Answer:
The mean is all the numbers added together divided by the number of numbers. Greater the numbers the greater the mean. Since the goal of the game is to have as few centimeters away as possible the lowest number (107 or Robin) is winning
Step-by-step explanation:
Answer:
Evelyn has the greater mean. It indicates that, on average, her objects landed farther away from the center than Robin’s. This difference means that Robin is winning the game.
Step-by-step explanation:
this is the answer on the curst platform
GEOMETRY! PLEASE SHOW YOUR WORK. (updated picture)
Given:
The base of the given triangle has two part:
Left( left side of the hypotenuse) = 25
Right ( right side of the hypotenuse) = x
The altitude (h) = 60
To find the value of x.
Formula:
By Altitude rule we know that, the altitude of a triangle is mean proportional between the right and left part of the hypotenuse,
[tex]\frac{left}{altitude} =\frac{altitude}{right}[/tex]
Now,
Putting,
left = 25, altitude = 60 and right = x we get,
[tex]\frac{25}{60} =\frac{60}{x}[/tex]
or, [tex](25)(x )=(60)(60)[/tex] [ by cross multiplication]
or, [tex]x = \frac{3600}{25}[/tex]
or, [tex]x = 144[/tex]
Hence,
The value of x is 144.
Answer:
x = 144
Step-by-step explanation:
Height Theorem
60² = 25·x
3600 = 25x
x = 3600 : 25
x = 144
A cow walks 1/2 mile in 1/4 of an hour. How many miles will the cow walk in 1 hour?
the cow will walk 2 miles
Step-by-step explanation:
half a mile - 0.5 miles
1/4 of an hour = 0.5 miles
2/4 of an hour = 1 Miles
3/4 of an hour = 1.5 miles
4/4 of an hour (one hour) = 2 miles
0.5 × 4 = 2
Nick wants to build a rectangular enclosure for his animals. one side of the pen will be against the barn, so he needs no fence on that side. the other three sides will be enclosed with wire fencing. if nick has 700 feet of fencing, you can find the dimensions that maximize the area of the enclosure.
Answer:
350 ft long facing the barn and 175 ft wide
Step-by-step explanation:
Let a and b be the length and width of his rectangular fence. Since he has 700 feet of fencing and one side does not need fencing. We have the following constraint equation:
a + 2b = 700
a = 700 - 2b
We want to maximize the following area formula
A = ab
We can substitute a = 700 - 2b
[tex]A = (700 - 2b)b = 700b - 2b^2[/tex]
To find the maximum value of this, simply take the 1st derivative, and set it to 0
A' = 700 - 4b = 0
b = 700 / 4 = 175 ft
a = 700 - 2b = 700 - 350 = 350 ft
Cylindrical tank A has 9/10 of the radius and 9/10 of the height of cylindrical tank B. If tank A can hold 20 gallons, approximately how many gallons can tank B hold?
Answer: Tank B can hold 27.4 gallons
Step-by-step explanation:
Volume of a cylinder = πr^2h
Given that Cylindrical tank A has 9/10 of the radius and 9/10 of the height of cylindrical tank B
Let the radius of A = r
Radius of B = R
Height of A = h
Height of B = H
r = 0.9R and h = 0.9H
Volume of A = πr^2h
= π(0.9R)^2(0.9H)
= 2.29R^2H
Given that tank A can hold 20 gallons, approximately
20 = 2.29R^2H
R^2H = 20/2.29 = 8.73 ..... (1)
Volume of B = πR^2H
Substitutes R^2H in equation (1) into Volume of B
Volume of B = 3.143 × 8.73
Volume of B = 27.4 gallons
Answer: Tank B can hold 27.43 gallons
Step-by-step explanation: Please see the attachments below
Which equation results from applying the secant and
tangent segment theorem to this figure?
O x(x + 2) = (x+4)
O x(x + 4) = (x + 2)
O x(x + 4) = (x + 2)2
O x(2x + 4) = (x + 2)2
22
+
2
Intro
✓ Done
00000000
Answer: x(2x+4) = (x+2)^2
The equation that results from applying the tangent segment theorem to the given figure is; x(2x + 4) = (x + 2)²
What is the correct equation?According to the secant and tangent segment theorem, the square of the tangent line is equal to the product of the secant segments. This is;
Tangent² = whole secant segment × External secant segment
DE² = AD × BD
We are given that;
DE = x
AD = 2x + 4
BD = x + 2
Thus, we have;
x(2x + 4) = (x + 2)²
Read more about segment theorem at; https://brainly.com/question/9330100
What is the shortest distance between points (-2, 1) and (2,-2)?
Select the appropriate response:
A) 1
B) 2
C) 3
D) 5
Distance = SQRT((X2 -x1)^2 + (y2-y1)^2)
Distance = sqrt((2 - (-2)^2) + (-2 - 1)^2))
Distance = sqrt(4^2 + -3^2)
Distance = sqrt(16 + 9)
Distance = sqrt(25)
Distance = 5
Answer is D. (5)
Answer:
D) 5
Step-by-step explanation:
sqrt[(-2 - 2)² + (1 - -2)²]
sqrt(25)
5
The population of a particular country was 22 million in 1985; in 1993, it was 31 million. The exponential growth function A=22e^kt describes the population of this country t years after 1985. Use the fact that 8 years after 1985 the population increased by 9 million to find k to three decimal places.
Answer:
0.043
Step-by-step explanation:
We are given that
Initially when t=0
Then, A=22 million
The population of a country after t years is given by
[tex]A=22e^{kt}[/tex]
When t=8 then A=31 million
Substitute the values
[tex]31=22e^{8k}[/tex]
[tex]\frac{31}{22}=e^{8k}[/tex]
[tex]1.409=e^{8k}[/tex]
[tex]8k=ln(1.409)=0.343[/tex]
[tex]k=\frac{0.343}{8}=0.043[/tex]
Jenelle invested $14600 in two mutual funds Fund A earned 5% profit during the first year, while Fund B suffered a 2.5% loss. If she received a total of $430 profit, how much had she invested in each mutual fund?
Answer:
Therefore she invested $10600 and $4000 in Fund A and Fund B respectively.
Step-by-step explanation:
Given that,
Jenelle invested $14600 in two mutual funds.
Fund A 5% profit during the first year.
Fund B suffered a 2.5% loss.
Let she invested $x in Fund A.
Then the amount of remaining money is =$(14600-x)
So, she invested $(14600-x) in fund B.
Since Fund A 5% profit during the first year.
The amount of profit from fund A is
= Invest amount in fund A × 5%
=[tex]x\times 5\%[/tex]
[tex]=x\times \frac{5}{100}[/tex]
[tex]=\frac{5x}{100}[/tex]
Since Fund B suffered a 2.5% loss.
The amount of loss in fund B is
=Invest amount in fund B ×2.5%
=(14600-x)×2.5%
[tex]=(14600-x)\times \frac{2.5}{100}[/tex]
Total profit
= Amount of profit - Amount of loss
[tex]=\frac{5x}{100}-(14600-x)\times \frac{2.5}{100}[/tex]
[tex]=\frac{5x-(14600-x)2.5}{100}[/tex]
[tex]=\frac{5x-36500+2.5x}{100}[/tex]
[tex]=\frac{7.5x-36500}{100}[/tex]
According to the problem,
[tex]\frac{7.5x-36500}{100}=430[/tex]
[tex]\Rightarrow 7.5x -36,500=430\times 100[/tex]
[tex]\Rightarrow 7.5x =43000+36,500[/tex]
[tex]\Rightarrow 7.5x =79,500[/tex]
[tex]\Rightarrow x =\frac{79,500}{7.5}[/tex]
⇒x=10,600
She invested in fund B = $(14600-10600)=$4000
Therefore she invested $10600 and $4000 in Fund A and Fund B respectively.
Final answer:
Jenelle invested $10,600 in Fund A which earned a 5% profit and $4,000 in Fund B which had a 2.5% loss. We used a system of equations to solve for the amounts invested in each fund, considering the total investment and the overall profit.
Explanation:
To determine how much Jenelle invested in each mutual fund, we can set up a system of linear equations. We will let x be the amount invested in Fund A, which earned a 5% profit, and let y be the amount invested in Fund B, which had a 2.5% loss. The total amount invested is $14,600, so our first equation is:
Equation 1: x + y = 14,600
The total profit earned from both funds is $430. The profit from Fund A is 5% of x, and the loss from Fund B is 2.5% of y. So, the second equation representing the profit is:
Equation 2: 0.05x - 0.025y = 430
To solve these equations, we can use the substitution or elimination method. For simplicity, let's multiply the second equation by 100 to get rid of the decimals:
5x - 2.5y = 43,000
Next, we can solve the equation for y using Equation 1:
y = 14,600 - x
Now we substitute this expression for y in the modified Equation 2:
5x - 2.5(14,600 - x) = 43,000
5x - 36,500 + 2.5x = 43,000
7.5x = 79,500
x = 10,600
Substitute x back into Equation 1 to find y:
10,600 + y = 14,600
y = 4,000
So, Jenelle invested $10,600 in Fund A and $4,000 in Fund B.
What is the surface area of the cylinder with height 5 in and radius 3 in? Round
answer to the nearest thousandth
The surface area of the cylinder with a height of 5 inches and a radius of 3 inches is calculated using the formula A = 2πrh + 2πr² and comes out to approximately 150.796 in² when rounded to the nearest thousandth.
Explanation:To calculate the surface area of a cylinder, we use the formula A = 2πrh + 2πr², where 'r' is the radius and 'h' is the height of the cylinder. Given the height 'h' is 5 inches and the radius 'r' is 3 inches, we substitute these values into the formula.
Calculating the lateral surface area (the area of the side):
A_lateral = 2πrh = 2π(3 in)(5 in) = 30π in².
Calculating the area of the two bases:
A_bases = 2πr² = 2π(3 in)² = 18π in².
Now, add the lateral area and the area of the bases to find the total surface area:
A_total = A_lateral + A_bases = 30π in² + 18π in² = 48π in².
Using π ≈ 3.14159, the total surface area is: A_total ≈ 48(3.14159) = 150.796 in². Rounded to the nearest thousandth, the surface area of the cylinder is 150.796 in².
Ben is 20 years older than Daniel. Ben and Daniel first met two years ago. Three years ago, Ben was 3 times as old as Daniel. How old is Daniel now?
The first thing to do is identify the unnecessary information (that they met 2 years ago).
From there, let's go back three years ago. We'll call Daniel's age x, and Ben's age will be 3x. Ben's age is also equal to x + 20.
3x = x+ 20
2x = 20
x = 10
Daniel was 10 three years ago, and Ben was 30. Now, Ben is 33.
Solve for x.
Geometry
Answer:
x =17
Step-by-step explanation:
Given shape is of a irregular hexagon.
Sum of all angles of an irregular hexagon
[tex]=(6 - 2) \times 180 \degree = 4 \times 180 \degree = 720 \degree \\ \\ \therefore \: (6x - 2)\degree + (7x + 19)\degree + 116 \degree \\ \: \: \: + (5x + 36)\degree + (8x - 1)\degree + 110 \degree \\ \: \: \: = 720 \degree \\ \\ \therefore \:(26x + 52)\degree + 226\degree = 720 \degree \\ \\ \therefore \:26x\degree + 278\degree = 720 \degree \\ \\ \therefore \:26x\degree = 720 \degree - 278\degree \\ \\ \therefore \:26x\degree = 442 \degree \\ \\ \therefore \:x = \frac{442\degree}{26\degree} \\ \\ \huge \red{ \boxed{\therefore \:x = 17}}[/tex]
Lex was chatting with his friends thomas and mike. He was wondering how much it will cost him to take a taxi from his house to work, a total of 12 km. Thomas and mike both recently tok a taxi from the same company that charge a intial fee and also a constant rate per km travelled. Neither can remember how much the rates were but they have the receipt. Thomas traveled 10km and paid %24.50. Mike traveled 15km and paid $35. How much wwill Lex pay to travel a distance of 12km.
Answer:
$28.3
Step-by-step explanation:
x=rate for 1km
y=initial fee
Mike: $35 for 15km -> 35 = 15x + y
Thomas: $24.50 for 10km -> 24.50 = 10x + y
Using those two equations we see the following:
Mike paid $10.5 more for 5 more km. The initial fee remains unchanged, so we can calculate the rate for 1km, which is 10.5/5=2.1.
35 = 15x + y
24.50 = 10x + y
10.5 = 5x
2.1=x
Using that value with one of the original equations we can calculate the initial fee.
35 = 15x + y
35 = 15*2.1 + y
35 = 31.5 + y
3.5 = y
Mike paid 15*2.1=31.5 ($2.1 for every km) plus the initial fee, his total was $35.
We subtract the 31.5 from the 35(total) and get the initial fee, which is $3.5.
Let's see what Lex will pay:
Km travelled times 2.1 (the rate for 1km) plus 3.5 (the initial fee).
12*2.1 + 3.5 = 28.3
Lex will pay $28.3 for the same taxi company to travel 12 km.
Final answer:
Using a system of equations derived from his friends' taxi fares, it's determined that Lex will pay $28.70 for a 12 km taxi ride to work.
Explanation:
Lex wants to find out how much it will cost him to take a taxi for a distance of 12 km using the information from his friends' taxi rides from the same company. Thomas traveled 10 km and paid $24.50, and Mike traveled 15 km and paid $35. We can solve this problem by setting up a system of linear equations and solving for the unknowns, which are the initial fee and the rate per kilometer.
Step 1: Set up the equations
Let x represent the initial fee and y represent the rate per km. We get two equations from the information given:
10y + x = 24.50 (Thomas's trip)
15y + x = 35 (Mike's trip)
Step 2: Solve the system of equations
Subtract the first equation from the second to eliminate x and solve for y:
5y = 10.50
y = 2.10
Substitute y = 2.10 back into one of the equations to solve for x:
10(2.10) + x = 24.50
x = 3.50
Step 3: Calculate Lex's cost
Now that we have x = 3.50 and y = 2.10, we can calculate the cost for Lex:
12(2.10) + 3.50 = $28.70
Therefore, Lex will pay $28.70 for his taxi ride to work.
Suppose Paul kicks a soccer ball straight up into the air with an initial velocity of 96 feet per second. The function f(x) = -16t2 + 96t gives the height, in feet, of the soccer ball after t seconds. This function is shown in the graph below.
How long will it take for the ball to hit the ground? Write your answer as an integer.
The ball will come to ground after 6 seconds.
We have a function of time given by -
f(x) = [tex]-16t^{2} +96t[/tex]
that gives the height of the ball in feet at ' t ' second.
We have to find out after how much time the ball will hit the ground.
In the question given to us above, the type of motion discussed is called ?The type of motion discussed in the above question is a two - dimensional projectile motion.
We have - h(t) = f(x) = [tex]-16t^{2} +96t[/tex]
Now, in order to find out the time at which the ball will hit the ground again, we will equate h(t) = f(x) = 0
[tex]-16t^{2} +96t=0\\-16t(t - 6)=0\\-16t =0\;\;\;\;\;\;t -6 = 0[/tex]
Now, time can never be 0.
Hence -
t - 6 = 0
t = 6 seconds.
Hence, the ball will come to ground after 6 seconds.
To solve more questions on projectile motion, visit the link below -
https://brainly.com/question/12496840
#SPJ2
h(x) = 3x + 2; Find h(-5)
Answer:
h(-5) = -13
Step-by-step explanation:
h(x) = 3x + 2
Let x = -5
h(-5) = 3(-5) +2
= -15 +2
= -13
Answer:
H(-5)= -13
Step-by-step explanation:
1) Plug in -5 for the variable X
2) Then Solve
h(-5)= 3(-5) + 2
h(-5)= -15 + 2
H(-5)= -13
Hope this Help!
The second hand on a clock is 8 \text{ cm}8 cm8, space, c, m long. What is the distance the tip of the second hand travels in 101010 minutes? Round your answer to the nearest \text{cm}cmc, m. \text{cm}cm
Answer:
The distance the tip of the second hand travels in 10 minutes is 502 cm.
Step-by-step explanation:
Given : The second hand on a clock is 8 cm long.
To find : What is the distance the tip of the second hand travels in 10 minutes?
Solution :
The circumference of clock is [tex]C=2\pi r[/tex]
The radius is r=8 cm
[tex]C=2\times 8\times \pi[/tex]
[tex]C=16\pi[/tex]
i.e. in 1 minute it cover [tex]16\pi[/tex]
In 10 minutes it cover [tex]16\pi\times 10[/tex]
In 10 minutes it cover [tex]160\times 3.14[/tex]
In 10 minutes it cover [tex]502.4[/tex]
Therefore, the distance the tip of the second hand travels in 10 minutes is 502 cm.
For a trip, one high school rented and filled 5 vans and 3 buses with 114 students. Another high school instead fit its 247 students into 7 vans and 8 buses. With each bus and van seating the same number of students, how many students could a bus carry? How many students could a van carry?
Answer:
Therefore a bus could carry 23 number of students and a van could carry 9 number of students.
Step-by-step explanation:
Assume a van and a bus could carry x and y number of students respectively.
Given that,
For a trip, one high school rented and fits 114 students into 5 van and 3 buses.
So,
A van could carry x number of students
5 van could carry 5x number of students.
A buses van could carry y number of students.
3 buses van could carry 3y number of students.
∴5x+3y=114 ....(1)
Another high school instead fit its 247 students into 7 vans and 8 buses.
A van could carry x number of students
7 van could carry 7x number of students.
A buses van could carry y number of students.
8 buses van could carry 8y number of students.
∴7x+8y=247 ....(2)
∴5x+3y=114 ....(1)
and
7x+8y=247 ....(2)
7 times of equation (1) subtracts from 5 times of equation (2)
35x + 40y = 1235
35x + 21y = 798
- - -
________________
40y-21y=1235-798
⇒19y=437
[tex]\Rightarrow y=\frac{437}{19}[/tex]
[tex]\Rightarrow y=23[/tex]
Putting the value y in equation (1)
5x+3.23=114
⇒5x=114-69
⇒5x=45
[tex]\Rightarrow x=\frac{45}{5}[/tex]
⇒ x=9
Therefore a bus could carry 23 number of students and a van could carry 9 number of students.
What does it mean to say there is an association between characteristics in a two-way frequency table?
Answer:
An "association" exists between two categorical variables if the row (or column) conditional relative frequencies are different for the rows (or columns) of the table. ... If the conditional relative frequencies are nearly equal for all categories, there may be no association between the variables.
Step-by-step explanation:
Write 0.000000123 as a power of 10.
Answer:
1.23 x 10^-7
Step-by-step explanation:
you went back 7 so its negative
Answer:
123 x 10^(-9)
Step-by-step explanation:
just put it in scientific notations and you will get 123 x 10^(-9)
Simplify 6xy - 20y + 7z - 8x + 25y - 11z
Answer:
6xy - 8x + 5y - 4z
Step-by-step explanation:
6xy - 20y + 7z - 8x + 25y - 11z
Group the ones with the variable first to make an equation:
6xy - 8x - 20y + 25y + 7z - 11z
Solve the equation
6xy - 8x +5y - 4z
Kenyl covers the front of a circular bulletin board with fabric that costs 1.48 per square foot. The bulletin board has a radius of 2.5 feet. Kenyl will count only the cost the exact amount of fabric he uses What is the cost of the fabric. Round to the nearest cent.
Answer:
29
Step-by-step explanation:
In this question we are trying to calculate the cost of exact amount of fabric used given the cost per area of the fabric.
To answer this question mathematically, we need to know the area of the bulletin board. To do this , we employ a mathematical approach. We know that the bulletin board is circular in shape from the question and thus we calculate the area of this shape.
Mathematically, the area of the circular bulletin board is pi * r^2 where r refers to the radius. From the question, we can identify that this radius is 2.5 feet. let’s insert this into the equation we have.
mathematically A = 2.5^2 * pi = 19.63 sq. feet
The cost of the fabric per square feet is 1.48.
now the cost for this area that we have will be 1.48 * 19.63 = 29.0524
This is nearest to 29
A triangle has a 40 degree angle and a 35 degree angle. What is the measure of the third triangle?
Answer:
105
Step-by-step explanation:
The sum of the angles of a triangle add to 180 degrees
<1 + <2 + <3 = 180
40 + 35 + <3 = 180
Combine like terms
75+ <3 = 180
Subtract 75 from each side
75-75 + <3 = 180-75
<3 = 105
Answer:
105 degrees
Step-by-step explanation:
In a triangle, the three interior angles always add to 180°
40 + 35 = 75
180-75 = 105 degrees
Rearrange the equation so r is the independent variable.
10q-5r=30
Independent variable is the variable that you change.
Dependent variable is the variable you measure that results from or depends on the independent variable.
Since you want "r" to be the independent variable, you isolate/get the variable "q" by itself in the equation: [this is because "r" would be the variable that changes, and "q" would be the variable you find/measure that depends on "r"]
10q - 5r = 30 Add 5r on both sides
10q = 5r + 20 Divide 10 on both sides to get "q" by itself
[tex]q=\frac{5r+30}{10}[/tex]
[tex]q=\frac{5r}{10} +3[/tex]
[tex]q=\frac{1}{2} r+3[/tex]
The value of r is the independent variable is [tex]\rm \dfrac{10q-30}{5}[/tex].
Given that,
Equation; [tex]\rm 10q-5r = 30[/tex]
We have to determine,
The value of r is the independent variable.
According to the question,
A variable whose values do not change is known as independent changes. They have their own value, which is not changed with the equation.
To determine the value of r is the independent variable following all the steps given below.
Therefore,
The value of r is the independent variable is,
[tex]\rm 10q-5r = 30\\\\10q=30+5r\\\\q = \dfrac{30+5r}{10}\\\\q = \dfrac{5}{5} \times \dfrac{6+r}{2}\\\\ q = \dfrac{1}{2}r + \dfrac{6}{2}\\\\ q = \dfrac{1}{2}r + 3\\\\[/tex]
Hence, The value of r is the independent variable is [tex]\rm \dfrac{1}{2}r + 3[/tex].
For more details refer to the link given below.
https://brainly.com/question/18826122
A young sumo wrestler decided to go on a special high-protein diet to gain weight rapidly and at a constant rate. After 8 88 months, he weighed 138 138138 kilograms. He started at 90 9090 kilograms. Let y yy represent the sumo wrestler's weight (in kilograms) after x xx months. Complete the equation for the relationship between the weight and number of months.
Final answer:
The equation representing the sumo wrestler's weight gain over time is y = 6x + 90, where y is the weight after x months, starting at 90 kilograms and increasing by 6 kilograms each month.
Explanation:
The student has provided the initial and final weights of the sumo wrestler, as well as the duration in months over which the weight gain occurred. We can use this information to calculate the rate of weight gain per month and create an equation to represent this relationship. The sumo wrestler started at 90 kilograms and reached 138 kilograms after 8 months. The equation will be in the form of y = mx + b, where m is the slope (rate of weight gain) and b is the y-intercept (initial weight).
To calculate the slope, m, we use the formula:
m = (Final weight - Initial weight) / (Final time - Initial time)
In this case, m = (138 kg - 90 kg) / (8 months - 0 months) = 48 kg / 8 months = 6 kg/month.
The y-intercept, b, is the initial weight of the sumo wrestler, which is 90 kilograms.
Therefore, the complete equation is y = 6x + 90, where y represents the sumo wrestler's weight after x months.
The national touring company Spice on Ice visited Seattle, Washington, last year. THe producers held a special promotional ticket sale for one hour. During this time, adult tickets sold for $5, junior tickets (ages 9-17) sold for $2, and children’s tickets (ages 0-8) sold for the ridiculously low price of 10 cents. During this sale, 120 tickets sold for exactly $119. How many of each kind of ticket were sold during the sale?
Answer: Adult 84
Children 34
Junior 2
Step-by-step explanation:
Adults tickets = $5
Children tickets = $.10
Junior tickets = $2
Total ticket sold = 120 at $119
Total tickets price
= Adults + junior + children
= 5 + 2 + 0.10 = 7.1
No of tickets sold for adults
= 5 / 7.1 × 119
= 84
No of tickets sold for children
= 2/7.1 × 119
= 34
No of tickets sold for junior
= 0.10/7.1 × 119
= 2
Total ticket sold
= 84 + 34 + 2
= 120
Final answer:
During the sale, 22 adult tickets, 67 junior tickets, and 31 children's tickets were sold.
Explanation:
Let's assume that the number of adult tickets sold is x, the number of junior tickets sold is y, and the number of children's tickets sold is z.
According to the information given, the cost of an adult ticket is $5, the cost of a junior ticket is $2, and the cost of a children's ticket is $0.10 (10 cents).
The total number of tickets sold is 120, so we can write the equation:
x + y + z = 120
Additionally, the total amount collected from the ticket sales is $119, so we can write the equation:
5x + 2y + 0.10z = 119
We now have a system of equations that we can solve to find the values of x, y, and z.
By using substitution or elimination methods, we can find that x = 22, y = 67, and z = 31.
Therefore, during the sale, 22 adult tickets, 67 junior tickets, and 31 children's tickets were sold.
While walking by a classroom, Linda sees two perfect squares written on a blackboard. She notices that their difference is her favorite number, 99. She also notices that there are exactly two other perfect squares between them. What is the sum of the two perfect squares on the blackboard
Answer:
15^2
18^2
Step-by-step explanation:
Answer:
549
Step-by-step explanation:
considering 'n²' to express first square on board.
Remember 'n' is an integer
Now expressing second square with (n+3)² on the board.
(Therefore, The other two perfect squares in between are (n+1)² and (n+2)².
If asking for the difference that is 99:
(n+3)² - n² = 99
Solving for n:
n² + 6n + 9 - n² = 99
6n + 9 = 99
6n = 90
n = 90/6
n = 15
So the perfect squares on the board are:
n² => 15² = 225
(n+3)²=> 18² = 324
The difference between the above is 99
and exactly two other perfect squares (16² = 256 and 17² = 289) are in between.
Thus, the sum of the two perfect squares on the blackboard is,
225 + 324 = 549
A local theater sells out their show. They sell all 500 tickets for a total of $8,070. The tickets were priced at $15 for students, $12 for children, and $18 for adults. If the band sold three times as many adult tickets as children’s tickets, how many of each type was sold?
Answer:
The number tickets sold was 120 student tickets, 95 children tickets and 285 adult tickets.
Step-by-step explanation:
Given:
A local theater sell all 500 tickets for a total of $8,070.
The price of tickets were $15 for students, $12 for children, and $18 for adults.
The adult tickets sold were three times as many as children’s tickets.
Now, to find the number of student tickets, children tickets and adult tickets sold.
Let the number of students ticket be [tex]x.[/tex]
Let the number of children ticket be [tex]y.[/tex]
So, the number of adults ticket be [tex]3y.[/tex]
Now, the total number of tickets sold:
[tex]x+y+3y=500\\\\x+4y=500\\\\x=500-4y\ \ \ ...(1)[/tex]
Now, the total cost of tickets:
[tex]x(15)+y(12)+3y(18)=8070\\\\15x+12y+54y=8070\\\\15x+66y=8070\\\\Substituting\ the\ value\ of\ x\ from\ equation\ (1):\\\\15(500-4y)+66y=8070\\\\7500-60y+66y=8070\\\\7500+6y=8070\\\\Subtracting\ both\ sides\ by\ 7500\ we\ get:\\\\6y=570\\\\Dividing\ both\ sides\ by\ 6\ we\ get:\\\\y=95.[/tex]
Thus, the number of children ticket is 95.
According the adult tickets sold were three times as many as children’s tickets.
Therefore, the number of adult tickets = 95 × 3 = 285.
Now, substituting the value of [tex]x[/tex] in equation (1) to get the number of student tickets:
[tex]x=500-4y\\\\x=500-4(95)\\\\x=500-380\\\\x=120.[/tex]
Hence, the number of student tickets is 120.
Therefore, the number tickets sold was 120 student tickets, 95 children tickets and 285 adult tickets.
The problem can be solved by creating a system of equations representing each type of ticket sales and their respective prices. Three equations are formed from the information provided and are then solved to find the numbers of each type of ticket sold.
Explanation:This problem can be solved using a system of equations, representing each type of ticket sales and their prices. Let's define the variables. Let's let x represent the number of student tickets, y represent the number of children's tickets, and z represent the number of adult tickets.
We know that the total number of tickets sold is 500, so we can form the equation:
x + y + z = 500.
Moreover, we know that the total amount of money made from the tickets is $8070, so we can form the equation:
15x + 12y + 18z = 8070.
Lastly, we know that the theater sold three times as many adult tickets as children's tickets, forming the equation:
z = 3y.
Using these three equations, we can substitute and simplify to find the values of x, y, and z, representing the numbers of student, children, and adult tickets sold respectively.
Learn more about system of equations here:https://brainly.com/question/35467992
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Find the area of a circle with a radius of 3
Either enter an exact answer in terms of π or use 3.143.143.143, point, 14 for π\piπpi and enter your answer as a decimal.
The area of the circle with a radius of 3 is approximately 28.26 square units using the approximation [tex]\( \pi \approx 3.14 \).[/tex]
The area [tex]\(A\)[/tex] of a circle with radius [tex]\(r\)[/tex] is given by the formula:
[tex]\[ A = \pi r^2 \][/tex]
Given that the radius [tex]\(r\)[/tex] is 3, we can substitute this value into the formula:
[tex]\[ A = \pi \times (3)^2 \][/tex]
[tex]\[ A = \pi \times 9 \][/tex]
Using the approximation [tex]\( \pi \approx 3.14 \),[/tex] we can calculate:
[tex]\[ A \approx 3.14 \times 9 \][/tex]
[tex]\[ A \approx 28.26 \][/tex]
Therefore, the area of the circle with a radius of 3 is approximately [tex]\(28.26\).[/tex]
What are the coordinates of Z?
A: (a – c, 0)
B: (c – 2a, 0)
C: (a, 0)
D: (0, b)
A small swimming pool has a circumference of 3π feet. Select the true statement about the pool.
a The radius is 3 ft.
b The diameter is 3 ft.
c The diameter is 1.5 ft.
d The radius is 6 ft.
Answer:
d dfghjkl
Step-by-step explanation:
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5x + 7 < -3 or 3x - 4 > 11
Answer:
x < -2; x > 5
Step-by-step explanation:
5x + 7 < - 3 3x - 4 > 11
-7 -7 +4 +4
5x < - 10 3x > 15
/ 5 /5 /3 /3
x < -2 x > 5
To solve two inequalities: 5x + 7 < -3 and 3x - 4 > 11. The solutions are x < -2 and x > 5, respectively.
1. 5x + 7 < -3
2. 3x - 4 > 11
Let's solve each inequality one by one.
For the first inequality, 5x + 7 < -3, subtract 7 from both sides to get 5x < -10, then divide both sides by 5 to find that x < -2.
For the second inequality, 3x - 4 > 11, add 4 to both sides to obtain 3x > 15, then divide by 3 yielding x > 5.
The solution to the system of inequalities is that x can be any number less than -2 or any number greater than 5.