Algebra
9x+5=32
x=3
There are three consecutive even numbers. Their sum is 372. What are the numbers?
The numbers are 122, 124, and 126.
Find the volume of a cylinder, if the diameter is 8cm and the height(H) is 12cm. Give your answer to the nearest tenths.
603.2cm3
There are 16 colorful marbles in a bag. Half of the marbles are red, one is blue, two are purple, and the rest are green. What is the probability that the marbles are green.
5/16
x2+5x+6
(x+2)(x+3)
Find the answer to 2x-5-5x-7=37-10x
x=7
Bob is 5 years older than his brother. In three years, he will be 2 times as old as his brother. What is the age of Bob and his brother now?
Bob is 7 years old and his brother is 2 years old.
A composite shape consists of a trapezoid on a rectangle. The rectangle has a length of 14cm and width of 3cm. The shorter parallel side of the trapezoid is 8cm. Both two nonparallel sides are 5cm. Calculate the area of the composite shape.
86cm2
Three coins are flipped. What is the probability?
1) P(3Hs)
2) P(2T and 1H)
1) P(3Hs)=1/8
2) P(2T and 1H)=1/2
x2+1-30
(x+6)(x-5)
3(3y-7)+6+9y=3
y=1
Andy buys a chocolate bar for $1.75 with dimes and nickels. He pays with a total of 13 coins. How many coins were dimes? How many coins were nickels?
11 coins were dimes and 2 were nickels.
The triangle is an isosceles triangle with two sides, each being 5 cm and the base is 6cm. The perimeter of the bottom rectangle with the base is 30cm. Find the surface area of the triangular prism.
168cm2
The probability of the soccer team Grizzlies winning the period is 35%. What are the odds in favor and against the Grizzlies winning the period?
Odds in favor= 7:13
Odds in favor=13:7
2x2-12x+10
2(x-5)(x-1)
((4x+3)/2)+(2(7x+2)/3)=1
x=3/4
A scientist needs to make 56% of 200mL acid solution. The scientist mixes 40% acid solution and 60% acid solution. How many milliliters of each solution must be mixed to make 56% acid solution.
The scientist needs to mix 40mL of 40% solution and 160mL of 60% solution to make 56% acid solution.
A cylindrical tube has a height of 12cm. The larger radius is 10cm and the smaller radius is 6cm. Find the surface area and give your answer to the nearest tenths.
1407.4cm2
A coin is tossed, a tetrahedron is rolled, and a spinner with numbers 1,2,3,4,5 is spun. Suppose the tetrahedron is marked with consecutive numbers on each face. List all possible outcomes.
H11, H12, H13, H14, H15, H21, H22, H23, H24, H25, H31, H32, H33, H34, H35, H41, H42, H43, H44, H45, T11, T12, T13, T14, T15, T21, T22, T23, T24, T25, T31, T32, T33, T34, T35, T41, T42, T43, T44, T45
6x2+13x-5
(2x+5)(3x-1)
((2x+10)/4)+((4x+11)/3)+(5(2x+2)/12)+(2(3x+4)/4)=8
x=2
A riverboat took 3h to travel 48km down a river with a current and 4h to make the return trip against the current. Find the speed of the boat still in water and the speed of the current.
The speed of the boat still in water is 10km/h and the speed of the current is 2km/h.
Explain clearly how to find the surface area of a cone.
The cone has a circle whose formula who is simply πr2,but what is the area of the part with the slant(s or l). Well if you unroll or flatten that part that many times, you would get a segment of a circle as a result. You can see that when you flatten or unroll the cone part, the slant becomes the radius of the segment. Then, we keep on dividing the segment infinite times. Due to the being cut into triangles infinite times, the triangles are small and their height is the slant. So the formula is A=(b1s)/2+(b2s)/2+(b3s)/2+...+(bns)/2 When grouping, you get the formula. A=s/2(b1+b2+b3+...+bn). b1+b2+b3+ ...+bn =C(circumference) as the bases together add up the circumference 2πr. So (s/2)*2πr, you cross out the twos and get πrs. SA of cone equals to πrs+πr2.
What is a simulation? What are odds? What are odds in favor and against? Explain.
A simulation is an experiment that is used to model a real-life situation to estimate the probability of an event. Odds is about the likelihood of an event occurring. Odds in favor is the ratio of number of favorable outcomes to unfavorable while odds against is the opposite.
Factor: 2a3b5c2d+4a2b4c5d-16ab7c3d2+a4b9c
2ab4c(a2bcd+2ac4d-8b3c2d2+ab4)