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
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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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.
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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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.
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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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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36% of a number is 9. What is the number
Answer:
25
Step-by-step explanation:
0.36 × (a number) = 9
9/0.36 = (a number) = 25 . . . . . divide by the coefficient of the variable
The number is 25.
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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In a survey, 480 people, or 75%, said they attended a movie at least once a month. How many people were surveyed?
Write a multiplication problem in which the product is between 0.05 and 0.75
If Cade shoots 275 free throw baskets in 2 hours, about how many can he shoot in 5 hours.
Find an identity for cos(4t) in terms of cos(t)
cos(4t)=
The employees from maintenance go for coffee together every day at 9 a.m. On Monday, Hector paid $5.35 for three cartons of milk, six cups of coffee, a seven doughnuts. On Tuesday, Guillermo paid 4.80 for four milks, two coffees, and eight doughnuts. On Wednesday, Anna paid $4.40 for two milks, five coffees, and six doughnuts. On Thursday, Alphonse had to pay for two milks, five coffees, and seven doughnuts. How much change did he get back from his $10bill?
a patient weighs 65 kilograms how much does the patient weigh in pounds
A room has an area of 456 square feet. One dimension is 5 feet more than the other. Find the dimensions of the room.
Dimensions of the room with area of 456 square feet is 19 feet by 24 feet.
To solve for the dimensions of a room where the area is 456 square feet and one dimension is 5 feet more than the other, we can set up the following equations:
Let the width be x feet.
Then the length will be (x + 5) feet.
The area of a rectangle is given by the multiplication of its length and width, so the equation to represent the area is x(x + 5) = 456.
Expanding this, we get x2 + 5x - 456 = 0.
This is a quadratic equation which can be factored or solved using the quadratic formula. Factoring gives us (x - 19)(x + 24) = 0.
Since a room cannot have a negative dimension, we take the positive value of x, which is 19 feet.
Therefore, the width of the room is 19 feet, and the length is 19 + 5 = 24 feet.
In 10 years a child will be 5 years older than twice her current age. What is her current age?
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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four accounting majors two economic majors and three marketing majors have interviewed for five different positions with a large company. find the number of different ways that five of these people could be hired if the first position is to be filled by an accounting major, the second by an economics.major, and the third by a marketing major, and the last two positions can be filled by any major
There are 1,152 different ways that five people can be hired for different positions in the company.
Explanation:In this question, we need to determine the number of different ways that five people can be hired for different positions in a company.
Given that the first position must be filled by an accounting major, the second position by an economics major, and the third position by a marketing major, we have 4 choices for the first position, 2 choices for the second position, and 3 choices for the third position.
For the last two positions, any major can be hired, so we have 9 choices for the fourth position and 8 choices for the fifth position.
To find the total number of ways, we multiply all the choices together: 4 * 2 * 3 * 9 * 8 = 1,152.
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1.enter a quadratic polynomial which has zeros at 11 and 3
2.enter a quadratic polynomial which has zeros at -2 and 6
3.enter a quadratic polynomial which has a double root at -6
An equation with zeroes at r1 and r2 factors to (x-r1)(x-r2).
double root at r1 just means (x-r1)^2
We have given that,
enter a quadratic polynomial which has zeros at 11 and 3
What is the quadratic polynomial?A quadratic polynomial is a second-degree polynomial where the value of the highest degree term is equal to 2. The general form of a quadratic equation is given ax^2+bx+C=0
1. f(x)=(x-11)(x-3)
2. f(x)=(x-(-2))(x-6) or f(x)=(x+2)(x-6)
3. f(x)=(x-(-6))^2 or f(x)=(x+6)^2
if you wanted an expanded form
1. f(x)=x²-14x+33
2. f(x)=x²-4x-12
3. f(x)=x²+12x+36
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does -x plus -x result in -x?
For Frank"s Funky Sounds, units of production depreciation on the trucks is a
a. variable cost. c. mixed cost.
b. fixed cost. d. high-low cost.
what is 494 divided by 14 and what is the remander
Answer:
35 and remainder is 4
Step-by-step explanation:
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.
list the following units in order of increasing length: meter, inch, centimeter, kilometer, yard, foot, mile, hectometer
The units listed in order of increasing length are: inch, centimeter, foot, yard, meter, hectometer, kilometer, mile.
To list the given units in order of increasing length, we need to understand both the metric and customary systems of measurement commonly used. The metric system is primarily used in the world and includes units like the meter, centimeter, and kilometer. The U.S. customary units include the inch, foot, yard, and mile. Here's the list from smallest to largest:
Inch (1 inch is approximately 2.54 centimeters)
Centimeter (1 centimeter is 1/100 meter)
Foot (1 foot is 12 inches)
Yard (1 yard is 3 feet)
Meter (1 meter is slightly more than 3 feet; 100 centimeters)
Hectometer (1 hectometer is 100 meters)
Kilometer (1 kilometer is 1000 meters)
Mile (1 mile is 5280 feet or approximately 1.609 kilometers
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.
Use a linear approximation (or differentials) to estimate the given number.
e^−0.01
The approximate value of e^-0.01 is 0.99
Given :
we use linear approximation to estimate the given number
[tex]e^{-0.01}[/tex]
For linear approximation we use equation
[tex]L(x)=f(a)+f'(a)(x-a)[/tex]
Lets assume some value for 'a' that is close to -0.01
Lets assume a=0
[tex]f(x)=e^x\\f(0)=e^0\\f'(x)=e^x\\f'(0)=e^0[/tex]
Lets plug in all the values
[tex]L(x)=f(a)+f'(a)(x-a)\\L(x)=e^0+e^0(x-0)\\L(x)=1+1(x-0)\\L(x)=1+1x[/tex]
Now we estimate e^-0.01
the value of x is -0.01
[tex]L(x)=1+x\\L(-0.01)=1-0.01\\L(-0.01)=0.99[/tex]
The approximate value is 0.99
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To estimate the value of e^−0.01 using linear approximation or differentials, we can use the fact that the derivative of e^x is e^x. Specifically, we can linearize the function at a point close to x = -0.01 and use the linear equation to estimate the value of e^−0.01.
Explanation:To estimate the value of e^−0.01 using linear approximation or differentials, we can use the fact that the derivative of e^x is e^x.
Specifically, we can linearize the function at a point close to x = -0.01 and use the linear equation to estimate the value of e^−0.01.
Let's use the point x = 0 as our approximation point.
The linear equation is given by y = f'(a)(x - a) + f(a), where y represents the value of e^x, f'(a) represents the derivative of e^a at x = a, and f(a) represents the value of e^a at x = a.
Since the derivative of e^x is simply e^x, we have f'(0) = e^0 = 1.
Plugging in the values, we get y = 1(x - 0) + e^0 = x + 1. Therefore, substituting x = -0.01 into the equation, we estimate that e^−0.01 ≈ -0.01 + 1 = 0.99.
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Christina has two pieces of lace trim with lengths as shown in the table.Complete the table give each length in inches,feet,and yards.
Answer:
Step-by-step explanation:
bs
How to find the are and perimeter
The Harper family is traveling to visit friends. The distance to the friend’s house is 276.45 miles. It takes the family 5.82 hours to complete the trip.
Rate is found by dividing distance by time.
What is the rate for the family’s trip in miles per hour?
need now plz
Answer: 47.5 miles per hour
Step-by-step explanation:
We know that ,
[tex]\text{Speed}=\dfrac{\text{Distance}}{\text{Time}}[/tex]
Given : The distance to the friend’s house is 276.45 miles. It takes the family 5.82 hours to complete the trip.
i.e. Distance = 276.45 miles
Time = 5.82 hours
Then, the rate(speed) for the family’s trip in miles per hour will be :-
[tex]\text{Speed}=\dfrac{276.45}{5.82}=47.5\text{ miles per hour}[/tex]
Hence, the rate for the family’s trip = 47.5 miles per hour