💡First, I need to determine how many students wore colored lipstick. Since half of the 200 students attended class wore colored lipstick, I divide 200 by 2 to get 100 students.Next, I need to find out how many of those 100 students wore red lipstick. Given that one quarter of the lipstick-wearing students wore red lipstick, I divide 100 by 4 to find that 25 students wore red lipstick.Finally, to determine the number of students who wore blue lipstick, I know that there were one-fifth as many students wearing blue lipstick as those wearing red lipstick. I divide the number of students who wore red lipstick (25) by 5 to find that 5 students wore blue lipstick.

💡I need to calculate the value of the expression (4 cdot 11 + 5 cdot 12 + 13 cdot 4 + 4 cdot 10).First, I'll perform each multiplication separately:- (4 cdot 11 = 44)- (5 cdot 12 = 60)- (13 cdot 4 = 52)- (4 cdot 10 = 40)Next, I'll add all the results together:- (44 + 60 = 104)- (104 + 52 = 156)- (156 + 40 = 196)So, the final value of the expression is 196.

💡First, I need to find the vector AC. Since AC is the sum of vectors AB and BC, I can calculate it by adding the corresponding components of AB and BC.Given:- Vector AB = (3, 7)- Vector BC = (-2, 3)Adding these vectors:AC = AB + BC = (3 + (-2), 7 + 3) = (1, 10)Next, I need to find -1/2 of vector AC. To do this, I multiply each component of AC by -1/2.Calculating -1/2 of AC:-1/2 * AC = (-1/2 * 1, -1/2 * 10) = (-1/2, -5)Finally, I compare this result with the given options to determine the correct answer.

💡First, I need to convert 126 kilometers per hour (km/h) to meters per second (m/s). To do this, I'll use the conversion factor that 1 kilometer is equal to 1000 meters and 1 hour is equal to 3600 seconds.Next, I'll multiply 126 km/h by the conversion factor of 1000 meters per kilometer divided by 3600 seconds per hour. This will give me the speed in meters per second.After performing the calculation, I'll round the result to the nearest whole number to obtain the final speed in meters per second.

💡Okay, so I have this equation here: the square root of (x plus 5) squared equals 8. Hmm, let me write that down to make sure I understand it correctly. It's √((x + 5)²) = 8. Alright, so I need to find all the values of x that satisfy this equation and then add them up.First, I remember that the square root of something squared is the absolute value of that something. So, √(a²) is equal to |a|. That makes sense because square roots are always non-negative, right? So, applying that to my equation, √((x + 5)²) would be |x + 5|. So, the equation simplifies to |x + 5| = 8.Now, absolute value equations can have two solutions because the expression inside the absolute value can be either positive or negative. So, if |x + 5| = 8, then x + 5 can be 8 or x + 5 can be -8. That gives me two separate equations to solve.Let me write those down:1. x + 5 = 82. x + 5 = -8Starting with the first equation: x + 5 = 8. To solve for x, I need to isolate it. So, I'll subtract 5 from both sides.x + 5 - 5 = 8 - 5x = 3Okay, so one solution is x = 3. That seems straightforward.Now, moving on to the second equation: x + 5 = -8. Again, I'll isolate x by subtracting 5 from both sides.x + 5 - 5 = -8 - 5x = -13Alright, so the other solution is x = -13.Now, the problem asks for the sum of all values of x. So, I need to add these two solutions together.3 + (-13) = ?Hmm, adding a positive and a negative number. I think I subtract the smaller absolute value from the larger one and take the sign of the larger. So, 13 - 3 is 10, and since -13 has a larger absolute value, the result is negative. So, 3 + (-13) = -10.Let me double-check my work to make sure I didn't make any mistakes. Starting from the original equation:√((x + 5)²) = 8Simplify to |x + 5| = 8Which leads to x + 5 = 8 or x + 5 = -8Solving both:x = 3 and x = -13Sum: 3 + (-13) = -10Yeah, that seems correct. I don't think I missed anything here. The key was recognizing that the square root of a square is the absolute value, which can be positive or negative. That gives two solutions, and adding them gives the final answer.I guess another way to think about it is squaring both sides of the original equation to eliminate the square root. Let's try that approach just to confirm.Starting with √((x + 5)²) = 8Square both sides:(√((x + 5)²))² = 8²Which simplifies to:(x + 5)² = 64Now, take the square root of both sides, but wait, I already did that. Hmm, maybe I should expand the left side.(x + 5)² = x² + 10x + 25 = 64So, x² + 10x + 25 - 64 = 0Simplify:x² + 10x - 39 = 0Now, I can try to factor this quadratic, but I don't think it factors nicely. Let me check the discriminant to see if it has real solutions.Discriminant D = b² - 4ac = 10² - 4*1*(-39) = 100 + 156 = 256Since the discriminant is positive, there are two real solutions. Let's use the quadratic formula:x = [-b ± √D]/(2a) = [-10 ± √256]/2 = [-10 ± 16]/2So, two solutions:1. [-10 + 16]/2 = 6/2 = 32. [-10 - 16]/2 = -26/2 = -13Same results as before: x = 3 and x = -13. So, the sum is still 3 + (-13) = -10.Okay, that confirms my earlier solution. Whether I approach it by recognizing the absolute value or by expanding and solving the quadratic, I end up with the same answers. So, I'm confident that the sum of all values of x is -10.I think I've covered all the steps and checked my work thoroughly. It's always good to verify using a different method to ensure there are no mistakes. In this case, both methods led me to the same conclusion, so I feel pretty certain about the answer.

💡First, I need to determine the total amount Maria has already saved and the amount her mother is contributing. Maria has saved 120, and her mother is giving her 250.Next, I'll add these two amounts together to find the total funds Maria has from her savings and her mother's contribution:120 (Maria's savings) + 250 (Mother's contribution) = 370.The retail price of the bike is 600. To find out how much more money Maria needs to earn, I'll subtract the total amount she has (370) from the bike's price (600):600 - 370 = 230.Therefore, Maria must earn 230 to be able to buy the bike she wants.