How many sixteens are in 15/16
How do u solve 24tenths-1 one 3 tenths
What is the sum of the first eight terms of a geometric series whose first term is 3 and whose common ratio is 1/2?
Answer:
[tex]\frac{765}{128}[/tex]
Step-by-step explanation:
We have been given that 1st term of a geometric series is 3 and common difference is 1/2 . We are asked to find the sum of 1st 8 terms of the given series.
We will use geometric series formula to solve our given problem.
[tex]S_n=\frac{a_1(1-r^n)}{1-r}[/tex]
Upon substituting our given values in the above formula we will get,
[tex]S_8=\frac{3(1-(\frac{1}{2})^8)}{1-\frac{1}{2}}[/tex]
[tex]S_8=\frac{3(1-\frac{1^8}{2}^8)}{\frac{2-1}{2}}[/tex]
[tex]S_8=\frac{3(1-\frac{1}{256})}{\frac{1}{2}}[/tex]
[tex]S_8=\frac{3(\frac{256-1}{256})}{\frac{1}{2}}[/tex]
[tex]S_8=\frac{3(\frac{255}{256})}{\frac{1}{2}}[/tex]
[tex]S_8=3(\frac{255}{256}\times\frac{2}{1})[/tex]
[tex]S_8=3(\frac{255}{128})[/tex]
[tex]S_8=\frac{765}{128}[/tex]
Therefore, the sum of our given series is [tex]\frac{765}{128}[/tex].
A european outlet supplies 220 v (rms) at 50 hz. how many times per second is the magnitude of the voltage equal to 220 v
Explains how many times per second the magnitude of the voltage equals 220 V in a European outlet at 50 Hz frequency.
Explanation:The frequency at which the magnitude of the voltage is equal to 220 V is:
Convert the given 220 V (rms) to peak voltage: 220 V x √2 = 311.13 VSince the voltage alternates sinusoidally, it will reach 311.13 V twice per cycle (positive and negative peaks).For a 50 Hz frequency, the number of times the magnitude of the voltage equals 220 V will be 2 x 50 = 100 times per second.Alana spent 21 dollars of her 300 dollar paycheck on a gift . What percent of her paycheck was spent on the gift
at the metal-casting company where i work, i must set up a conveyor system to move castings from the furnace to the heat treatment area 55 yards away. the castings cool at the rate of 0.03 degrees fahrehnheit per second and must not be allowed to cool more that 7 degree's fahrenheit before being heat rtreated. what is the minimum speed per second that the conveyor must move?
The ratio is boys to girls is 3:5. If there are 24 boys how many girls are in the class
Mrs marks has 9 1/4 ounces of fertilizer for her plants. She plans on using 3/4 ounce of fertilizer for each plant. How many plants can she fertilize?
which statement describes the function below f(x)=2x^3-3x+1
The given function is f(x)=2x^3+2x^2-x. In this case, the highest degree among the terms is 3. According to the Fundamental Theorem of Algebra, the number of zeros or roots of the equation is equal to the highest degree among the terms. Hence for every value of y, there are 3 equivalent x's. The answer thus is B. It is a many-to-one function.
a company must select 4 candidates to interview from a list of 12, which consist of 8 men and 4 women.
How many selections of 4 candidates regardless of gender?
How many selections are possible, if 2 women must be selected?
How many selections are possible, if at least 2 women must be selected?
Which second-degree polynomial function has a leading coefficient of –1 and root 5 with multiplicity 2?
Answer:
f(x) = 2x2 – 4x – 30
Step-by-step explanation:
Got it right
Why do you sometimes have only one multiplication sentence for an array?
Evaluate the polynomial xyz^2-z when x=6, y=-4, and z=-2
Which metric unit would you use to measure: 1.The length of a newspaper. 2. The height of a lamp post. 3. The length of a bus route. 4. The width of a ruler.
One slice of cheese pizza contains 310 calories. A medium-size orange has one-fifth that number of calories. How many calories are in a medium-size orange? -Please help me understand!
What is the largest place value of 585
Write the whole number as an equivalent fraction with the indicated denominator.
how can you use a mapping diagram to determine the domain and the range of a relation?
The method of using a mapping diagram to determine the domain and the range of a relation is outlined in; Steps 1 to 3 below.
A mapping diagram is one that shows how the elements are paired. Furthermore It is drawn like a flow chart for a function to depict the input and output values.Now, mapping diagrams consists of two parallel columns. The first column is one that represents the domain of a function while the second column represents the range of the function.
Now the steps in using a mapping diagram to determine the domain and the range of a relation are;
Step 1: Draw the mapping diagram for the given function relation.Step 2: A relation from the mapping diagram will be tagged as a function if each element in the domain column is paired with only one element in the range columnStep 3: However, if an element in the domain column of the mapping diagram can be paired to than 1 element in the range column, then the relation is said to not be a function.Read more about mapping diagrams at; https://brainly.com/question/1625866
store decreased its price on a computer by $112 to $478. What was the original price
Answer:
$590.
Step-by-step explanation:
Let x be the original price of computer.
We have been given that a store decreased its price on a computer by $112 to $478.
This means x minus 112 equals to 478. We can represent this information in an equation as:
[tex]x-\$112=\$478[/tex]
Let us add $112 to both sides of our equation.
[tex]x-\$112+\$112=\$478+\$112[/tex]
[tex]x=\$590[/tex]
Therefore, the original price of computer was $590.
an office has an area 120 square meters and a width of 12 meters write an equation to represent the area
Anne is comparing savings accounts. One account has an interest rate of 1.2 percent compounded yearly, and one account has an interest rate of 1.2 percent compounded monthly. Which account will earn more money in interest?
Final answer:
An account with an interest rate of 1.2 percent compounded monthly will earn more money than one compounded yearly because of how compound interest works, earning 'interest on interest' throughout the year.
Explanation:
The student's question asks which savings account would earn more money, one with an interest rate of 1.2 percent compounded yearly, or one with the same interest rate but compounded monthly. When interest is compounded, it means the bank pays interest on both the original amount of money and any interest that account has already earned. With compounded interest, you end up earning interest on interest.
For the account with yearly compounding at a rate of 1.2 percent, the formula to calculate the amount after one year would be A = P(1 + r/n)^(nt), where P is the principal amount, r is the annual interest rate (decimal), n is the number of times interest is compounded per year, and t is the time in years. In this case, n is 1 because the interest is compounded annually. Therefore, the amount after one year would be A = P(1 + 0.012/1)^(1×1) or A = P(1.012).
For the monthly compounded account, the same formula applies, but n would be 12 because the interest is compounded monthly. So, the amount after one year would be A = P(1 + 0.012/12)^(12×1).
When you perform these calculations, the account with the monthly compounding will yield a slightly higher amount than the annually compounded account because interest is being added more frequently. Each month's interest is then earning interest in the following months, leading to a process known as 'interest on interest'. Though the difference may not be substantial for small amounts and low interest rates, over longer periods, or with higher rates and balances, the difference can become significant.
Suppose you go shopping for a new futon bed for your apartment/home. The model you really like happens to be on sale for $675. It's original price is $900. What percent of the original price will you save if you purchase it?
Answer:
[tex]25\%[/tex]
Step-by-step explanation:
Given: you go shopping for a new futon bed for your apartment/home.The model you really like happens to be on sale for [tex]\$675[/tex]. It's original price is [tex]\$900[/tex].
To Find: What percent of the original price will you save if you purchase it.
Solution:
Original price of model [tex]=\$900[/tex]
discounted price of model on sale [tex]=\$675[/tex]
Now,
money saved by buying model from sale [tex]=\text{original price}-\text{price on sale}[/tex]
[tex]900-675[/tex]
[tex]\$225[/tex]
percentage of the original price saved [tex]=\frac{\text{Amount saved}}{\text{original price of model}}\times100[/tex]
putting values
[tex]\frac{225}{900}\times100[/tex]
[tex]\frac{225}{9}[/tex]
[tex]25\%[/tex]
[tex]25\%[/tex] of original price can be saved if model is purchased from sale.
What is the equation of a line, in point-slope form, that passes through (−2, −6) and has a slope of 13 ?
A)y−2=13(x−6)
B) y+6=13(x+2)
C) y−6=13(x−2)
D) y+2=13(x+6)
how do i graph y=1/2Sinø/2?
Beth purchased a computer, and its value depreciated exponentially each year. Beth will sketch a graph of the situation, where x represents the number of years since she purchased the computer, and y represents its value that year.
Beth will only sketch the graph in the quadrant or quadrants for which it makes sense to.
In which quadrant or quadrants will Beth sketch the graph?
1. Quadrants I and IV only
2. Quadrant I only
3. Quadrants I, II, III, and IV
4. Quadrants I and II only
Please help, thank you
So we need a quadrant where x is positive and y in positive. It is the first quadrant.
Answer choice 2 is right.
ANSWER: Answer Choice #2 (Quadrant I only)
The mean water temperature downstream from a discharge pipe at a power plant cooling tower should be no more than 100°f. past experience has indicated that the (population) standard deviation of temperature is 2°f. the water temperature is measured on nine randomly chosen days, and the average temperature is found to be 98°f. if you were to do a hypothesis test using the data from this problem to test the hypothesis that the population mean temperature is 97 degrees f, which test statistic would you need to use?
Actually in this case we will make use of the z test statistic. In which we calculate for the z score and then use the standard normal distribution tables to find for the P value at the calculate z score.
z = (x – u) / s
z = (97 – 98) / 2
z = -0.5
The z value should be greater than 1.65 to for the null hypothesis to be accepted. Hence rejected.
A multivitamin tablet contains 0.16g of vitamin C. How much vitamin C does a bottle of 60 tablets contain?
two pumps of different sizes, working together, can empty a fuel tank in 3 hours. the larger pump can empty the tank in 4 hours less than the smaller one. if the larger pump is not working, how long will it take the smaller pump to do the job alone?
To find the time it takes for the smaller pump to empty the tank alone, we need to first determine the rate of the smaller pump and solve an equation involving the rates of both pumps.
Explanation:Let's denote the rate at which the smaller pump can empty the tank as x gallons per hour. Since the larger pump can empty the tank in 4 hours less than the smaller pump, its rate would be x+4 gallons per hour.
Working together, the total rate at which they can empty the tank is the sum of their individual rates:
x + (x+4) = 1/3 gallons per hour.
Solving this equation will give us the rate of the smaller pump (x), and we can then calculate how long it would take the smaller pump to empty the tank alone.
Final answer:
To find the time it takes for the smaller pump to empty the tank alone, we calculate the combined rate of both pumps and set up an equation based on their separate rates. After solving, we find that it takes the smaller pump 6 hours to empty the tank by itself.
Explanation:
To solve this problem, we can set up a system of equations based on the rates at which the pumps work. Let's denote the time it takes the smaller pump to empty the tank alone as x hours. According to the problem, the larger pump can do this in x - 4 hours. When working together, they can empty the tank in 3 hours.
If the smaller pump's rate is 1/x tanks per hour and the larger pump's rate is 1/(x-4) tanks per hour, the combined rate when they work together is the sum of their individual rates, which is 1/3 tanks per hour.
We can set up the equation as follows:
1/x + 1/(x-4) = 1/3
To solve for x, find a common denominator and combine terms:
(x-4 + x)/(x(x-4)) = 1/3
Multiply all terms by the common denominator x(x-4) to clear the fractions:
2x - 4 = x(x-4)/3
Multiply both sides by 3 to get rid of the fraction:
6x - 12 = x2 - 4x
Rearrange the equation to set it to zero and solve for x:
x² - 10x + 12 = 0
By factoring, we find that x equals 6 or 2. However, since x - 4 must be greater than zero (a pump can't empty a tank in negative time), we discard the solution x = 2 and keep x = 6 hours as the correct answer.
Therefore, the smaller pump will take 6 hours to empty the tank alone.
the difference between two integers is 13 and their sum is 87. What are the two integers
it would be 50 and 37
How many weeks correspond to 56 days? Explain
Answer:
8 weeks
56 days equals 8 weeks or 8x7 = 56
Step-by-step explanation: