣ - 3  is shifted down 3 units compared to the graph of f(x) = 4ˣ

An exponential function is in the form:

y = abˣ

Where y,x are variables, a is the initial value of y and b is the multiplication factor.

The graph of f(x) = 4ˣ - 3 and f(x) = 4ˣ is attached.

The graph of f(x) = 4ˣ - 3  is shifted down 3 units compared to the graph of f(x) = 4ˣ

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Answer:

[tex] R = 28.07^\circ [/tex]

Step-by-step explanation:

Since you have the lengths of all the sides, you can use sine, cosine, or tangent to find the answer. Let's use the tangent ratio.

For angle R, PQ is the opposite leg, and QR is the adjacent leg.

[tex] \tan R = \dfrac{opp}{adj} [/tex]

[tex] \tan R = \dfrac{8}{15} [/tex]

[tex] R = \tan^{-1} \dfrac{8}{15} [/tex]

[tex] R = 28.07^\circ [/tex]

Answer:

were are the answer selection

Step-by-step explanation:

Answer:

(F-G)(x) = -1

Step-by-step explanation:

The notation (F - G)(x) means to subtract each function when x = 6. According to the sets when x = 6 then F is (6,8) and G is (6,9). To subtract the functions, subtract their output values. (F-G)(x) = 8 - 9 = -1.

Answer:

Choice D is correct

Step-by-step explanation:

The eccentricity of the conic section is 1, implying we are looking at a parabola. Parabolas are the only conic sections with an eccentricity of 1.

Next, the directrix of this parabola is located at x = 4. This implies that the parabola opens towards the left and thus the denominator of its polar equation contains a positive cosine function.

Finally, the value of k in the numerator is simply the product of the eccentricity and the absolute value of the directrix;

k = 1*4 = 4

This polar equation is given by alternative D

Answer:

60π

Step-by-step explanation:

If the circle has radius of 30 units, substitute r=30 into the formula C = 2πr.

C = 2π(30)

C = 60π

To find the circumference of the circle shown here, let's start with writing the formula down.

Circumference = 2[tex]\pi[/tex]r

We have to divide 60 by 2 because the radius is always half the diameter. Now, we can plug in 30 for r in the formula.

Now we have

circumference = 2[tex]\pi[/tex]30.

This equals 60[tex]\pi[/tex].

Answer:

Step-by-step explanation:

Let x be the amount of colored pencils she buys, and let y be the number of jelly beans that she buys. We have the following inequalities..

4x + 2y ≤ 20     (the cost times the amount has to be less than or equal to 20)

4x + 2y > 8       (she spends more than $8)

We can rewrite the inequality like this...

8 < 4x + 2y ≤ 20

Now reduce since all coefficients are even, they can be divided by 2

4 < 2x + y ≤ 10

We want values of x and y that can satisfy the situation.  

There are many points,

If x = 1, then you can have y =3 to 8

If x = 2,  then you can have y = 1 to 6  

If x = 3, then you can have y = 1 to 4

If x = 4, then you can have y = 1 or 2

x = 5,  the y = o

Final answer:

To find the possible number of pounds of jelly beans Cindy could purchase, we set up a compound inequality considering the $4 spent on colored pencils and the $2 per pound cost of jelly beans. Solving the inequality 4 < 4 + 2x < 20 gives us the range 0 < x < 8, meaning Cindy could have bought more than 0 pounds but less than 8 pounds of jelly beans.

Explanation:

To solve the problem involving Cindy's shopping at the store, let's create a compound inequality with the following conditions: she has $20 to spend, she has already spent $4 on colored pencils, and the jelly beans cost $2 per pound. Cindy wants to spend more than $8 in total at the store, which includes the cost of the pencils and the jelly beans.

Let's define x as the number of pounds of jelly beans that Cindy can purchase. The cost of the jelly beans is $2 per pound, so the total cost for the jelly beans is $2x.

Since she spent $4 on pencils, adding the cost of the jelly beans needs to be more than $4 (to exceed the $8 total spending) but less than $20 (to stay within her budget). Hence, the compound inequality will be:

4 < 4 + 2x < 20

Now let's solve for x:

First, subtract 4 from all parts of the inequality:

0 < 2x < 16

Next, divide all parts by 2:

0 < x < 8

The solution tells us that Cindy could have purchased more than 0 but less than 8 pounds of jelly beans.

Tom walks at a rate of 4/3 miles per hour, which means he will walk 1.333 miles in one hour at this rate.

To find out how many miles Tom will walk in 1 hour, we need to determine the distance he covers in 1/4 of an hour and then calculate how much he would walk in 1 hour at that rate.

Given Tom walks 1/3 of a mile in 1/4 of an hour, first find how much he walks in 1 hour:
1/3 mile ÷ (1/4 hour) = 1/3 mile * 4/1 hour = 4/3 miles in 1 hour

Therefore, Tom will walk 4/3 miles in 1 hour at that pace.

Tom would walk 4/3 miles or 1 and 1/3 miles in 1 hour given that he walks 1/3 of a mile in 1/4 of an hour based on the unit rate calculation.

The question deals with finding out how many miles Tom will walk in 1 hour if he walks 1/3 of a mile in 1/4 of an hour. To calculate this, we use the concept of a unit rate, which is finding how much of something is done in one unit of something else, in this case, miles per hour. Since Tom walks 1/3 of a mile in 1/4 of an hour, we can set up a proportion to find out how many miles he would walk in 1 full hour.

The proportion is: (1/3) miles / (1/4) hour = x miles / 1 hour. To solve for x, we multiply both sides of the equation by 1 hour so x would equal (1/3) miles \/ (1/4) hour. To simplify the right side, we invert the fraction in the denominator and multiply:
x = (1/3) miles \/ (1/4). When we multiply by the reciprocal of 1/4, which is 4, we get x = (1/3) \/ 1 \/ 4 = 4/3 miles.

Therefore, at this rate, Tom would walk 4/3 miles or 1 and 1/3 miles in 1 hour.