what is 100 . 23/25 x 3/16
carla travels on a high speed train for 30 minutes. If she travels 160 km, how many kilometers will she travel in one hour
plz help
25 Points to answer this question. What are the roots of the equation? x2+24=14x Enter your answers in the boxes. x1= x2=
The roots of the Given quadratic equation are x₁ = -2 and x₂ = -12.
What is a Quadratic equation?ax²+bx+c=0, with a not, equal to 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.
Given a quadratic equation, x² + 24 = 14 x
Simplifying the equation using the factorization method,
=> x² + 24 = 14 x
=> x² +14 x +24 = 0
factorize the "x term"
=> x² +12x + 2x +24 = 0
=> x(x +12)+2(x + 12) = 0
=>(x + 2)(x + 12) = 0
x = -2, -12
thus,
the value of x will be either -12 or -2
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whatcis 72/90 reduced
NEED HELP The value of x is
.
turn 1/8 into a percent
Brainliest Awarded
See attachment
It is the bottom left.
During a laboratory experiment, the average number of radioactive particles passing through a counter in 1 millisecond is 4. what is the probability that 6 particles enter the counter in a given millisecond?
The probability of exactly 6 radioactive particles passing through a counter in 1 millisecond, with an average rate of 4, is approximately 0.1041 or 10.41%.
To find the probability of a specific number of events occurring in a Poisson distribution, use the formula:
P(X = k) = [tex](e^{(-\lambda)} \times \lambda^k) / k![/tex]
Where:
P(X = k) is the probability of observing k events.
e is the base of the natural logarithm, approximately equal to 2.71828.
λ (lambda) is the average rate of events occurring in a given time period.
k is the number of events you want to find the probability for.
k! is the factorial of k.
λ is the average number of radioactive particles passing through the counter in 1 millisecond, which is 4.
So, to find the probability of 6 particles entering the counter in a given millisecond:
P(X = 6) = (e⁻⁴) × 4⁶) / 6!
Let's calculate it step by step:
Calculate 6! (6 factorial):
6! = 6 x 5 x 4 x 3 x 2 x 1
= 720
Calculate e⁻⁴:
e⁻⁴ ≈ 0.01832 (rounded to five decimal places)
Calculate 4⁶:
4⁶ = 4 x 4 x 4 x 4 x 4 x 4
= 4,096
Now, plug these values into the formula:
P(X = 6) = (0.01832 × 4,096) / 720
P(X = 6) ≈ 0.1041
Therefore, the probability that exactly 6 radioactive particles enter the counter in a given millisecond is approximately 0.1041, or about 10.41%.
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adding fractions with denominators of 10 and 100
what is a real world triangle area problem
Final answer:
A real-world problem involving the calculation of a triangle's area could include finding the area of a triangular plot of land to determine how much grass seed is needed for landscaping. By using the formula for the area of a right-angled triangle, we can calculate the area in square meters and subsequently determine the required quantity of grass seed.
Explanation:
Real World Triangle Area Problem
Calculating the area of a triangle is a common problem in real-world applications. For instance, consider a scenario where you need to find the area of a triangular plot of land to determine how much grass seed to purchase for landscaping. If the plot is a right-angled triangle with one leg measuring 50 meters and the other leg measuring 40 meters, you can use the formula for the area of a right-angled triangle, which is ½ × base × height.
In this case, the base would be one leg of the triangle (50 meters), and the height would be the other leg (40 meters). Therefore, the area would be:
Area = ½ × 50 m × 40 m
Area = 25 m × 40 m
Area = 1000 square meters
Knowing the area of the triangular plot, you can then calculate the amount of grass seed needed, based on the recommended seeding rate per square meter. This practical example demonstrates how mathematics, specifically triangular area calculation, is applied in landscaping projects.
Rhono has a part-time job at the local supermarket working 3 hours after school each night and 5 hours on saturdays. His gross hourly pay is $8.75. Estimate and then calculate his next wages for the month, after 20% tax is deducted. Each month his expenses are: Entertainment $35.00, health and beauty $21.00, transport $18.00, clothing $24.00, hire purhases payments $15.75. Calculate the amount Rhono has left over at the end of each month, and how much he would have saved at the end of 12 months.
Rhono earns a net monthly pay of $560.00 after taxes, with monthly expenses totaling $113.75. This leaves him with $446.25 per month, resulting in a total savings of $5,355.00 at the end of 12 months.
Let's calculate Rhono's monthly wages first.Rhono works:
- 3 hours each night after school
- 5 hours on Saturdays
His gross hourly pay is $8.75.
To calculate his monthly wages, we need to find his total hours worked per month.In a week, he works 3 hours × 5 days from Monday to Friday and 5 hours on Saturday,
which totals 15 hours + 5 hours
= 20 hours per week.
In a month (considering approximately 4 weeks per month), he works 20 hours × 4 weeks
= 80 hours per month.
Now, let's calculate his gross monthly income before tax deductions:Gross monthly income = hourly wage × total hours worked per month
Gross monthly income = 8.75 × 80
Gross monthly income = $700
Now, let's calculate the amount of tax that will be deducted.Rhono's gross monthly income is $700, and 20% of this will be deducted.
Tax deduction = 0.20 × 700
Tax deduction = 140
Now, let's calculate his total monthly expenses:Total monthly expenses = 35.00 + 21.00 + 18.00 + 24.00 + 15.75
Total monthly expenses = $113.75
Now, let's calculate the amount Rhono has left over after tax and expenses:Net monthly income = Gross monthly income - Tax deduction - Total monthly expenses
Net monthly income = 700 - 140 - 113.75
Net monthly income = $446.25
This is the amount Rhono has left over at the end of each month.
To calculate how much he would have saved at the end of 12 months, we multiply this amount by 12:Total savings after 12 months = 446.25 × 12
Total savings after 12 months = $5,355
So, Rhono would have saved $5,355 at the end of 12 months.
A toll bridge charges $1.00 for passenger cars and $2.50 for other vehicles. suppose that during daytime hours, 60% of all vehicles are passenger cars. if 25 vehicles cross the bridge during a particular daytime period, what is the resulting expected toll revenue? hint: let ???? = the number of passenger cars out of 25. start by identifying the type of discrete random variable ???? is. then, create a linear function of ???? to represent the toll revenue. finally, find the expected value of the function that represents the toll revenue.
WILL MARK BRAINLIEST FOR CORRECT ANSWER Which statements about the opposite of −12 are true? Select each correct answer. −12 and its opposite are located the same distance from zero on a number line. The opposite of the opposite of −12 is −12 . −12 and its opposite are on located on the same side of zero on a number line. The opposite of −12 is −1 1/2 .
Assume the $12,000 Treasury bill, 7% for 15 weeks. Calculate the effective rate of interest. (Use calendar year. Round your answer to the nearest hundredth percent.)
Answer:
7.25%
Step-by-step explanation:
You want the effective rate of interest on a $12,000 Treasury bill with a nominal interest rate of 7% and maturity in 15 weeks.
InterestThe Treasury computes the selling price of the bill by subtracting the interest from the face value. The interest is computed as "ordinary interest" using a 360-day year. 15 weeks is 105 days.
I = Prt
I = $12000·0.07·(105/360) = $245
Then the cost of the bill is $12,000 -245 = $11,755.
RateUsing the formula for the maturity value with a 365-day year, we have ...
A = P(1 +rt)
12000 = 11755(1 +r(105/365))
Solving for r gives ...
[tex]r=\left(\dfrac{12000}{11755}-1\right)\cdot\left(\dfrac{365}{105}\right)\approx0.0724514\approx\boxed{7.25\%}[/tex]
The effective rate of interest is about 7.25%.
Grass can grow up to six inches in a week depending on temperature, humidity, and time of year. At this rate , how tall will grass grow in 24 days?
Grass can grow up to six inches in a week depending on temperature, humidity, and time of year
We have to calculate how tall will grass grow in 24 days
we know there are seven days in a week
so in one day grass can grow up to 6/7 inches
therefore we could say that grass can grow up to 24*6/7 inches
so the answer is 20.57 inches
so in 24 days grass can grow up to 20.57 inches
Grass can grow approximately 20.58 inches in 24 days.
Explanation:To calculate the height that grass will grow in 24 days, we need to find out how much it grows in 1 week, and then multiply that by the number of weeks in 24 days. If grass can grow up to six inches in a week, we can calculate the height it will grow in 24 days as follows:
Calculate the number of weeks in 24 days: 24 days ÷ 7 days/week = 3.43 weeks (rounded to the nearest hundredth).Multiply the growth per week (6 inches) by the number of weeks: 6 inches/week × 3.43 weeks = 20.58 inches.Therefore, grass will grow approximately 20.58 inches in 24 days.
Exhibit 4-3 x: 10, 12, 6, 8, 9, 11, 13, 13, 5, 0, 1 refer to exhibit 4-3. what is the mean?
Karim was planning for his vacation to the Bahamas. To cover his costs, he took out a $15,800, 4% simple discount note and paid a $40 bank discount. What was the approximate length of his loan in days? Assume a 360-day year.
An acute angle θ is in a right triangle with cos θ =2/3 . What is the value of sec θ?
Final answer:
The secant of an angle is the reciprocal of its cosine. Given cos θ = 2/3 for an acute angle in a right triangle, the sec θ equals 3/2.
Explanation:
In the context of trigonometry, the secant (sec) of an angle is the reciprocal of the cosine (cos) of that angle.
Given that cos θ = 2/3 for an acute angle in a right triangle, we can find the value of sec θ by taking the reciprocal of the cosine value. Hence, the value of sec θ is simply the reciprocal of 2/3, which is 3/2.
A calculus student takes a 20-question, multiple choice test with 5 answer choices for each question. find the mean and standard deviation of the number of questions that he/she gets correct
Leo bought 6 chew toys for his new puppy each chew toy cost $4 how much did Leo spend for the chew toys
Find two numbers, if their sum is 6 and their difference is 36
The two numbers will be 21.5 and -14.5. Addition, subtraction, multiplication, and division are the four basic math operations.
What is an arithmetic operation?Arithmetic is an area of mathematics involving the study of numbers and the different operations that can be performed on them.
Let the two numbers will be x and y
The sum of the two numbers is 7
x+y=7 ------ 1
The difference between the two numbers is 36
x-y=36 -------2
On subtracting the equation 2 by equation 1 we get;
x-y-x-y=36-7
-2y=29
y= -14.5
From equation 1
x+y=7
x-14.5=7
x=7+14.5
x=-21.5
Hence the two numbers will be 21.5 and -14.5.
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Nadia cuts 3 pieces pf equal length from 8 yards of ribbon. How long is each piece?
Answer: Each piece is 2.6 long
Step-by-step explanation: All you have to do is divide 8 and 3 and you will get 2.6
(sorry if i'm wrong)
There were 48 blue, 48 green and 48 yellow crayons. Also there were 72 red crayons and 120 colored pictures. What is the largest number of identical sets can be made of these crayons and pictures?
24 is the largest number of identical sets can be made of these crayons and pictures
What is Number system?A number system is defined as a system of writing to express numbers.
To find out the largest number of identical sets that can be made, we need to determine the common factors of the total number of crayons and pictures.
The prime factorization of 48 is 2 x 2 x 2 x 2 x 3, and since all three colors have the same number of crayons, we can say that there are 48 x 3 = 144 crayons in total.
The prime factorization of 72 is 2 x 2 x 2 x 3 x 3, and the prime factorization of 120 is 2 x 2 x 2 x 3 x 5.
The common factors of 144, 72, and 120 are 2 x 2 x 2 x 3 = 24. This means that we can make 24 identical sets.
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Find the first three iterates of the function f(z) = 2z + (3 - 2i) with an initial value of z0 = 5i.
The first three iterates of the function f(z) = 2z + (3 - 2i) with z0 = 5i are 3 + 8i, 9 + 14i, and 21 + 26i after consecutive substitutions. The first three iterates of the function are 3 + 8i, 9 + 14i, and 21 + 26i.
Explanation:To find the first three iterates of the function f(z) = 2z + (3 - 2i) with the initial value z0 = 5i, we perform successive substitutions into the function.
First iterate (f1): Substitute z0 into f(z)Second iterate (f2): Substitute f1 into f(z)Third iterate (f3): Substitute f2 into f(z)Thus, the first three iterates of the function are 3 + 8i, 9 + 14i, and 21 + 26i.
Final answer:
To find the first three iterates of the function f(z) = 2z + (3 - 2i) with an initial value of z0 = 5i, substitute the initial value into the function to get the first iterate. Then, substitute the first result back into the function to find the second iterate. Finally, substitute the second result back into the function to find the third iterate.
Explanation:
To find the first three iterates of the function f(z) = 2z + (3 - 2i) with an initial value of z0 = 5i, we substitute the initial value into the function:
f(z0) = 2(5i) + (3 - 2i) = 10i + 3 - 2i = 3 + 8i.
Then, we substitute the result back into the function to find the second iterate:
f(3 + 8i) = 2(3 + 8i) + (3 - 2i) = 6 + 16i + 3 - 2i = 9 + 14i.
Finally, we substitute the second result back into the function to find the third iterate:
f(9 + 14i) = 2(9 + 14i) + (3 - 2i) = 18 + 28i + 3 - 2i = 21 + 26i.
Sam counted Out Loud by 6's Jorge counted Out Loud by 8s what are the first three numbers both Sam and George said
How would you write this equation in terms of sin and cos as well as simplify it from there?
(1+cotx)(1-cotx)-csc^2 x
find the unknown in the equation. Blake ×1/6=1/6+1/6+1/6
The height of a triangle is increasing at a rate of 2 cm/min while the area of the triangle is increasing at a rate of 12 square cm/min. at what rate is the base of the triangle changing when the height is 4 centimeters and the area is 12 square centimeters?
When the height of a triangle is 4 cm and the area is 12 square cm, with the height increasing at 2 cm/min and the area increasing at 12 square cm/min, then the base of the triangle is changing at a rate of 5 cm/min.
Explanation:The subject of this question is Mathematics and is at the High School level. This question deals with the concept of related rates in calculus. First and foremost, remember the formula for the area of a triangle, which is A = 1/2bh, where A is the area, b is the base, and h is the height. Since we're given the rate of change of the height (dh/dt=2 cm/min) and the area (dA/dt=12 square cm/min), we can use this information in combination with the formula for the area of a triangle to derive an implicit function representing the rate of change of the base. By differentiating with respect to time t, we get dA/dt = 1/2b dh/dt + 1/2h db/dt. Plugging in the given values and solving for db/dt (the rate of change of the base length), we get db/dt = (2*dA/dt/h) - dh/dt. Then input the specific values at the given point, h = 4 cm and dA/dt = 12 square cm/min, dh/dt = 2 cm/min. The calculation results in db/dt = 5 cm/min. Therefore, the base of the triangle changes at a rate of 5 cm/min when the height is 4 cm and the area is 12 square cm.
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In response to very high demand, a basketball jersey has been marked up by 25% and is now selling for $95.00. How much was the jersey before the mark-up?
76 is the correct answer
The price of the jersey before the mark-up = $76
What is percentage?"A number that can be expressed as a fraction of 100."
What is an equation?"It is a mathematical statement which consists of equal symbol between two algebraic expressions."
For given question,
A basketball jersey has been marked up by 25% and is now selling for $95.00
Let 'm' be the price of the jersey before the mark-up.
So, we get an equation,
⇒ m + (25 percent of m) = 95
25 percent of m
= [tex]\frac{25}{100}\times m[/tex]
= 0.25 m
so, the equation becomes,
⇒ m + 0.25 m = 95
⇒ 1.25 m = 95
⇒ m = 76
Therefore, the price of the jersey before the mark-up = $76
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The Treasury Department auctioned $15 billion in 3-month bills in denominations of $10,000 at a discount rate of 3.750%.
What would be the effective rate of interest? (Use calendar year. Do not round intermediate calculations. Round your answer to the nearest hundredth percent.)