In which case do you need to reverse the inequality sign when solving an inequality?
when adding or subtracting a negative number
when multiplying or dividing by a negative number
when there is a line under the equality symbol
where there is no line under the equality symbol

The error interval will be [3.65,3.75).

The error interval is the limit or range of accuracy where the number is truncated or rounded. This interval simply shows the range which it could be before rounding.

Given here the decimal number is 3.7 which is after rounded to 1 decimal place.

As the number is rounded to the nearest 0.1 unit, therefore, the error will be half of 0.1 which is 0.1/2= 0.05

Then the lower limit of the error interval will be 3.7-0.05= 3.65

the higher limit of the error interval will be 3.7+0.05= 3.75

the error interval will be 3.65≤x<3.75

As we are rounding 1st decimal unit, if the second decimal unit is greater than 5 then the first decimal unit will be 6. Similarly, if the second decimal unit is less than 5 then the first decimal unit will be 7.

There are the numbers below which on rounding give 3.7

3.65 ,3.66,3.67 ,3.68,3.69,3.70,3.71,3.72,3.73,3.74

Therefore the error interval will be [3.65,3.75).

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The error interval for a number x, which when rounded to one decimal place is 3.7, is [3.65, 3.75).

When a number, x, rounded to one decimal place is 3.7, the error interval for x represents the range of actual values x could be to give that rounded figure. So, if x is rounded to 3.7, it means that the value must be at least 3.65 and less than 3.75 when considering rounding to one decimal place. Essentially, the number must be in the half-open interval [3.65, 3.75).

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Answer: 8 L of 100% pure acid and 64 L of 10% acid must be combined

Step-by-step explanation:

According to the dilution law,

[tex]C_1V_1+C_2V_2=C_3V_3[/tex]

where,

[tex]C_1[/tex] = concentration of pure acid solution = 100 %

[tex]V_1[/tex] = volume of pure acid solution = x L

[tex]C_2[/tex] = concentration of another acid solution= 10%

[tex]V_2[/tex] = volume of another acid solution= (72-x) L

[tex]C_3[/tex] = concentration of resulting acid solution = 20 %

[tex]V_1[/tex] = volume of resulting acid solution = 72 L

Putting the values in the equation:

[tex]100\times x+10\times (72-x)=20\times 72[/tex]

[tex]x=8L[/tex]

Therefore, the laboratory technician must take 8 L of 100% pure acid and (72-8) = 64 L of 10% acid to get 72​-liter batch of a 20​% acid solution.

A point in the polar plane can have multiple representations due to the periodic nature of angles and the possibility of using negative radii to represent a point in the opposite direction from the pole.

The question asks to explain why a point in the polar plane cannot be named by a unique ordered pair (r, θ). In the polar coordinate system, each point is determined by a radius (r) and an angle (θ).

However, a point can have multiple representations due to the periodic nature of angles. If you add or subtract multiples of 2π radians (or 360 degrees) from θ, you will land on the same point in the polar plane.

Additionally, if the radius (r) is negative, the direction is reversed, which also leads to the same point being represented by (-r, θ + π), where θ is the initial angle.

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Let the depth of the river = d

So in order to find the product, you simply multiply

so the product of 86 and the depth of the river would be 86 * d

or 86d.

Hope this answers your question. Have a great day!

Answer:

both alicia and jamal

Step-by-step explanation:

From the given steps we can see that both Alicia and Jamal completed the proof correctly.

Option C

Given :

3x+7=x-5

prove: x=-6

Alicia's workout

3x+7=x-5 : given

2x+7=-5: subtraction property of equality

2x=-12: subtraction property of quality

x=-6: division property of equality

Alicia's steps are correct. She proved x=-6

jamal's work

3x+7=x-5 : given

7=-2x-5 : subtraction property of equality

12=-2x: addition property of equality

-6=x proved

Jamal's steps are also correct. Jamal started by subtracting 3x from both sides. That approach is also correct. He proved x=-6

so, both Alicia and Jamal are correct

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Answer:

45 or more

Step-by-step explanation:

If x is the amount of pastries they sell, we need to multiply it by $3.00 to know how much they raise. Total earnings: $3.00x

They need to raise at least $135, that is $135 or more.

So, $3.00x has to be greater than $135 or equal.

Written as an inequality is:

$3.00x [tex]\geq[/tex] $135

We divide both sides by $3.00 and we have:

x [tex]\geq[/tex] $135/$3.00 = 45

Therefore, they need to sell 45 or more pastries to meet the goal.

To solve for R in the equation [tex]C=2\pi R[/tex] divide both sides by 2π to get [tex]R = C / (2\pi )[/tex].

To solve the equation [tex]C=2\pi R[/tex] for R, we need to isolate R on one side of the equation. Here are the steps to do this:

Start with the original equation: [tex]C=2\pi R[/tex]

Divide both sides of the equation by 2π to isolate [tex]R: R = C / (2\pi ).[/tex]

Given variation, this is also equivalent to [tex]r=1/2\pi C[/tex].

Now, R is the subject of the equation, and you can use this formula to find the radius (R) if you know the circumference (C) of a circle.

Answer:

Its B and D.

Step-by-step explanation:

Answer: [tex]x<-8[/tex]

Step-by-step explanation:

The given inequality : [tex]3-(2x-5)<-4(x+2)[/tex]

To solve the inequality for x , first we open the parenthesis , we get

 [tex]3-2x+5<-4x+(-4)2[/tex]

 [tex]\Rightarrow\ 3-2x+5<-4x-8[/tex]   [Note : (-)(+)=(-)]

[tex]\Rightarrow\ 3+5-2x<-4x-8[/tex]

[tex]\Rightarrow\ 8-2x<-4x-8[/tex]

Add 4x on both sides , we get

[tex]8-2x+4x<-4x-8+4x[/tex]

[tex]8+2x<-8[/tex]

Subtract 8 from both sides , we get

[tex]2x<-16[/tex]

Divide both sides by 2 , we get

[tex]x<-8[/tex]

Hence, the correct answer is : [tex]x<-8[/tex]

Answer:

$33.60 is the correct answer.

Step-by-step explanation:

Price of the shirt = $40.00

discount rate = 20% or 20/100

so price of the shirt = 40 × 0.20 = 8

Shirt's price after 20% discount = 40 - 8 = $32.00

Now she paid 5% tax on the price after discount.

5% tax of 32.00

0.05 × 32 = $1.60

This amount will be added to his discounted price of a shirt.

= 32.00 + 1.60 = $33.60

Lydia pay $33.60 for the shirt.

The probability that the number on the tile is a multiple of 7 or a multiple of 8 is 0.24 or 24%.

To find the probability that a tile picked at random has a number that is a multiple of 7 or a multiple of 8, we need to count the number of tiles that satisfy this condition and divide it by the total number of tiles.

First, let's find how many numbers from 1 to 50 are multiples of 7 and multiples of 8 separately.

Multiples of 7:

7, 14, 21, 28, 35, 42, 49

There are 7 multiples of 7 between 1 and 50.

Multiples of 8:

8, 16, 24, 32, 40, 48

There are 6 multiples of 8 between 1 and 50.

However, we need to be careful not to count the numbers that are multiples of both 7 and 8 (multiples of 56). There's only one such number in the range (56).

So, the total number of tiles with numbers that are multiples of 7 or multiples of 8 is 7 + 6 - 1 = 12.

The total number of tiles from 1 to 50 is 50.

Now, we can find the probability:

Probability = [tex]\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}[/tex]

Probability = [tex]\frac{12}{50}[/tex]

Probability = 0.24

So, the probability that the number on the tile is a multiple of 7 or a multiple of 8 is 0.24 or 24%.

To find the amount of time it takes for your neighbor to be 30 ft from you, you set up and solve an equation using the given information.

To find the amount of time it takes for your neighbor to be 30 ft from you, we need to set up an equation and solve for t. The distance d is given by d = |120 - 4t|. The absolute value represents the distance in one direction, so it does not matter if your neighbor is walking towards you or past you. We want to find when the distance is 30 ft, so we set up the equation 30 = |120 - 4t|.

Solving this equation gives us two possibilities: 30 = 120 - 4t and 30 = -(120 - 4t). We can solve each equation separately.

For the first equation, 30 = 120 - 4t, we subtract 120 from both sides to get -90 = -4t. Dividing both sides by -4 gives us t = 22.5.

For the second equation, 30 = -(120 - 4t), we multiply both sides by -1 to get -30 = 120 - 4t. Subtracting 120 from both sides gives us -150 = -4t. Dividing both sides by -4 gives us t = 37.5.

So your neighbor is 30 ft from you after 22.5 seconds and 37.5 seconds.

It's not. The absolute value of any number is the positive version of that number except for the absolute value of 0. This is the only situation where the absolute value of a number is not positive. The absolute value of 0 is just 0.

The height of the building is approximately 78.4 meters.

To find the height of the building, we can use the formula d = v0t + 1/2gt2, where d is the height, v0 is the initial horizontal speed, t is the time, and g is the acceleration due to gravity. In this case, since the ball is thrown horizontally, the initial vertical speed is 0 and there is no initial vertical acceleration. So, d = 0(4.0) + 1/2(9.8)(4.0)2. Solving this equation gives us a height of approximately 78.4 meters.