The probability of rolling a sum greater than 9 (Event A) on two fair dice is 1/6, and the probability of rolling a sum divisible by 5 or 6 (Event B) is 1/3.
Explanation:To compute the probability of Event A, where the sum is greater than 9, we first identify the possible combinations that yield a sum greater than 9: (4,6), (5,5), (5,6), (6,4), (6,5), and (6,6). Since there are 6 possible outcomes and 36 total possible outcomes when rolling two dice (6 for the first die × 6 for the second die), the probability is 6/36 or 1/6.
For Event B, we look for sums divisible by 5 or 6. These sums are 5, 6, 10, 12, 15, 18, and 20. The combinations yielding these sums are (1,4), (2,3), (2,6), (3,2), (3,6), (4,1), (4,6), (5,1), (5,5), (6,2), (6,3), (6,6). By counting these results, we have 12 outcomes that meet the Event B criteria out of 36, so the probability is 12/36 or 1/3.
The probability of Event A, the sum being greater than 9, is 1/6, and the probability of Event B, the sum being divisible by 5 or 6, is 1/3.
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Prehistoric cave paintings were discovered in a cave in France. The paint contained
23% of the original carbon-14. The half-life of carbon-14 is 5730 years. Estimate the age of the paintings
A store received 300 containers of milk to be sold by February 1. Each container cost the store $0.79 and sold for $1.55. The store signed a contract with the distributor in which the distributor agreed to a $0.50 refund for every container not sold by February 1. If 270 containers were sold by February 1, how much profit did the store make?
The total profit did the store make is $196.5 and this can be determined by using the formula of profit and using the given data.
Given :
A store received 300 containers of milk to be sold by February 1. Each container cost the store $0.79 and sold for $1.55. The store signed a contract with the distributor in which the distributor agreed to a $0.50 refund for every container not sold by February 1.The formula of profit is given below:
Profit = Revenue - Expenses --- (1)
So, first determine the total cost of the 300 containers.
Total Cost = 300 [tex]\times[/tex] 0.79
= $237
Now, determine the revenue for the 270 sold containers.
Revenue = 270 [tex]\times[/tex] 1.55
= $418.5
Now, the determine the revenue for the 30 unsold containers.
Revenue = 30 [tex]\times[/tex] 0.50
= $15
So, the total revenue is given by:
Total Revenue = 418.5 + 15
= $433.5
Now, substitute the known terms in the equation (1).
Profit = 433.5 - 237
= $196.5
So, the total profit did the store make is $196.5.
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how do you sketch sin, cos and tan waves?
To sketch sin, cos, and tan waves, determine the amplitude and period, plot points on a graph, and connect them smoothly.
Explanation:For a sine wave, start by determining the amplitude (A), which represents the maximum height of the wave. Then calculate the period (T) using 2π divided by the coefficient of x. Use these values to plot points on a graph and connect them smoothly to create a wave.For a cosine wave, follow the same steps as for a sine wave, but start with a different phase shift (p) value in the wave function.To sketch a tangent wave, start by finding the period using π divided by the coefficient of x. Plot points on a graph using tangent values at regular intervals and connect them.Find an identity for cos(4t) in terms of cos(t)
cos(4t)=
a recipe for 1 batch of cookies uses 3/4 cup of sugar. How many cups of sugar are used 1 1/2 batches of these cookies?
The ratio will remain constant. Then the number of cups of sugar used in 1 and 1/2 batches of these cookies will be 1.125.
What are ratio and proportion?A ratio is an ordered set of integers a and b expressed as a/b, with b never equaling 0. A percentage is a mathematical expression in which two things are equal.
A recipe for 1 batch of cookies uses 3/4 cup of sugar.
Then the number of cups of sugar used in 1 and 1/2 batches of these cookies will be
We know that the ratio will remain constant. Then we have
1 and 1/2 can be written as 3/2.
Let x be the number of cups of sugar.
Then the ratio will be
[tex]\rm \dfrac{x}{3/2} = \dfrac{3/4}{1}\\\\x = \dfrac{3 \times 3}{2 \times 4}[/tex]
Then we have
x = 9/8
x = 1.125 cups of sugar
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A carpenter has 166 doorknobs in his workshop. Of those doorknobs, 98 are round and the rest are square. If he wants to place 7 square doorknobs in each bin, about how many bins would he need?
Answer:
about 10 bins
Step-by-step explanation:
First, we need to find out how many doorknobs are square:
166 - 98 = 68
Then, we need to divide the number of square doorknobs, 68, by the number of square doorknobs in each bin, 7: 68 ÷ 7
68 is closer to 70. So,
68 ÷ 7 is about 70 ÷ 7.
So, 68 ÷ 7 is about 10.
Jodi poured herself a cold soda that had an initial temperature 36 degrees F and immediately went outside to sunbathe where the temperature was a steady 99 degree F. After 5minutes the temperature of the soda was 46 degree F .Jodi had to run back into the house to answer the phone . What is the expected temperature of the soda after an additional 13 minutes ?
The expected temperature of the soda after an additional 13 minutes is estimated to be 72°F. This estimation is based on the assumption of a linear temperature increase, calculated from the temperature change observed during the first 5 minutes outside.
Explanation:The student's question involves the expected temperature of soda after a certain time outside in a hotter environment. Since this scenario does not involve a phase change like melting ice, but rather heating up from the surrounding air, we can infer that Newton's Law of Cooling may be applicable. The Law states that the rate of heat transfer between an object and its surroundings is proportional to the difference in temperature between them. However, without a specific rate of heat transfer given, we cannot apply a formula directly. Therefore, we might assume an approximate linear relationship based on the information provided.
Here's a possible approach:
Initial temperature of soda: 36°FTemperature of soda after 5 minutes: 46°FIncrease over 5 minutes: 46°F - 36°F = 10°FAverage rate of temperature increase: 10°F / 5 minutes = 2°F per minuteExpected additional increase after 13 minutes: 13 minutes * 2°F per minute = 26°FStarting temperature for this period: 46°FExpected temperature after an additional 13 minutes: 46°F + 26°F = 72°FThis logic assumes a simple linear rate, which might not be precisely accurate but should provide an estimated answer.
identify the decimals labeled with the letters A,B and C on the scale below
The solution is :
A represents the decimal 3.23
B represents the decimal 3.34
C represents the decimal 3.17
What is decimal?A decimal is a number that consists of a whole and a fractional part. Decimal numbers lie between integers and represent numerical value for quantities that are whole plus some part of a whole.
here, we have,
Calculating the decimal values:
We can see that there are 10 divisions between 3.2 and 3.3.
The difference between the two points for 10 divisions is 3.3 -3.2 = 0.1 unit.
Therefore, one division will be equal to 0.1/10 = 0.01 unit
So, point A is 3 divisions after 3.2, thus
A = 3.2 + 0.01×3
A = 3.23
Similarly,
B = 3.3 + 0.01×4
B = 3.34
And,
C = 3.2 - 0.01×3
C = 3.17
Hence, The solution is :
A represents the decimal 3.23
B represents the decimal 3.34
C represents the decimal 3.17
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Carrie pays a monthly fee of $8 to stream movies online. She also pays a fee every time she rents a movie. Last month Carrie rented 6 movies, and her total bill for the month was $32.
The first term of a geometric sequence is 15 and the second term is 6. Find the fourth term.
To find the fourth term of a geometric sequence with a first term of 15 and a second term of 6, we first calculate the common ratio (r = 2/5), and then successively multiply by the common ratio to find subsequent terms. The fourth term is determined to be 24/25.
The question involves finding the fourth term of a geometric sequence where the first term (a₁) is 15, and the second term (a₂) is 6. In any geometric sequence, each term is found by multiplying the previous term by a common ratio (r). Thus, we can find r by dividing the second term by the first term: r = a₂ / a₁ = 6 / 15 = 2 / 5.
Now that we have the common ratio, we can find the third term by multiplying the second term by the ratio: a₃ = a₂ × r = 6 × 2 / 5 = 12 / 5. Finally, we find the fourth term by multiplying the third term by the ratio: a₄ = a₃ × r = (12 / 5) × (2 / 5) = 24 / 25.
Therefore, the fourth term of the geometric sequence is 24/25.
write the slope- intercept form of the equation of the line parallel to - x+5y=25, passing through the point (-5,-5). simplify
To find the equation of a line parallel to -x+5y=25 and passing through (-5, -5), we determine that the slope of the given line is 1/5. Using the point-slope form with the given point and the slope, we derive the slope-intercept form of the equation as y = 1/5x - 4.
To write the slope-intercept form of the equation of the line parallel to -x+5y=25 and passing through the point (-5, -5), we first need to find the slope of the given line. To do this, we rearrange the equation into slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept.
Starting with the given equation:
-x + 5y = 25
Add x to both sides to isolate the y-terms:
5y = x + 25
Now divide everything by 5 to solve for y:
y = (1/5)x + 5
From this, we can see that the slope (m) of the line is 1/5. Since parallel lines have the same slope, the slope of our new line will also be 1/5.
Now we will use the point-slope form of the equation to find the line that passes through (-5, -5) with a slope of 1/5. The point-slope form is y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line.
Substituting the given point and the slope into the point-slope form, we get:
y - (-5) = 1/5(x - (-5))
Simplify the equation:
y + 5 = 1/5(x + 5)
Now distribute the slope:
y + 5 = 1/5x + 1
Finally, subtract 5 from both sides to find the y-intercept (b):
y = 1/5x - 4
This is the slope-intercept form of the equation of our line: y = 1/5x - 4.
In 10 years a child will be 5 years older than twice her current age. What is her current age?
Determine if the statement is true or false, and justify your answer. the product of the eigenvalues (counting multiplicities) of a is equal to the constant term of the characteristic polynomial of
a.
a new fax machine cost miller ltd $2670. they are to pay it off in 18 months at 9% intetest. what will each monthly payment be and how much interest will they pay
Simple interest is the interest calculated on the principal at a given rate for a time period.
The formula for simple interest:
SI = PRT / 100
P = principal
R = rate
T = time in years
The monthly payment is $168.35.
The interest amount to pay is $360.45.
What is simple interest?It is the interest calculated on the principal at a given rate for a time period.
The formula for simple interest:
SI = PRT / 100
P = principal
R = rate
T = time in years
We have,
Principal = $2670
Time = 18 months = 18/12 = 1.5 years
Rate = 9%
Simple interest:
SI = P x R x T / 100
SI = (2670 x 9 x 1.5) / 100
SI = $360.45
Now,
Total amount to pay:
= Principal + SI
= 2670 + 360.45
= 3030.45
The monthly payment:
= 3030.45 / 18
= $168.35
Thus,
The monthly payment is $168.35.
The interest amount to pay is $360.45.
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Final answer:
The monthly payment is $168.35, and the interest amount to pay is $360.45.
Explanation:
Simple interest is calculated on the principal amount at a given rate over a specific time period. The formula for simple interest is SI = PRT / 100, where P represents the principal, R denotes the rate, and T signifies the time in years. In this scenario, the principal is $2670, the time is 18 months (or 1.5 years), and the rate is 9%. Substituting these values into the formula, we find that the simple interest amounts to $360.45. Adding this interest to the principal, the total amount to pay becomes $3030.45. Finally, by dividing this total by the time in years (18 months or 1.5 years), we determine that the monthly payment is $168.35. Therefore, the monthly payment is $168.35, and the interest amount to pay is $360.45.
If the square of a positive integer is added to 2 times the integer, the result is 195 . Find the integer
The positive integer for which its square added to two times the integer equals 195 is 13. This is found by solving the quadratic equation x² + 2x - 195 = 0, which factors to (x + 15)(x - 13) = 0.
To find the positive integer where the square of the integer added to two times the integer equals 195, we need to represent this algebraically. Let's denote the integer as x. The equation based on the given condition is:
x² + 2x = 195
To solve for x, we rearrange the equation into a standard quadratic form:
x² + 2x - 195 = 0
We can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. The factoring method seems suitable here, as we can look for two numbers that multiply to -195 and add to 2. In this case, the integers are 13 and -15.
So our factored equation is:
(x + 15)(x - 13) = 0,
giving us the solutions x = -15 and x = 13. Since we are looking for a positive integer, the answer is x = 13.
a stadium holds 50000 people. the stadium is dived into 250 different seating section. how many seats are in each section?
A rectangular room is 4 meters longer than it is wide, and its perimeter is 28 meters. Find the dimension of the room.
Answer: The width of the room = 5 meters
The length of the room = 9 meters
Step-by-step explanation:
Let the w denotes the width of the room , then length of the room will be :-
[tex]\text{length}=4+w[/tex]
The formula of perimeter of rectangle :-
[tex]\text{Perimeter}=2(l+w)\\\\\Rightarrow\ 28=2(4+w+w)\\\\\Rightarrow\ 28=2(4+2w)\\\\\Rightarrow\ 28 =8+4w\\\\\Rightarrow\ 4w=20\\\\\Rightarrow\ w=5[/tex]
Hence, The width of the room = 5 meters
The length of the room = 5+4 = 9 meters
The width of the room is 5 meters, and the length is 9 meters.
Explanation:To find the dimensions of the rectangular room, let's assign variables. Let x be the width of the room. Since the length is 4 meters longer than the width, we can represent the length as x + 4.
Given that the perimeter is 28 meters, we can write an equation: 2(x + 4) + 2x = 28.
Simplifying the equation, we get 4x + 8 = 28. Subtracting 8 from both sides gives 4x = 20. Dividing both sides by 4, we find x = 5. The width of the room is 5 meters, and the length is 5 + 4 = 9 meters.
Identify a pattern in the given list of numbers.Then use this pattern to find the next number.
1,4,1,20,1,100,1
The number sequence alternates between 1 and multiples of 5. The pattern of the multiples of 5 increases by a factor of 5 each time, next number in the sequence being 500.
The sequence shown is 1, 4, 1, 20, 1, 100, 1.
To find the next number in this sequence, we can observe that the sequence of numbers (not including the 1's) is increasing by a factor of 5 each time =(4, 20, 100, ...).
Since 100 =5*20, to find the next number after the last 1, we need to multiply 100 * 5.
So, the next number after the last 1 would be 100* 5 = 500.
what is 494 divided by 14 and what is the remander
Answer:
35 and remainder is 4
Step-by-step explanation:
Two cars leave towns 300 kilometers apart at the same time and travel toward each other. One car's rate is 16 kilometers per hour more than the other's. If they meet in 2 hours, what is the rate of the faster car?
To find the rate of the faster car, set the speed of the slower car as 'x' km/h and the speed of the faster car as 'x + 16' km/h. Since they meet in 2 hours, and the total distance is 300 km, the equation is 2x + 2(x + 16) = 300. The faster car's speed is found to be 83 km/h.
Explanation:The question involves solving for the rate of the faster car when two cars travel towards each other from a distance of 300 kilometers apart and meet after 2 hours. We'll designate the speed of the slower car as 'x' km/h, which implies the speed of the faster car is 'x + 16' km/h. Since they meet in 2 hours, the total distance covered by both cars together is 300 kilometers.
Using the formula for distance (distance = rate × time), we can set up an equation:
2x + 2(x + 16) = 300
Simplifying this equation:
2x + 2x + 32 = 300
4x = 268
x = 67
The speed of the slower car is 67 km/h, and therefore, the rate of the faster car must be 67 + 16, which is 83 km/h.
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The fox population in a certain region has an annual growth rate of 8% per year. In the year 2012, there were 24,900 foxes counted in the area. What is the fox population predicted to be in the year 2020? (Round your answer to the nearest whole number.)
The fox population predicted to be in the year 2020 is 46090.
We have,
The population growth can be represented using the equation:
= [tex]I (1 +R)^n[/tex]
Where I is the initial population, R is the growth rate and n is the number of years.
Now,
I = 24,900
R = 8% = 8/100 = 0.08
n = 2020 - 2012 = 8
Substituting the values.
The population growth
= [tex]I (1 +R)^n[/tex]
= [tex]24900 \times (1 + 0.08)^8[/tex]
= 24900 x [tex]1.08^8[/tex]
= 24900 x 1.8509302102819
= 46089.9
= 46090
Thus,
The fox population predicted to be in the year 2020 is 46090.
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liberty middle school is holding a fundraiser the sixth graders have raised 52% of thier goal amount the seventh and eighth graders have raised 0.57 and 2/5 of thier goal amounts respectively list the classes in order from least to greatest of thier goal amounts
The correct answer would be, from least to greatest:
8th graders = 2/5 x 100 = 40%
6th graders = 52%
7th graders = 0.57x100 = 57%
Step-by-step explanation:
Liberty middle school holds a fundraising. Many classes participated in the fundraising event. The data for sixth, seventh and eighth grades are given in the question. According to question:
6th Grade raised 52% of their goal.
7th Grade raised 0.57 of their goal, which will be 0.57 * 100 = 57%
8th Grade raised 2/5 of their goal, which will be 0.4 = 0.4 * 100 = 40%
So in the order from least to greatest, The classes are classified as below:
8th Graders: 40%
6th Graders: 52%
7th Graders: 57%
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Given the figure below, find the values of x and z .
There is a picture below to see it clearly.
Two angles whose sum is 180° are called supplementary angles. The value of x is 10, while the value of z is 96.
What are supplementary angles?Two angles whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two-two angles are two pairs of supplementary angles. That means, that if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.
The measure of ∠Z will be equal to 96° because ∠AOB and ∠COD are vertically opposite angles.
The sum of the measure of ∠AOB and ∠BOC will be equal to 180°, since both lie on the same line, therefore,
∠AOB + ∠BOC = 180°
96° + (14x - 56)° = 180°
14x - 56 = 180 - 96
14x = 140
x = 10°
Hence, the value of x is 10, while the value of z is 96.
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find the degree of the polynomial and determine whether it is a monomial, binomial,trinomial, or none of these 5x+7
Final answer:
The degree of the polynomial 5x+7 is 1; it has two terms, 5x and 7, and therefore, it is classified as a binomial.
Explanation:
To find the degree of the polynomial 5x+7 and determine whether it is a monomial, binomial, or trinomial, we first examine the terms of the polynomial. This polynomial has two terms, which are separated by a plus sign. The first term is 5x and the second term is 7. The degree of a polynomial is the highest power of the variable x that appears in the polynomial. In the term 5x, x is to the first power (since x is equivalent to x^1), and in the term 7, x is to the zero power (since any number to the zero power is 1, and the term does not contain x). Therefore, the degree of the polynomial is 1, which is the degree of the term 5x.
Since 5x+7 consists of two terms, it is known as a binomial. A monomial would have only one term, a binomial has two terms, and a trinomial has three terms. Therefore, the polynomial 5x+7 is a binomial of degree 1.
the pressure of a gas p(v) varies inversely with the volume of the gas v. The pressure of a gas measure 15 kg/cm2 when its volume 300 cm3
p(v)=20v
p(v)=20/v
p(v)=4500v
p(v)=4500/v
Answer:
p(v)= 4500/v
Step-by-step explanation:
took it
the difference of 9 and the quotient of a number x and 4 is 65
You have 24 homework problems for math class. You finish 1/2 of them during some extra time in class. If you complete 4 more problems while waiting for the bus, what fraction of the 24 problems will remain?
Answer:
[tex]\frac{8}{24} =\frac{1}{3}[/tex]
Step-by-step explanation:
In order to solve this, you just have to add up the fractions and calculate how much is that:
[tex]\frac{24}{24}- (24(\frac{1}{2} )+\frac{4}{24} )\\[/tex]
Now you just have to add up and then withdraw from the total:
[tex]\frac{24}{24}- (24(\frac{1}{2} )+\frac{4}{24} )\\\frac{24}{24}- \frac{12+4}{24} \\\frac{24}{24}- \frac{16}{24} =\frac{8}{24}[/tex]
SO now we know that he has 8/24 problems to do, if we reduce that we have that he still has to do 1/3 of the problems.
What's the unit rate for 1 1/4 gallons per 44 1/2 miles
Answer:
5/178 gal/mi
35.6 mi/gal . . . . . take your pick
Step-by-step explanation:
As you have written the question, it is
(1.25 gal)/(44.5 mi) = (5/178) gal/mi ≈ 0.0280899 gal/mi
___
Usually, mileage is expressed in miles per gallon in the US. The unit rate in those units is ...
178/5 mi/gal = 35.6 mi/gal
_____
Comment on mileage unit rates
A "unit rate" is any rate that has 1 unit in the denominator. That is, the rate 5 gal/(178 mi) is not a unit rate, but (5/178) gal/mi is a units rate. They both use the same fraction, but the latter has 1 unit in the denominator and the fraction in the numerator: (5/178 gal)/mi.
Outside the US, mileage (energy use for transportation) is often expressed in terms of (amount of fuel)/(given distance). For example, the above mileage might be expressed as 1.745 gal/(100 km), or 6.607 L/(100 km). The "unit" in this scenario is 100 km.
In the US, the typical mileage specification is (distance)/(gallons). So, your question in terms of gallons per mile could mean that is the unit rate you're looking for (.028 gal/mi). Or it could mean we need to convert it to the typical US mileage specification. We cannot tell.
write a 5 digit number that when rounded to the nearest thousand and hundred will have a result that is the same explain
The measure of the angle is fourteen times greater than its supplement