A radio station gives away $15 to every 15th caller, $25 to every 25th caller, and free concert tickets to every 100th caller. When will the station first give away all three prizes to one caller? PLEASE HELP. Show your work !!
We want to find the lowest common multiple of 3 numbers.
We will see that the 300th caller will get the 3 prizes.
Ok, we know that:
each 15th caller gets $15.each 25th caller gets $25.each 100th caller gets free concert tickets.We want to see the first time that the 3 prizes will be given at the same time (at the same caller).
This will happen for the lowest common multiple of 15, 25 and 100
Now, to find the lowest common multiple we can use brute force, this is, writing all the multiples of the 3 numbers and watching which one is the first to appear in the 3 lists, but here we can do another thing.
One of the numbers is 100, so its multiples are:
100, 200, 300.
And we know that with 25 we can make all of these numbers:
25*4 = 100
25*8 = 200
25*12 = 300
So all the multiples of 100 are also multiples of 25.
Then we just need to find the first common multiple between 100 and 15.
To get this, we can decompose both numbers as a product of primes:
15 = 3*5
100 = 10*10 = 2*5*2*5
Now we multiply these, but if there is some factor that appears in both numbers we remove it (only from one).
For example, here we can see that the factor 5 appears in both numbers, so we need to remove one of the fives in the product.
We will get:
(3*5)*(2*5*2) = 300
So the lowest common multiple is 300.
This means that the 300th caller will get the 3 prizes.
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The 55 bridesmaids want to make 325 favors for a wedding. Each favor takes about 2 1/2 minutes to make.
About how long will each bridesmaid have to spend making favors?
A.First pic
B.2nd
C.3rd pic
Does a negative exponent result in a negative answer
Using the sample statistics, construct a 9999% confidence interval estimate of the mean body temperature of all healthy humans. do the confidence interval limits contain 98.6degrees°f? what does the sample suggest about the use of 98.6degrees°f as the mean body temperature?
The ratio of the number of Mimi’s Eminem CD’s to the number of Rita’s Eminem CD’s is 5:8. Rita has 18 more Eminem CD’s than Mimi. If Rita gives 22 CD’s to Mimi, what will be the new ratio of the number of Mimi’s Eminem CD’s to Rita’s?
A market sells a six-pound bag of potatoes for $6.27 and a 7.5-pound bag of potatoes for $7.65. Which bag of potatoes is a better buy??
What is the quotient of 59,584 ÷ 14?
A. 4,156
B. 4,256
C. 5,156
D. 5,256
Answer:
B
Step-by-step explanation:
We can divide using the calculator by entering in 59, 584 first followed by 14 before the division sign.
We can also perform long division:
__4256_____
14 | 59, 584
-56____
35
-28____
78
-70____
84
-84____
0
The independent variable of a data set is s, while the dependent variable is t. Which of these is an explanatory variable?
A. s
B. t
C. Both s and t
D. neither s and t
Answer: S
Step-by-step explanation:
On Ap
find cos B.
a. cosB= 41/40
b. cosB=9/41
c. cosB=40/41
d. cosB=9/40
Sanjay rides his bike to work 15 kilometers in two days. He works five days per week. How many weeks will Sanjay need to ride his bike to work in order to ride 150 kilometers?
Sanjay needs to ride his bike for 3 weeks to cover a distance of
150 kilometers.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, Sanjay rides his bike to work 15 kilometers in two days.
∴ In one day he rides (15/2) = 7.5 kilometers.
So, to ride his bike for 150 kilometers he needs (150/7.5) = 20 days.
We know 1 week is 7 days.
∴ Sanjay needs (20/7) = 2.86 weeks, but weeks comes in integers and we'll choose 3 weeks as in 2 weeks he won't be able to cover a distance of 150 kilometers.
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James has 24 shirts, 18 pairs of pants , and 16 pairs of shoes in his closet, but one oc the shirts is his favorite. How many combinations of shirt, pants and shoes are possible assuming james wears his favorite shirt
multiply number of pants and number of shoes
18 * 16 = 288 combinations
Bernard solved the equation 5x+(-4)=6x+4 using algebra tiles. Which explains why Bernard added 5 negative x-tiles to both sides in the first step of the solution?
A) He wanted to create zero pairs on the left side of the equation to get a positive coefficient of x on the right side.
B) He wanted to combine more negative tiles with the 4 negative tiles on the left side of the equation.
C) He wanted to remove the larger coefficient on the left side of the equation.
D) He wanted to have 10 x-tiles on the left side of the equation.
Answer:
a
Step-by-step explanation:
if dont want to read
Ellen garcia earns $23.68 an hour as an assistant aircraft mechanic at a local airport. she must work _____ hours a week to earn $850 a week. (enter only the number and round to the nearest whole hour.)
divide the amount she wants to make ( 850) by her hourly pay (23.68)
850 / 23.68 = 35.895
rounded to the nearest whole hour is 36 hours
Sal brought $7.50 to the fair and Karma brought $8.75 to the fair. Which expression shows the total amount they brought?
A) $8.75 - $7.50 = $16.25
B) $8.75 + $7.50 = $15.25
C) $8.75 - $7.50 = $1.25
D) $8.75 + $7.50 = $16.25
Answer:
The answer to the question is a
Lester worked 12 hours last week at the grocery store and earned $93.00. if he continues to earn the same hourly pay, how many additional hours must he work to earn another$62.00?lester worked 12 hours last week at the grocery store and earned $93.00. if he continues to earn the same hourly pay, how many additional hours must he work to earn another$62.00?
The expression 0.00222 x 10^n is greater than 2 (and n is an integer). what is the smallest possible value for n
Suppose you have already been waiting for one hour for a taxi. what is the probability that one arrives within the next 10 minutes?
The probability of one arrives within the next 10 minutes when he already been waiting for one jour for a taxi is,
P (X > 70 | X > 60) = P (X > 10) = 1 – P (X ≤ 10) = 1 – {1 – e ^ -((1 / 10) 10)} = e ^ -1
= 0.3679
The probability of one arrives within the next 10 minutes when he already been waiting for one hour for a taxi is 0.3679
20 POINTS if you answer!!!!
Clarence sells yearly subscriptions to a particular magazine. He sells at least 10 and no more than 25 subscriptions each week. The function f(t)=48tf(t)=48t represents the amount of money earned for selling t subscriptions each week. What is the practical range of the function?
Answer:
All multiples of 48 between 480 and 1200, inclusive
Step-by-step explanation:
I took the test;)
The practical range of the function is [480, 1200].
Explanation:The function f(t)=48t represents the amount of money earned by Clarence for selling t subscriptions each week. To find the practical range of the function, we need to determine the minimum and maximum value of t that satisfy the given conditions. Since Clarence sells at least 10 and no more than 25 subscriptions each week, the practical range of the function is [480, 1200]. This means that the amount of money earned by Clarence each week can range from $480 to $1200.
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in an isosceles triangle there are two sided, called legs, that are the same length. the 3rd side is the base. if an isosceles triangle has a perimeter 345 cm and the base length 85 cm. what is the length of each leg
Answer:130
Step-by-step explanation:
The graph shows the number of each kind of book in Hero's personal library. A book is chosen randomly. What is the probability that the book chosen is a biography?
A)2/15
B)4/15
C)1/30
D)1/4
Answer: A is the right answer .Probability of the book chosen is a biography is [tex]\frac{2}{15}[/tex].
Step-by-step explanation:
According to the given graph or pie chart
The number of biography books=4
Total books= Romance books+ Science fiction books+ Biography books+Adventure books =2+14+4+10=30
Let B be the event of choosing a biography book then
Probability of the book chosen is a biography P(B)=[tex]=\frac{biography\ books}{total\ books}=\frac{4}{30}=\frac{2}{15}[/tex]
Therefore, Probability of the book chosen is a biography is [tex]\frac{2}{15}[/tex].
From the graph, it is found that there is a [tex]\mathbf{\frac{2}{15}}[/tex] probability that the book chosen is a biography, and the correct option is given by option A.
A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem:
There are 4 + 2 + 10 + 14 = 30 books in the hero's library.Of those, 4 are biographies.[tex]p = \frac{4}{30} = \frac{2}{15}[/tex]
Thus:
[tex]\mathbf{\frac{2}{15}}[/tex] probability that the book chosen is a biography, and the correct option is given by option A.
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Which pair of angles shares ray A-F as a common side?
Given : FA is a ray.
Find out the pair of angles share the common side FA.
To proof
As shown in the diagram
∠ BAF and ∠DAF are th.e pair of angles shares FA as a common side
REASON
Adjacent Angles are those angles that share a common side, a common vertex, and no common interior points.
as ∠ BAF and ∠DAF shares common vertex A and common side FA.
Therefore
∠ BAF and ∠DAF are th.e pair of angles shares FA as a common side
A researcher wants to know if the average time in jail for robbery has increased from what it was when the average sentence was 7 years. he obtains data on 400 more-recent robberies and finds an average time served of 7.5 years. find a 95% confidence interval for the average time served (assume jail time follows a normal distribution with standard deviation 3 years).
At 95% confidence interval, the z score is 1.96. Using the formula:
Confidence Interval = x ± z s / sqrt (n)
where x is the average time served, s is standard deviation and n is number of samples
Confidence interval = 7.5 ± (1.96 * 3) / sqrt (400)
Confidence interval = 7.5 ± 0.294
Confidence interval = 7.206 to 7.794
Beatrice's house is assessed at $102,000 and her property tax rate is 3.6%. How much are her annual property taxes?
Answer:
The annual property taxes is $3672 .
Step-by-step explanation:
As given in the question
Beatrice's house is assessed at $102,000 and her property tax rate is 3.6%.
3.6% is written in the decimal form
[tex]= \frac{3.6}{100}[/tex]
= 0.036
Property tax price = 0.036 × $102000
= $3672
Therefore the annual property taxes is $3672 .
Felicia installed a new pool for $17,190 using a 12-month deferred payment plan with an interest rate of 18.67%. What is the balance after the deferment period if payments of $589 are made each month?
a. $10,122.00
b. $20,688.76
c. $13,620.76
d. $17,190.00
Answer:
a. $10,122.00
Step-by-step explanation:
By definition the deferment period is a time during which a borrower does not have to pay interest or repay the principal on a loan.
In this case the balance should be the initial value $17,190, but Felicia made 12 payments of $589 each one.
So, $589 x 12 = $ 7,068.
$17,190- $ 7,068 = $10,122
−3.1+(−0.35)
Write your answer as a decimal.
The answer in decimal to the expression −3.1+(−0.35) is - 3.45.
What is decimal?A decimal is a number with a whole and a fractional component. Decimal numbers, which are in between integers, are used to express the numerical value of full and partially whole amounts.
Given:
The expression: - 3.1 + (-0.35)
Use the sign convention given below to solve the above expression,
[tex]+ + - =[/tex] sign of the larger number,
[tex]-+- = -[/tex]
[tex]+\times - = -[/tex]
Here when the bracket opens use the second sign convention,
- 3.1 - 0.35 = - 3.45
Therefore, the answer in decimal to the expression −3.1+(−0.35) is - 3.45.
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3h = 7 ( 2/7 - 3/7h ) -10 what does the variable equal
A marble is drawn at random from the bag shown below. The bag contains 3 green, 4 yellow, 5 blue, and 8 pink marbles.What is the probability that the marble drawn is a green or blue?
3 + 4+ 5+8 = 20 total marbles
3 green +5 blue = 8 marbles
probability = 8/20 reduces to 2/5
Need both answers please
What is 6b/24b to the second in simplest form?
Write an expression to find the difference in the maximum area and minimum area of a nys high school soccer field. Then evaluate the expression.
Max length 100yards
Max length 120 yards
Minimum width 55 yards
Maximum width 80 yards
The difference between the maximum and minimum area of the soccer field is found by calculating the maximum and minimum area using the given dimensions, and then subtracting the minimum area from the maximum area. Result is 4100 square yards.
Explanation:First, the area of a rectangle (like a soccer field) can be found with the formula Area = Length x Width. To find the difference between the maximum area and the minimum area of the field, we'll need to do two calculations.
For the maximum area, we'll use the maximum length of 120 yards and the maximum width of 80 yards: Max Area = 120 yards x 80 yards = 9600 square yards.
For the minimum area, we'll use the minimum length of 100 yards and the minimum width of 55 yards: Min Area = 100 yards x 55 yards = 5500 square yards.
Now you subtract the minimum area from the maximum area: 9600 square yards - 5500 square yards = 4100 square yards. This is the difference in area between the smallest and largest possible soccer fields.
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