Proportionately, if $170,500 profits in the second year of operation represent 576% of the company's first-year profits, the first-year profits will be $29,600.
What is a proportion?A proportion describes two ratios equated to each other.
Proportion is a fractional value that compares one value or quantity to another.
The profits for the second year of operation = $170,500
Let the profits for the first year of operation = x
Proportionately, if $170,500 is 576% of x, x = $29,600 ($170,500 ÷ 576%)
Using equations, 5.76x = $170,500
x = $29,600 ($170,500 ÷ 5.76)
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. A and B completed a work together in 5 days. Had A worked at twice the speed and B at half the
speed, it would have taken them four days to complete the job. How much time would it take for
A alone to do the work
So it would take A 10 days to do the whole job alone.
What is equation?An equation is a statement that asserts the equality of two expressions. It typically contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponentiation, etc. The goal of solving an equation is to find the values of the variables that make the equation true. Equations are used in a variety of mathematical contexts, including algebra, calculus, and geometry, as well as in physics, engineering, and many other fields.
Here,
Let's denote A's speed as "a" and B's speed as "b" (in units of work per day). Then, we know that:
In 5 days, A and B together completed the job, so we can write: 5(a + b) = 1 (where 1 represents the whole job).
If A worked at twice the speed (2a) and B worked at half the speed (0.5b), then they would complete the job in 4 days, so we can write: 4(2a + 0.5b) = 1.
We can simplify the second equation by multiplying out the brackets and collecting like terms:
8a + 2b = 1
Now we have two equations with two unknowns. We can solve for one of the variables in terms of the other, and substitute the result into the other equation to find the value of the remaining variable. Let's solve for "b" in terms of "a" from the first equation:
5(a + b) = 1
5b = 1 - 5a
b = (1/5) - a
Now we can substitute this expression for "b" into the second equation:
8a + 2b = 1
8a + 2((1/5) - a) = 1
8a + (2/5) - 2a = 1
6a = (3/5)
a = (1/10)
So A can do 1/10 of the job in one day. To find out how long it would take A to do the whole job alone, we can use the formula:
time = amount of work / rate
Since A can do the whole job alone, the amount of work is 1, and A's rate is 1/10. Therefore:
time = 1 / (1/10)
= 10 days
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The components of v = 210i + 300i represent the respective number of gallons of regular and premium gas sold at a station. The components of w = 2.8i + 2.99i represent the respective prices per gallon for each kind of gas. Find Vw and describe what the answer means in practical terms.
The station earned $1485 in revenue from selling the gas.
In this problem, we are given two vectors, v and w, representing the number of gallons of gas sold at a station and the corresponding prices per gallon, respectively. We are asked to find the dot product of these two vectors, which is a scalar quantity known as the "Vw". We will then interpret the meaning of this dot product in practical terms.
To find the dot product of v and w, we will use the formula:
Vw = v . w = (210)(2.8) + (300)(2.99)
Vw = 588 + 897 = 1485
Therefore, the value of Vw is 1485.
Practical terms: The dot product of two vectors is a scalar quantity that represents the "projection" of one vector onto the other. In this case, the dot product Vw represents the total revenue earned by selling regular and premium gasoline at the given station.
The components of v represent the number of gallons of regular and premium gas sold, while the components of w represent the respective prices per gallon for each kind of gas. Multiplying the number of gallons sold by the price per gallon gives the total revenue earned for each type of gas. Adding these two values together gives the total revenue earned for both types of gas.
Therefore, the dot product Vw represents the total revenue earned by selling all the gas at the given station. In practical terms, this means that the station earned $1485 in revenue from selling the gas.
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It’s due tomorrow I really need help
Answer:
B.
Step-by-step explanation:
As the steps imply,
Step 1 is to first convert the 3.5% (0.035) and then multiply it by 16 to find out by how many grams the amount should decrease (0.035 * 16 = 0.56). Step 2 is to subtract this amount from 16 to find the amount remaining after one hour (16 - 0.56 = 15.44). Step 3 is to convert 4.25% to a decimal (0.0425) and multiply it by the amount remaining at the end of one hour to find out by how many grams this amount should decrease after two hours (0.0425 * 15.44 = 0.6562)Step 4 finally is to subtract this amount from 15.44 to find the amount remaining after two hours (15.44 - 0.6562 = 14.7838)A radioactive substance decays at a continuous rate of 14.4 % per day. After 15 days, what amount of the substance will be left if you started with 140 mg? (a) First write the rate of decay in decimal form. r = (b) Now calculate the remaining amount of the substance. Round your answer to two decimal places.
Answer:(a) The rate of decay is 14.4% per day, which can be written as a decimal by dividing by 100: r = 0.144.
(b) The formula for continuous decay is given by:
A = A₀ * e^(-rt)
where A is the remaining amount of the substance after time t, A₀ is the initial amount, r is the rate of decay, and e is the mathematical constant approximately equal to 2.71828.
Plugging in the given values, we get:
A = 140 * e^(-0.144*15)
A = 140 * e^(-2.16)
A ≈ 47.23
Therefore, after 15 days, approximately 47.23 mg of the radioactive substance will be left, rounded to two decimal places.
Step-by-step explanation:
The earrings that Mrs.Moore wants to buy are $55.00. She won’t buy them until they are at least 45% off. What is the most that Mrs.Moore is willing to spend?
Answer:
$30.25
Step-by-step explanation:
55% of 55$ is $30.25. she wants 45 % off of 55$. which is $24.75. 55-24.75 is 30.25
$30.25
since it's 45% off, you need to subtract 45% from 100%
100%-45%=55%
then turn the % into a decimal
55%/100=0.55
now multiply the original price by 0.55
0.55*55=30.25
At the time of her grandson's birth, a grandmother deposits $14,000 in an account that pays 4.5% compounded
monthly. What will be the value of the account at the child's twenty-first birthday, assuming that no other deposits
or withdrawals are made during this period?
i Click the icon to view some finance formulas.
The value of the account will be $
(Round to the nearest dollar as needed.)
4
Answer:
The value of the account will be $5,628
Step-by-step explanation:
Step-by-step explanation:
we know that
The compound interest formula is equal to
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
substitute in the formula above
therefore
The value of the account will be $5,628
The table represents the quadratic functions f(x) and g(x).
x f(x) g(x)
−8 16 4
−4 4 1
0 0 0
4 4 1
8 16 4
What transformation of f(x) will produce g(x)?
g of x equals one fourth times f of x
g of x equals f of the quantity of one fourth times x end quantity
g(x) = 4f(x)
g(x) = f(4x)
The transformation of f(x) that will produce g(x) is given as follows:
g(x) = f(x)/4.
How to obtain the function g(x)?If we observe at the table, we have that each value of g(x) is one fourth of the value of the function f(x).
Hence the transformation of f(x) that will produce g(x) is given as follows:
g(x) = f(x)/4.
The transformation means that the function g(x) is a vertical compression by a factor of 4 of the function f(x).
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WILL AWARD BRAINLIEST!!
The base of a right prism ABC is an isosceles triangle with AB = BC and m∠ACB 35°. The diagonal of lateral face ABA is 18 cm and m∠BAB = 50°. Find the volume of the prism. Round your answer to the nearest cm
Answer:
351 cm^3
Step-by-step explanation:
The base of a right prism ABC is an isosceles triangle with AB = BC and m∠ACB 35°. The diagonal of lateral face ABA is 18 cm and m∠BAB = 50°. Find the volume of the prism. Round your answer to the nearest cm
ChatGPT
Let AB = BC = x be the base of the isosceles triangle ABC. Then, the third side AC is:
AC = 2x * sin(35°)
Using the sine rule in triangle ABA, we have:
AB / sin(50°) = 18 / sin(80°)
Solving for AB, we get:
AB = 18 * sin(50°) / sin(80°)
The height of the prism is AB * cos(35°). Therefore, the volume of the prism is:
V = (1/2) * x^2 * 2x * sin(35°) * AB * cos(35°)
Substituting the values we have calculated, we get:
V = (1/2) * x^2 * 2x * sin(35°) * [18 * sin(50°) / sin(80°)] * cos(35°)
V ≈ 351 cm^3
Therefore, the volume of the prism is approximately 351 cubic centimeters.
Solve the following quadratic equation by completing the square. Simplify the solutions and rationalize denominators, if necessary.
3x^2−30x=−2
The solutions to this quadratic equation are x = √(73/3) + 5 or x = -√(73/3) + 5.
What is a quadratic equation?In Mathematics and Geometry, the standard form of a quadratic equation is represented by the following equation;
ax² + bx + c = 0
Next, we would solve the given quadratic equation by using the completing the square method;
3x² - 30x = -2
By dividing all through by 3, we have:
x² - 10x = -2/3
In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:
x² - 10x + (-10/2)² = -2/3 + (-10/2)²
x² - 10x + 25 = -2/3 + 25
x² - 10x + 25 = 73/3
By simplifying, we have;
(x - 5)² = 73/3
x = √(73/3) + 5 or x = -√(73/3) + 5
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find the area of the shaded region
The area of the shaded region is 51.75 in².
From the figure
Radius of semicircle = √25² - 20²
=√625- 400 = 15 inch
Now, Area of Trapezium = 1/02 ( a +b ) h
= 1/2 (17 + 37) x 15
= 1/2 (54) x 15
= 27 x 15
= 405 in²
Then, Area of Shaded region
= Area of Trapezium - Area of semicircle
= (405 - πr²)
= 405 - 353.25
= 51.75 in²
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what is the probability that either event will occur
The probability that either event will occur is 7/25
What is probability?A probability is a number that reflects the chance or likelihood that a particular event will occur. The certainty of an event is 1 which is equivalent to 100% in percentage.
Probability = sample space /Total outcome
P(A or B) = P(A) +P(B) -P(A and B)
The total element = 25+5+15+5 = 50
therefore total outcome = 50
P(A) = 25/50
P(B) = 15/50
P(A and B) = 5/40
Therefore P(A and B) = 25/50+15/50 - 5/50
= 35/50 = 7/25
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Anna baked 4 batches of cookies with c cookies in each batch she then ate 8 cookies there were 72 cookies left after Anna ate her cookies
The expression for the number of cookies Anna has left is [tex]3c - 8[/tex].
What does an expression means?An expression refers to statement that have minimum of two numbers or variables or both and an operator connecting them.
The total number of cookies Anna baked is:
= 3 batches * c cookies/batch
= 3c cookies
After eating 8 cookies, Anna has left:
= 3c cookies - 8 cookies
So, the expression for the number of cookies Anna has left is [tex]3c - 8[/tex].
Full question "Anna baked 3 batches of cookies with c cookies in each batch she then ate 8 cookies. How many cookies does anna have left write your answer as an expression.
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the probability of rolling a 4 or an even number of the die is thrown 2 times. (6 sided dice)
The probability of rolling a 4 on a single throw of a fair 6-sided die is 1/6, since there is only one way to roll a 4 and there are 6 equally likely outcomes in total.
The probability of rolling an even number on a single throw of a fair 6-sided die is 3/6, or 1/2, since there are three even numbers (2, 4, and 6) out of six possible outcomes.
To find the probability of rolling a 4 or an even number on a single throw, we can add the probabilities of these two events:
P(4 or even) = P(4) + P(even) - P(4 and even)
where P(4 and even) is the probability of rolling a 4 and an even number on the same throw. Since there is only one outcome (rolling a 4), which is not even, this probability is 0.
Therefore:
P(4 or even) = P(4) + P(even) - P(4 and even)
= 1/6 + 1/2 - 0
= 2/3
So the probability of rolling a 4 or an even number on a single throw of a 6-sided die is 2/3.
If the die is thrown 2 times, the probability of rolling a 4 or an even number on both throws is the product of the probabilities of rolling a 4 or an even number on each throw:
P(4 or even on both throws) = P(4 or even) × P(4 or even)
= (2/3) × (2/3)
= 4/9
Therefore, the probability of rolling a 4 or an even number on both throws of a 6-sided die is 4/9.
Graphing Geometry. Show work
A graph of the reflection of line segment AB is shown on the coordinate plane below.
What is a reflection across the x-axis?In Mathematics, a reflection across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate changes from positive to negative.
Furthermore, a reflection across the line y = x would interchange (switch) the x-coordinate and y-coordinate and this is represented by the following transformation rule:
(x, y) → (y, x)
Ordered pair A = (4, -1) → Ordered pair A' = (-1, 4).
Ordered pair B = (4, 5) → Ordered pair B' = (5, 4).
In this exercise, we would use an online graphing calculator to plot the image of line segment AB after a reflection about the line y = x.
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A store has 300 televisions on order, and 90% are high definition. How many televisions on order are high
definition? You may find the bar model useful in completing this problem.
20% 30% 40%
70%
0%
0
10%
30
The store has
50% 60%
high-definition televisions on order.
80%
90%
100%
300
Answer:
90% of 300 = .90 × 300 = 270 high- definition televisions on order.
Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
n = 109, x = 65; 88% confidence
Rounding to three decimal places, the confidence interval is (0.419, 0.574).
How can a confidence interval for a sample proportion be created?The sample proportion, p′ = 0.842, which is the point estimate of the population proportion, must be determined in order to calculate the confidence interval. Given that CL = 0.95 is the requested confidence level, = 1 - CL = 1 - 0.95 = 0.05 ( 2) ( 2) = 0.025.
Confidence interval=proportion±margin of error
CI = p ± ME
The proportion is:
p = x / n
p = 55/110
p = 0.5
Margin of error=critical value × standard error
ME = CV × SE
n > 30, so we can approximate CV with a normal distribution.
At P=88%, CV=1.55.
SE = √(pq / n)
SE = √(0.5 (1−0.5)/110)
SE = 0.048
So the margin of error is:
ME = 1.55 × 0.048
ME = 0.074
So the confidence interval is:
CI = 0.5 ± 0.074
CI = (0.426, 0.574)
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Question:
Use the given degree of confidence and Sample data to construct income confidence interval for the population proportion p. n=110, x=55; 88% confidence
A) 0.426 B)0.442 C)0.425 D)0.421
50 Points! Solve the equation or inequality. Please show as much work as possible. Photo attached. Thank you!
The equation 5ʷ ⁺ ³ = 17 when solved for w is approximately w = 0.41
Solving the equations or inequalities for wFrom the question, we have the following parameters that can be used in our computation:
5ʷ ⁺ ³ = 17
Take the logarithm of both sides of the equation
So, we have
w + 3 = ln(17)/ln(3)
Evaluate the quotient on the left side of the equation
This gives
w + 3 = 2.59
So, we have
-3 + w + 3 = 2.59 - 3
Evaluate
w = 0.41
Hence, the equation when solved for w is approximately w = 0.41
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1. Which of the following is a set or not?
(a) A=Set of tall man
(b) B=Set of beautiful women
(c) C=Set of tall students of class 10
(d) D=Set of counting number
(e) E=Set of good students
(f) F=Set of yellow roses
Which function does the dotted line represent explain how do you know
Answer:
Step-by-step explanation:
An inequality can be represented graphically as a region on one side of a line. Inequalities that use < or > symbols are plotted with a dashed line to show that the line is not included in the region. Inequalities that use ≤ or ≥ symbols are plotted with a solid line to show that the line is included in the region.
Suppose the probability density function of a random variable X is
f(x)=[tex]\left \{ {{cx^{2}, 1\leq x\leq 2 } \atop {0, else}} \right.[/tex]
a. Find the value of constant c
b. Find the value of P(X>3/2)
The value of,
constant c is 3/7 andP(x>3/2) is 27/18Given function f(x) = cx for 1 ≤ x ≤ 2
a) To find the value of constant x, we have to use the following p.d.f condition as shown below,
[tex]\int\limits^a_b {x} \, dx =1[/tex]
here, a is -∞ and b is ∞.
From the above condition to find the value of c,
[tex]\int\limits^2_1{cx^2} \, dx[/tex] = 1
c * [[tex]\frac{x^3}{3}[/tex]]²₁ = 1
c * [8/3 - 1/3] = 1
c * 7/3 = 1
c = 3/7.
b) To find the value of P(x>3/2) we have to substitute the value of 3/2 in the given expression of f(x) = 3/7 * x²
f(3/2) = 3/7 * (3/2)²
= 3/7 * 9/4
= 27/28.
From the above solution, we solved both problems.
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Please help me who knows how to do this
Solve the equation for the indicated variable
X= (simplify your answer)
B = (715x) / (h^2)
Step 1: Get rid of the denominator by multiplying both sides by h^2
(B)(h^2) = 715x
Step 2: Isolate x by dividing both sides by 715
(Bh^2) / 715 = x
Answer: x = Bh^2 / 715
Hope this helps!
How do you find area?
The area of a shape is calculated by calculating the amount of space on the shape
How do you find area?By definitinon, the area of a shape is the amount of space on the shape
using the above as a guide, we have the following:
Area of rectangle = Length * WidthArea of square = Length²Area of triangle = 1/2 * base * heightArea of circle = π * radius²Area of parallelogram = base * heightThere are several formulas to calculate area
The formula to use is dependent on the shape whose area is being calculated
This means that the area of trapezoid cannot be calculated using the area of parallelogram
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Which number is irrational?
0.020202
0.8
0.333...
All the numbers are rational numbers.
We have,
Rational numbers are those numbers that are terminating and recurring non-terminating.
Irrational numbers are those numbers that are non-terminating and non-recurring.
The numbers are:
1)
0.020202
This is non terminating recurring number.
It is a rational number.
2)
0.8
This is a terminating number.
It is a rational number.
3)
0.020202
This is non terminating recurring number.
It is a rational number.
Thus,
All the numbers are rational numbers.
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Help please!!!!
Whoever answers right gets brainliest!
Answer:
25
Step-by-step explanation:
To solve this problem you have to use this formula [tex](\frac{b}{2})^{2}[/tex] it. So in this case b is the term next to the x term. This number is 10. So all we have to do is insert it into the formula. This would give us:
[tex]=(\frac{10}{2})^{2}\\\\=(5)^{2}\\\\= 25[/tex]
The constant term is 25.
Could I get Brainilest, please? I'm trying to get to the expert level
The height y(in feet) of a ball thrown by a child isy=−114x2+2x+3
where x is the horizontal distance in feet from the point at which the ball is thrown.
(a) How high is the ball when it leaves the child's hand? (Hint: Find y
when x=0)
Your answer is y=____
(b) What is the maximum height of the ball? _____
(c) How far from the child does the ball strike the ground?_____
9. (a) The scale model of the rocket stood 54 inches high. What was the height of the actual rocket?
(b) Find the height of the actual rocket in feet.
10. The volume of the rocket in problem 9 is how many times the volume of the model?
The actual rocket height is 1080 inches and the height of the actual rocket is 90 feet.
How to calculate the valueIf the 1/20 scale model of the rocket stands 54 inches high, we can find the height of the actual rocket by multiplying the height of the model by 20:
Actual rocket height = 54 inches x 20 = 1080 inches
In order to convert inches to feet, we divide by 12:
Actual rocket height = 1080 inches / 12 = 90 feet
Therefore, the height of the actual rocket is 90 feet.
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The 1/20 scale model of the rocket stood 54 inches high What was the height of the actual rocket?
(b) Find the height of the actual rocket in feet.
Rebecca invests 600 into an account with a 2.7% interest rate that is compounded quarterly. How much money will she have in this account if she keeps it for 10 years
The accrued value of the account in 10 years is $641.75
Determining the accrued value of the account in 10 yearsFrom the question, we have the following parameters that can be used in our computation:
Rebecca invests 600 in an account2.7% interest compounded quarterlyUsing the above as a guide, we have the following:
Amount = P * (1 + 0.25r)ᵗ
Where
P = Principal = 600
r = Rate = 2.7% = 0.27
t = time = 10
Substitute the known values in the above equation, so, we have the following representation
Amount = 600 * (1 + 0.25 * 0.27)¹⁰
Evaluate
Amount = 641.75
Hence, the amount is 641.75
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Select all equations that have infinitely many solutions
2nd and 4th is correct. Hope you got it!
Part 1
For the experiment of rolling a single fair die, find the probability of being even or divisible by 3.
The probability of rolling an even or divisible by 3 numbers is 2/3
When a single fair die is rolled, there are six possible outcomes:
1, 2, 3, 4, 5, or 6.
Of these outcomes, three are even (2, 4, and 6) and two are divisible by 3 (3 and 6). However, since the number 6 is both even and divisible by 3, we must count it only once to avoid overcounting. Thus, four outcomes are either even or divisible by 3: 2, 3, 4, and 6.
The probability of rolling an even or divisible by 3 number is the sum of the probabilities of these four outcomes, which is:
P(even or divisible by 3) = P(2) + P(3) + P(4) + P(6)
= 1/6 + 1/6 + 1/6 + 1/6
= 4/6
= 2/3
Therefore, the probability of rolling an even or divisible by 3 numbers is 2/3
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