The amounts of people in attendance are given as follows:
Children: 190.Parents: 140.Grandparents: 70.How to obtain the amounts?The amounts are obtained by a system of equations, for which the variables are given as follows:
Variable x: amount of children.Variable y: amount of parents.Variable z: amount of grandparents.There were 400 people total, hence:
x + y + z = 400.
There were twice as many parents as grandparents, hence:
y = 2z.
50 more children than parents, hence:
x = y + 50
x = 2z + 50.
Replacing on the first equation, the value of z is obtained as follows:
2z + 50 + 2z + z = 400
5z = 350
z = 70.
Then the values of x and y are given as follows:
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Cellular phone service is available for $71 per month for 1793 minutes. What is the
monthly cost per minute? Round your answer to the nearest tenth of a cent.
Answer:
0.039 or 0.040
Step-by-step explanation:
this is due to how when u get things like 3.9 and you need to round u just round up bye it to get the closest answer
Miriana rolled two fair number cubes for one experiment. She rolled a three then a six 7 times in 180 experiments. How many more times did she roll this sequence than what the theoretical probability would have predicted?
Miriana rolled the sequence of 3 and then 6 two more times than the theoretical probability would have predicted.
The theoretical probability of rolling a three-on-one number cube is 1/6, and the same is true for rolling a six. Since the two rolls are independent,
The probability of rolling a three and then a six in the sequence is the product of the probabilities: (1/6) x (1/6) = 1/36.
To find the expected number of times this sequence would occur in 180 experiments, we multiply the probability by the number of experiments: (1/36) x 180 = 5.
So, if Miriana had rolled the number of cubes according to the theoretical probability, we would have expected her to roll the sequence of 3 and then 6 five times in 180 experiments.
However, she actually rolled this sequence 7 times, so she rolled it 2 more times than the theoretical probability would have predicted.
Therefore, Miriana rolled the sequence of 3 and then 6 two more times than the theoretical probability would have predicted.
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4x+4y=16 into slope-intercept form, simplifying all fractions.
Answer:
y = -x + 4
Step-by-step explanation:
The slope-intercept form is y = mx + b
4x + 4y = 16
4y = - 4x + 16
y = -x + 4
So, the answer y = -x + 4
Graph the following features: Slope = − 2 −2 Y-intercept = 3 3
Answer: graphed and attached
Step-by-step explanation:
to graph a y intercept and slope, first find the y intercept on the graph and place your point. here the y intercept is 3, so (0, 3) because x=0 at a y intercept.
next use slope to find your next point. slope of -2 is the same as -2/1 or down -2 and right +1. so from your y intercept of 3, go down -2 and right 1 and place your point (1, 1). do this again for a 3rd point at (2, -1).
graph is attached.
just a quick answer
The time it will take for him to have enough money for the project is given as follows:
t = 8.5 years.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
P is the principal, which is the value of deposit/loan/....r is the interest rate, as a decimal value.n is the number of times that interest is compounded per year, annually n = 1, semi-annually n = 2, quarterly n = 4, monthly n = 12.The parameters for this problem are given as follows:
P = 4000, r = 0.062, n = 2, A(t) = 6720.
Hence the time needed is obtained as follows:
[tex]4000\left(1 + \frac{0.062}{2}\right)^{2t} = 6720[/tex]
(1.031)^2t = 672/400
(1.031)^2t = 1.68
2tlog(1.031) = log(1.68)
t = log(1.68)/[2 x log(1.031)]
t = 8.5 years.
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Three janitors work the night shift at the local hospital. Working alone, it takes Marla five more hours than it takes Tom, and it takes Bob four times as long as it takes Marla. So in one hour, Tom can clean 1 1 of the building. Marla can clean of the building and Bob can clean of the building. If x + 5 4x + 20 all three janitors work together, how much of the building can they clean in one hour?
The time it takes (1/x) + (1/(x + 5)) + (1/(4x + 20))
How to solve for the expressionFrom the question,
Marla takes 5 hours more than Tom: M = T + 5
Bob takes 4 times as long as Marla: B = 4M
work is inversely proportional to the time hence
Tom: 1/T
Marla: 1/M
Bob: 1/B
When we express this,
Marla: 1/(T + 5)
Bob: 1/(4*(T + 5))
We would have to solve for the total work in a given hour
= (1/T) + (1/(T + 5)) + (1/(4*(T + 5))
In one hour, Tom cаn clеan 1/х оf thе building, Mаrlа cаn clеan 1/(x + 5) оf thе building, and Вob cаn clеan 1/(4х + 20) оf thе building.
then 1/T = 1/x
1/(T + 5) = 1/(x + 5)
1/(4*(T + 5)) = 1/(4x + 20)
The expression would be written as:
work in one hour = (1/x) + (1/(x + 5)) + (1/(4x + 20))
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CAN SOMEONE HELP WITH THIS QUESTION?✨
The numeric value of the function f(x) at x = 5 is given as follows:
f(5) = 74.75.
How to obtain the function f(x)?The second derivative of the function f(x) is given as follows:
f''(x) = 2x + 6sin(x).
Integrating the second derivative, the first derivative of the function is given as follows:
f'(x) = x² - 6cos(x) + K.
When x = 0, y' = 2, hence the constant K is given as follows:
2 = -6 + K
K = 8.
Hence:
f'(x) = x² - 6cos(x) + 8.
Integrating the first derivative, the function is given as follows:
f(x) = x³/3 - 6sin(x) + 8x + K.
When x = 0, y = 4, hence the constant K is given as follows:
K = 4.
Then:
f(x) = x³/3 - 6sin(x) + 8x + 4.
The numeric value at x = 5 is given as follows:
f(5) = 5³/5 - 6sin(5) + 8(5) + 4
f(5) = 74.75.
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The variables x and y vary inversely. Use the given values to write an equation relating x and y. Then find y when x = 2.
x = 4
y = -1
The value of y when x = 2 is -2.
We are given that;
x = 4
y = -1
Now,
To write an equation relating x and y for inverse variation, you can use the formula123:
xy = k
where k is a constant.
To find the value of k, you can use the given values of x and y:
x = 4
y = -1
xy = k
(4)(-1) = k
k = -4
So, the equation relating x and y is:
xy = -4
To find y when x = 2, you can substitute x = 2 in the equation and solve for y:
xy = -4
(2)y = -4
y = -4/2
y = -2
Therefore, by the given equations the answer will be -2.
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(Score for Question 2: ____ of 7 points) 2. Aisha and Jordan do some research to find out the prices and sizes of carpet tiles and rugs for the floor of the treehouse. Carpet Tiles Rugs • Each square tile has a side length of 1.5 feet. • They can only use whole tiles. • Each tile costs $5.75. • Each 3 feet by 5 feet rug costs $35.99. • Each 4 feet by 6 feet rug costs $55.99. (a) How many carpet tiles do they need to cover as much of the floor as possible? You can use the grid to help you. Each square on the grid has a side length of 1 foot. What is the area of the greatest amount of floor they can cover with carpet tiles?
Aisha and Jordan need 63 carpet tiles to cover the maximum amount of floor with the whole tiles.
To find the area of the greatest amount of floor that can be covered with carpet tiles, we need to figure out how many tiles can fit in that area. Since each tile has a side length of 1.5 feet, we can divide the grid into squares with side lengths of 1.5 feet to see how many tiles can fit.
Dividing the grid in this way, we can see that the area of each square is 2.25 square feet (1.5 ft x 1.5 ft). To find the maximum area that can be covered with whole tiles, we need to find the dimensions of the largest rectangle that can be formed using these squares.
In the grid, the longest side that can be formed using whole tiles is 9 squares long (13.5 feet), and the shortest side that can be formed using whole tiles is 7 squares long (10.5 feet). Therefore, the maximum area that can be covered with whole tiles is:
Area = Length x Width = 13.5 ft x 10.5 ft = 141.75 square feet
To find out how many tiles are needed to cover this area, we need to divide the area by the area of each tile:
Number of tiles = Area / Area of each tile = 141.75 sq ft / 2.25 sq ft per tile = 63 tiles
Therefore, Aisha and Jordan need 63 carpet tiles to cover the maximum amount of floor with the whole tiles.
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pls help due today, select the correct option
Answer: 2b.[tex]\frac{1}{a^{18} }[/tex]
what kind of number is -15/3?
A) whole number
B) integer
C) rational
D) irrational
Answer:
Rational
Step-by-step explanation:
Improper fractions are always rational.
What is the length of AB
The length of AB in the right triangle is 8 units.
How to find the side of a right triangle?The sides of a right angle triangle can be found as follows:
The right angle triangle has one of its angles as 30 degrees. The side AB can be found using trigonometric ratios.
Hence,
sin 30 = opposite / hypotenuse
where
opposite side = AB
hypotenuse side = 16 units
Therefore,
sin 30 = AB / 16
cross multiply
AB = 16 sin 30
AB = 16 × 0.5
AB = 8 units
Therefore,
AB = 8 units
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70 decreased by twice chai’s height
The statement "70 decreased by twice chai’s height" as an expression is 70 - 2c
Writing the statement as an expressionFrom the question, we have the following parameters that can be used in our computation:
70 decreased by twice chai’s height
Represent chai’s height with c
So, we have the following representation
70 decreased by 2c
When the above statement is then represented as an expression, we have the following
Expression: 70 - 2c
Hence, the expression of the statement "70 decreased by twice chai’s height" is 70 - 2c
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l want the solution
The equation of tangent line related to the parametric equations is equal to y = 3 · x - 22.
How to find the equation of a tangent line
In this question we find the case of two parametric equations evaluated at t = - 1, whose tangent line equation must be found. Equation of the tangent line is introduced below:
y = m · x + b
Where:
x - Independent variable.y - Dependent variable.m - Slopeb - Intercept.First, determine the slope of the tangent line:
dx / dt = 1 + 2 · t
dx / dt = 1 - 2
dx / dt = - 1
dy / dt = 2 · t - 1
dy / dt = - 2 - 1
dy / dt = - 3
m = (dy / dt) / (dx / dt)
m = (- 3) / (- 1)
m = 3
Second, evaluate the parametric functions at t = - 1:
x = - 1 + (- 1)² + 8
x = 8
y = (- 1)² - (- 1)
y = 2
Third, determine the intercept of the tangent line:
b = y - m · x
(m = 3, x = 8, y = 2)
b = 2 - 3 · 8
b = 2 - 24
b = - 22
Fourth, write the equation of the tangent line:
y = 3 · x - 22
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Suppose there are four shelves of books in a library with 12 books, 18 books, 25 books, and 30 books respectively. In how many ways can a person choose three books, one from each shelf? Explain the rule used to solve the problem.
Answer:
Step-by-step explanation:
To solve this problem, we can use the multiplication principle of counting, which states that if there are k choices for one task and m choices for a second task, then there are k x m choices for both tasks combined.
In this case, we can apply this principle to each shelf of books, as there are different numbers of books on each shelf. For the first shelf, there are 12 choices, for the second shelf there are 18 choices, for the third shelf there are 25 choices, and for the fourth shelf there are 30 choices.
To choose one book from each shelf, we need to multiply the number of choices for each shelf together, which gives us:
12 x 18 x 25 x 30 = 16,200,000
Therefore, there are 16,200,000 ways to choose three books, one from each shelf, in the library.
The total number of ways of choosing three books , one from each shelf is given by A = 162,000 ways
What are Combinations?The number of ways of selecting r objects from n unlike objects is given by combinations
ⁿCₓ = n! / ( ( n - x )! x! )
where
n = total number of objects
x = number of choosing objects from the set
Given data ,
There are 12 ways to choose a book from the first shelf, 18 ways to choose a book from the second shelf, 25 ways to choose a book from the third shelf, and 30 ways to choose a book from the fourth shelf
So , the total number of ways = 12 x 18 x 25 x 30
A = 162,000 ways
Hence , the combination is solved and there are 162,000 ways
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Create an equation that has an initial value of 10 and has a rate of change of 4.
The equation that has an initial value of 10 and has a rate of change of 4 is y= 4x+ 10.
We have,
Initial value= 10
Rate pf change= 4
We know from slope intercept form
y= mx+ b
where is m is slope or rate of change and b is y intercept or initial value.
So, we can take m = 4 and b= 10
Then, the required equation is
y= 4x +10.
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The difference in length of a spring on a pogo stick from its non-compressed length when a teenager is jumping on it after θ seconds can be described by the function f of theta equals 2 times sine theta plus radical 2 period
Part A: Determine all values where the pogo stick's spring will be equal to its non-compressed length. (5 points)
Part B: If the angle was doubled, that is θ became 2θ, what are the solutions in the interval [0, 2π)? How do these compare to the original function? (5 points)
Part C: A toddler is jumping on another pogo stick whose length of its spring can be represented by the function g of theta equals 1 minus cosine squared theta plus radical 2 period At what times are the springs from the original pogo stick and the toddler's pogo stick lengths equal? (5 points)
The values of θ for different conditions were calculated with the help of trigonometric functions.
Given that;
The difference in length of a spring on a pogo stick from its non-compressed length when a teenager is jumping on it after θ seconds can be described by the function,
f (θ) = 2 sin θ + √ 2
Hence, We can simplify as;
A) Function is,
f (θ) = 2 sin θ + √ 2
f (θ) = 2 sin θ + √ 2 = 0
2 sin θ + √ 2 = 0
2 sin θ = - √ 2
sin θ = - 1/√2
θ = nπ ± π/4
Where, n = 1, 3, 5, 7, ...
So, At θ = nπ ± π/4 pogo stick's spring will be equal to its non compressed length.
2) If the angle was doubled, the function will look like this,
f (θ) = 2 sin 2θ + √ 2
f (θ) = 2 sin 2θ + √ 2 = 0
2 sin 2θ + √ 2 = 0
2 sin 2θ = - √ 2
sin 2θ = - 1/√2
θ = nπ/2 + π/8
Where, n = 1, 3, 5, 7, ...
n = 1;
θ = π/2 + π/8
θ = 5π/8
n = 2;
θ = π + π//8
θ = 9π/8
Hence, Solutions are, 5π/8, 9π/8, ...
3) g (θ) = 1 - cos²θ + √2
g (θ) = sin²θ + √2
sin²θ + √2 = 2 sinθ + √2
sin²θ - 2 sinθ= 0
sinθ (sinθ - 2) = 0
sinθ = 0
θ = nπ
Where, n = 1, 3, 5, 7, ..
So, θ = nπ , the lengths of springs from the original pogo stick and the toddler's pogo stick are equal.
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I need help with this question
Which of the following is not a money market mutual fund?(1 point)
Responses
a pension fund that tracks growth stocks
a fund with a minimum investment that tracks the value of cash
a fund that tracks the S&P 500
a fund that tracks commodities such as gold and silver
Answer:
Step-by-step explanation:
1. $4,076.92
2. Assets = Liabilities + Equity
3. They can be used to make online purchases.
4. by using an emergency fund for this unplanned expense
5. a fund with a minimum investment that tracks the value of cash (This question)
6. 1930s
7. Banks because they are highly regulated by the government, so the loan terms will not be predatory.
8. their vacation cabin
9. You should shop around for the best overall deal.
10. If you use a credit card, it is easy to run up huge debts.
11. They are tied directly to your bank account.
12. preventative care
13. $100,000 per person bodily injury, $300,000 per incident for bodily injury, $50,000 for property damage
14. how long the coverage lasts, how much the premium costs, and the cash value
15. 1-year renewable group term life
16. Identity thieves can intercept unencrypted data being sent to Wi-Fi hot spots.
17. Wells Fargo employees were opening unauthorized deposit and credit accounts for its customers.
18. 2 year in state community college degree
19. tuition assistance
20. -a sundae, -movie tickets
Explanation: All of these answers are correct!
Personal Finance Semester Exam
5/11/2023
Set up an equation for x and solve to the nearest degree
In the right triangle, the value of x is approximately 64°
Trigonometry: Solving for the value of xFrom the question, we are to set up an equation for x and then solve for the value of x.
To determine the value of x, we will use SOH CAH TOA
sin (angle) = Opposite / Hypotenuse
cos (angle) = Adjacent / Hypotenuse
tan (angle) = Opposite / Adjacent
In the given diagram,
x is the included angle
Adjacent = 12
Opposite = 25
Thus,
We can write that
tan (x) = 25/12
tan (x) = 2.0833
x = tan⁻¹ (2.0833)
x = 64.3586
x ≈ 64° (to the nearest degree)
Hence,
The value of x is approximately 64°
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Which account will make more money, an account that starts out with $4,500 with a 7.75% APR
compounded monthly or an account that begins with $5,500 with a 6.75% APR continuously
compounded? Calculate the two accounts for 10yrs, 20yrs, 50yrs, 85yrs.
Answer:
second account makes more for the first 20 years; after 20.6 years, the first account makes more.first account: 10 yrs: $9743; 20 yrs: $21096; 50 yrs: $214,137; 85 yrs: $3,198,369second account: 10 yrs: $10802; 20 yrs: $21216; 50 yrs: $160,734; 85 yrs: $1,706,582Step-by-step explanation:
You want to compare the future values of two accounts after 10, 20, 50, and 85 years:
$4500 at 7.75%, compounded monthly$5500 at 6.75%, compounded continuouslyCompounded monthlyThe formula for account value with compounding monthly is ...
A = P(1 +r/12)^(12t) . . . . . . principal P invested at rate r for t years
A = 4500(1 +0.075/12)^(12·t) . . . . . using given values for P and r
The first line of calculator output shown in the attachment gives the value after 10, 20, 50, and 85 years.
Compounded continuouslyThe formula for account value with continuous compounding is ...
A = P·e^(rt)
A = 5500·e^(0.0675t) . . . . . using given values for P and r
The second line of calculator output shown in the attachment gives the value after 10, 20, 50, and 85 years.
You will notice this (second) account has higher value up to 20 years, then lower value after that.
The account with the higher interest rate will make more money after the "break-even" period of about 20.6 years.
__
Additional comment
We have rounded the account values to the nearest dollar. For the purpose of value comparison, three significant figures would be sufficient.
The second attachment shows the different account values over the long term. You can see the higher interest rate really makes a difference.
The third attachment shows the shorter-term account values, and the "break-even" time period of about 20.6 years, when the values in both accounts are about $22,063.
Please help me I have no idea how to do it
The length QT of the given chords is determined as 14.5.
What is the length QT?The length QT is calculated by applying the following formula for intersecting chord theorem.
QS x QT = OR x TR
Substitute the given values;
10.5QT = 10(OR)
We don't know the length of the radius, so we are going to form another equation.
Since O is the center, angle QRT is a right angle, and we will apply Pythagoras theorem do determine the length QT.
Also, QS = QR
QT² = TR² + QR²
QT² = 10² + 10.5²
QT = √ (10² + 10.5²)
QT = 14.5
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Divide the following polynomials (x^4-x²-6)/ (x² + 8)
Answer:
Step-by-step explanation:
which choice represents the fraction below as a single exponential expression?
Answer:
C
Step-by-step explanation:
Let f(g(x)) = 3sin (pi/4(x − 1)) and g(f(x)) = pi/4(3 sin(x) − 1). Find a single formula for f and a single formula for g so that both compositions hold true.
Assume that g(x) does not equal x and f(x) does not equal x.
The single formulas for f and g so that both compositions hold true are f(x) = 3sin(x) and g(x) = π/4(x − 1)
Calculating the functions f(x) and g(x)From the question, we have the following parameters that can be used in our computation:
f(g(x)) = 3sin (pi/4(x − 1))
g(f(x)) = pi/4(3 sin(x) − 1)
Express pi as π
So, we have
f(g(x)) = 3sin (π/4(x − 1))
g(f(x)) = π/4(3 sin(x) − 1)
In f(g(x)) = 3sin (π/4(x − 1)), replace the expression in bracket with g(x)
So, we have
f(g(x)) = 3sin (g(x))
This means that
f(x) = 3sin(x) and also, it means
g(x) = π/4(x − 1)
Hence, the single formulas that both compositions hold true are f(x) = 3sin(x) and g(x) = π/4(x − 1)
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The diameter of a circle is 9 cm. Find the circumference to the nearest tenth to the nearest tenth
Answer:28
Step-by-step explanation:
•C= 2(3.14 x r)
•C= 2(3.14 x4.5)
•C=2(14.13)
•C=28.26
need help with number 19
The probability of picking L and another A with replacement is: 2/49
Probability of picking A and then another A with replacement is: 1/49
How to find the probability of selection?We are given the letter DALLAS.
There are a total of 7 letters. Thus, the probability of picking L is:
2/7
Probability of picking A after that with replacement is: 1/7
Thus, probability of picking L and another A with replacement is:
(2/7) * (1/7) = 2/49
Probability of picking A and then another A with replacement is:
(1/7) * (1/7) = 1/49
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The same honey is sold in 2 different size jars. Large jar=540 for £4.10 small jar= 360 for £2.81 which jar is the best value for money?
The large jar has better value for money than the smaller one.
Which jar is the best value for money?To see which jar is the best value for the money, we need to take the quotient between the cost of each jar and the size. The smaller that value gets, the best value we have.
For the first jar we have:
q = £4.10/540 = 0.0075
For the second jar we have:
q' = £2.81/360 = 0.0078
Then we can see that the large jar has the best value for money.
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Answer is below ⬇️.
We can see here that filling up the remaining spaces:
AB ≅ CD: Opposite sides are congruent.
∠ABC and ∠BCD are supplementary: Consecutive angles are supplementary.
What is an angle?An angle is actually known to be a geometric figure that is formed by the joining together of two rays or endpoints which are known as vertex.
The sides or legs of the angle are known to be make up the rays.
Angles are actually known to be measured in degrees, with a full circle containing 360 degrees.
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geometry please helpp
Answer:
(1)
Step-by-step explanation:
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