Let's assume the price of a citron is "x" units and the price of a fragrant wood apple is "y" units.
From the given information, we can form two equations:
7x + 9y = 135 ...(1)
9x + 7y = 137 ...(2)
We can solve this system of equations using the elimination method. Multiplying equation (1) by 9 and equation (2) by 7, we get:
63x + 81y = 1215 ...(3)
63x + 49y = 959 ...(4)
Subtracting equation (4) from equation (3), we get:
32y = 256
y = 8
Substituting the value of y in equation (1), we get:
7x + 9(8) = 135
7x + 72 = 135
7x = 63
x = 9
Therefore, the price of a citron is 9 units and the price of a fragrant wood apple is 8 units.
At Burnt Mesa Pueblo, archaeological studies have used the method of tree-ring dating in an effort to determine when prehistoric people lived in the pueblo. Wood from several excavations gave a mean of (year) 1252 with a standard deviation of 39 years. The distribution of dates was more or less mound-shaped and symmetric about the mean. Use the empirical rule to estimate the following.
(a) a range of years centered about the mean in which about 68% of the data (tree-ring dates) will be found
between
and
A.D.
(b) a range of years centered about the mean in which about 95% of the data (tree-ring dates) will be found
between
and
A.D.
(c) a range of years centered about the mean in which almost all the data (tree-ring dates) will be found
between
and
A.D.
a) The range of years centered about the mean in which about 68% of the data in between 1291 or 1213.
b) The range of years centered about the mean in which about 95% of the data in between 1330 or 1174.
c) The range of years centered about the mean in which about 95% of the data in between 1369 or 1135.
We have,
Mean= 1252
Standard deviation= 39
a) The range of years centered about the mean in which about 68% of the data
= 1252 ±39
= 1252 + 39 or 1252 -39
= 1291 or 1213
b) The range of years centered about the mean in which about 95% of the data
= 1252 ± 2(39)
= 1252 + 78 or 1252- 78
= 1330 or 1174
c) The range of years centered about the mean in which about 95% of the data
= 1252 ± 3(39)
= 1252 + 117 or 1252- 117
= 1369 or 1135
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An element with a mass of 640 grams decays by 19.3% per minute. To the nearest
tenth of a minute, how long will it be until there are 50 grams of the element
remaining?
it will take approximately 6.8 minutes until there are 50 grams of the element remaining.
We can use exponential decay formula to solve this problem:
A = A₀ ×e²(-rt)
where A is the amount of the element remaining, A₀ is the initial amount, r is the decay rate (as a decimal), t is the time elapsed.
We know that the initial mass of the element is 640 grams, the decay rate is 19.3% per minute, and we want to find the time it takes for there to be 50 grams of the element remaining. So we can write:
50 = 640 ×e²(-0.193t)
Dividing both sides by 640, we get:
0.078125 = e²(-0.193t)
Taking the natural logarithm of both sides, we get:
ln(0.078125) = -0.193t
Solving for t, we get:
t = ln(0.078125) / (-0.193)
t ≈ 6.8 minutes
Therefore, it will take approximately 6.8 minutes until there are 50 grams of the element remaining.
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Answer:
Please mark me the brainliest
Let's denote the time in minutes by t, and the mass of the element at time t by m(t). Then we can write an exponential decay equation:
m(t) = m(0) * (1 - r)^t
where m(0) is the initial mass of the element, r is the decay rate as a decimal (19.3% = 0.193), and t is the time in minutes.
We know that the initial mass is m(0) = 640 grams, and we want to find the time t when the mass has decreased to 50 grams. So we can set up the following equation:
50 = 640 * (1 - 0.193)^t
Simplifying:
0.07796875 = 0.807^t
Taking the natural logarithm of both sides:
ln(0.07796875) = ln(0.807^t)
Using the property of logarithms that ln(a^b) = b * ln(a):
ln(0.07796875) = t * ln(0.807)
Dividing both sides by ln(0.807):
t = ln(0.07796875) / ln(0.807)
Using a calculator, we get:
t ≈ 24.9
Therefore, to the nearest tenth of a minute, it will take 24.9 minutes until there are 50 grams of the element remaining.
Step-by-step explanation:
what is area of rectangular 1 5/6 ,4 1/3
Answer:
Area = 7 7/18 or 39/2 square units
Step-by-step explanation:
To find the area of a rectangle, you need to multiply its length by its width.
Given:
Length = 1 5/6
Width = 4 1/3
Convert mixed numbers to improper fractions:
Length = (6 + 5) / 6 = 11/6
Width = (3 x 4 + 1) / 3 = 13/3
Area = Length x Width
Area = (11/6) x (13/3)
Area = (143/18)
Simplify the result to mixed number or improper fraction:
Area = 7 7/18 or 39/2 square units (if we want the answer in fraction form)
Nicholas and his father went fishing.
Nicholas caught a fish that weighed
14 1/2 pounds. His father caught a fish
that weighed half as much as the fish
Nicholas caught. What was the total
weight of the fish Nicholas and his
father caught, in pounds? Enter the
weight as an improper fraction.
The value of total weight of the fish Nicholas and his father caught, in pounds is,
⇒ 87/4 pounds
We have to given that;
Nicholas caught a fish that weighed 14 1/2 pounds.
And, His father caught a fish that weighed half as much as the fish Nicholas caught.
Hence, The weight of fish caught by his father is,
⇒ 14 1/2 ÷ 2
⇒ 29/2 × 1/2
⇒ 29/4
Thus, The value of total weight of the fish Nicholas and his father caught, in pounds is,
⇒ 14 1/2 + 29/4
⇒ 29/2 + 29/4
⇒ 58/4 + 29/4
⇒ 87/4 pounds
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Find the missing side of the triangle round your answer to the nearest tenth
Answer:
x = 6 feet
Step-by-step explanation:
using Pythagoras' identity in the right triangle.
the square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
x² + 8² = 10²
x² + 64 = 100 ( subtract 64 from both sides )
x² = 36 ( take square root of both sides )
x = [tex]\sqrt{36}[/tex] = 6 feet
One notebook and 2 packs of pencils cost $7.20 two notebooks and 2 packs of paper cost $10.90.How much does 1 pack of paper cost
Answer:
5.45
Step-by-step explanation:
literally do 10.9/2
A particular movie theater charges $7.00 per adult and $2.50 per child. If 600 people attended a movie and the total revenue from ticket sales was, which of the following models the given information if x represents the number of adults and y represents the number of children?
Answer:
Step-by-step explanation:
7x+2.50y=600
A sale transaction on rental property closes on December 10th. The landlord received the December rent of $4,400 on December 1. Assuming the closing day is the seller's, and that the 360-day method is used for prorating, how much will the seller owe the buyer?
The seller will owe the buyer an amount of $2,933.40.
How much will the seller owe the buyer?To be able to compute the owed amount, first, we have to compute the daily rate per day which is shown below:
= Rent received / number of days in a month
= $4,400 / 30 days
= 146.67 per day
Data:
Number of days in a month = 30 days
Landlord received a rent on December 10
The remaining days would be = 30 days - 10 days = 20 days
Now, the owed amount would be calculated as:
= Remaining days × per day rate
= 20 days × 146.67
= $2,933.40
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Can you help me with this question?
A Ferris wheel has a diameter of 14 meters determine the distance to the nearest meter that a rider travels after 2 complete laps.
Answer:
88
Step-by-step explanation:
The distance traveled by a rider on a Ferris wheel can be calculated by finding the circumference of the wheel and then multiplying it by the number of complete laps.
The formula for the circumference of a circle is:
C = πd
where C is the circumference, d is the diameter, and π is a constant approximately equal to 3.14.
In this case, the diameter of the Ferris wheel is 14 meters, so the radius (half the diameter) is 7 meters.
C = πd = π(14) = 43.9823 meters (rounded to 4 decimal places)
To find the distance traveled after 2 complete laps, we need to multiply the circumference by 2:
distance = 2C = 2(43.9823) = 87.9646 meters
Rounding to the nearest meter, the distance traveled by a rider after 2 complete laps is 88 meters.
Que tipo de corriente circula por el océano glaciar ártico ??
Answer:Transpolar Drift Stream y el anticiclónico Beaufort Gyre
Step-by-step explanation:
In a roll of 50 pennies, 15 were made before 1985. What percent of the pennies in the roll were made before 1985?
30% of the pennies in the roll were made before 1985.
To find the percentage of pennies made before 1985, we need to divide the number of pennies made before 1985 by the total number of pennies and then multiply by 100 to convert the answer into a percentage.
Number of pennies made before 1985 = 15
Total number of pennies = 50
Percentage of pennies made before 1985
= (15/50) x 100%
= 30%
Therefore, 30% of the pennies in the roll were made before 1985.
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use the Pythagorean theorem to find the missing length and then round the result to the nearest ten
a=12, b=12, c=
Answer:
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. Hence, we use this formula to solve for the missing length:
c^2 = a^2 + b^2
Plugging in the given values, we get:
c^2 = 12^2 + 12^2 c^2 = 144 + 144 c^2 = 288 c ≈ √288
Rounding √288 to the nearest ten gives 17. Therefore, the missing length is approximately 17.
Hence, c ≈ 17 is the answer.
Step-by-step explanation:
Please help me solve question 19!
Answer:
Step-by-step explanation:
what point on number line is 7/9 the way from the point -3.6 to the point 10?
The point on the number line that is 7/9 of the way from -3.6 to 10 is approximately 6.97777777778.
To find the point on the number line that is 7/9 of the way from -3.6 to 10, we can use the following formula:
Point = Starting point + (Fraction of distance) x (Total distance)
In this case, the starting point is -3.6, the total distance is the distance from -3.6 to 10 (which is 10 - (-3.6) = 13.6), and the fraction of distance is 7/9.
Plugging in these values, we get:
Point = -3.6 + (7/9) x (13.6)
Simplifying,
Point = -3.6 + (7/9) x (13.6)
Point = -3.6 + 9.9556
Point = 6.97777777778
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What value of x satisfies the equation
(793x)3 = 343q36?
The value of x satisfies the equation is 4
What are index forms?Index forms are described as mathematical forms that are used to represent numbers or values that are too large or small in more convenient ways.
From the information given, we have that;
(7q³ˣ)³ = 343q³⁶
expand the bracket for the values
7³. q⁹ˣ = 343q³⁶
Now find the common exponents, we have;
7³. q⁹ˣ= 7³. q³⁶
Divide the values, we have;
q⁹ˣ = q³⁶
Equate the exponents, we get;
9x = 36
Divide both sides by the coefficient of x, we get
9x/9 = 36/9
Divide the values
x = 4
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Need help??? With this question
Answer:
[tex]28 + y + 36 = 180[/tex]
[tex]64 + y = 180[/tex]
[tex]y = 116[/tex]
Gus has a fish tank that holds
4710
47104710 inches
3
3
cubed of water. He is using a cylinder shaped bucket with a radius of
5
55 inches and a height of
20
2020 inches to fill the tank.
How many times will Gus need to fill the bucket to completely fill the fish tank if he doesn't spill a drop?
Use
3.14
3.143, point, 14 for
π
Gus will need to fill the bucket 3 times to completely fill the fish tank, assuming he doesn't spill any water.
To find how many times Gus will need to fill the bucket to completely fill the fish tank, we first need to calculate the volume of the bucket. The formula for the volume of a cylinder is:
V = πr²h
where V is the volume, r is the radius, and h is the height.
Substituting the given values into the formula gives:
V = 3.14 x 5² x 20
V = 3.14 x 25 x 20
V = 1570 inches³
Therefore, each time Gus fills the bucket, he will add 1570 inches³ of water to the fish tank. To calculate how many times he needs to fill the bucket to fill the entire fish tank, we can divide the total volume of the fish tank by the volume of the bucket:
4710 / 1570 = 3
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Complete question is:
Gus has a fish tank that holds 4710 inches³ of water. He is using a cylinder shaped bucket with a radius of 5 inches and a height of 20 inches to fill the tank. How many times will Gus need to fill the bucket to completely fill the fish tank if he doesn't spill a drop?
Please help with my geometry.
What is the area of the segment?
r = 3m
central angle = 98°
A function, f(x), has degree of 4. If f(x) has 2 complex zeros then how many real zeros does it have?
If it has 2 complex zeros, then it must have 2 real zeros.
How many real zeros does it have?Remember that the number of zeros that a polynomial of degree N has is also N.
For example in functions like:
f(x) = x^N
We can say that the zero x = 0 has a multiplicity of N, so we have N equal zeros.
Then a polynomial of degree 4 has 4 zeros, if two are complex, then the other two are real zeros.
So we conclude that the answer is 2.
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Find the area of the triangle ABC with the given parts. Round to the nearest tenth when necessary
The area of the triangle is equal to 1337 square feet. (Correct choice: A)
How to determine the area of the triangle
In this problem we must determine the area of the triangle given the lengths of all sides, this can be done by using Heron's formula:
A = √[s · (s - a) · (s - b) · (s - c)]
s = 0.5 · (a + b + c)
Where:
s - Semiperimetera, b, c - Sides of the triangle.If we know that a = 47 ft, b = 59 ft and c = 65 ft, then the area of the triangle is:
s = 0.5 · (47 ft + 59 ft + 65 ft)
s = 85.5 ft
A = √[(85.5 ft) · (85.5 ft - 47 ft) · (85.5 ft - 59 ft) · (85.5 ft - 65 ft)]
A = 1337.252 ft²
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Find the ratio specified in the picture.
Find sin A.
A
12
13
C 5 B
The value of sin A using trigonometric ratios is: 12/13
How to solve trigonometric ratios?There are three main trigonometric ratios in right angle triangles and they are:
sin x = opposite/hypotenuse
cos x = adjacent/hypotenuse
tan x = opposite/adjacent
We want to find sin A and as such using trigonometric ratios on the attached right angle triangle, we have:
sin A = 12/13
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Use Heron's formula to find the area of the triangle with side lengths 9, 12, and 18, as shown below.
Answer: the answer is 48 or b
Step-by-step explanation:
Heron's formula states that the area (A) of a triangle with side lengths a, b, and c is given by:
A = √(s(s-a)(s-b)(s-c))
where s is the semiperimeter, which is half the perimeter of the triangle:
s = (a + b + c) / 2
In this case, the side lengths are a = 9, b = 12, and c = 18. Therefore, the semiperimeter is:
s = (9 + 12 + 18) / 2 = 39 / 2
Using Heron's formula, we can now calculate the area of the triangle:
Which function has the graph shown?
A. y = secx
B. y = sinx
C. y = cotx
D. y = tanx
Answer:
tanx
Step-by-step explanation:
Can you please help with this question i dont understand thank you.
1. Cost is proportional to Area includes;
-Carpeting that cost $22 for every 3 square yard
-Cost ($) and Area (ft^2) table
-Mulch that cost a set amount to cover a square foot
2. Cost is not proportional to Area;
- Linear graph
- Asphalt sealant that is quoted at a set price per square foot, plus a labor fee
3. Not enough information
- A wood deck quoted at a bulk cost for 25 square feet.
Why is the Linear graph not proportional to area?The Linear graph is not proportional to the area looking at the coordinates that has been provided. The cost to the yard area does not have a consistent progression. By this, $1,600 should cove 60 yd² instead of 80
The above answer is based on the information provided in the picture as seen below;
Drag each object to show whether cost is proportional to area in the situation represented.
Cost is proportional to Area Cost is not proportional to Area Not enough information
a. A wood deck quoted at a bulk cost for 25 square feet.
d. Asphalt sealant That is quoted at a set price per square foot, plus a labor fee.
c. Carpeting that cost $22 for every 3 square yard
d. Mulch that cost a set amount to cover a square foot
e. Cost ($) Area (ft^2)
500 400
750 600
1000 800
f. A cost ($) and area (yd^2) that has coordinates (0, 0), (20, 1200) (80, 1600)
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Which point is located at (4, –2)? On a coordinate plane, point A is 2 units to the left and 4 units up. Point B is 4 units to the right and 2 units down. Point C is 4 units to the left and 2 units up. Point D is 2 units to the right and 4 units down. A B C D Mark this and retu
Answer:
Point B is 4 units to the right and 2 units down
Step-by-step explanation:
Since our x is positive, we are going to the right of the x-axis (where positive values lay).
Since our y is negative, we are going down in the y-axis (where negative values lay).
Classify the triangle described below.
A triangle with measures of x°, 4x°, and 4x° is a(n) triangle.
We can see that the triangle has two equal angles, then it is an isosceles triangle.
How to classify the triangle?Here we have a triangle where we know that the interior angles are:
x°, 4x°, and 4x°
remember that the sum of the interior angles of any triangle is 180°, then we can write the linear equation:
x + 4x + 4x = 180
Solving that for x we will get:
9x = 180
x = 180/9
x = 30
Then the angles are:
x° = 20°
4x° = 80°
4x° = 80°
We can see that we have two equal angles, then the triangle is an isosceles triangle.
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A list of the outcomes in a sample space and the number of times each outcomes occurs is a
A. Frequency table
B. Conditional probability
C. Cumulative probability
D. Probability distribution
The list of the outcomes in a sample space and the number of times each outcomes occurs is a frequency table
Given data ,
The outcomes in a sample space and the frequency with which each event happens are displayed in a frequency table, which is a tabular representation of data.
It shows the frequency or count of each result, which makes the data distribution easier to see. In statistics and probability, frequency tables are frequently used to compile and analyze data from experiments, surveys, or other data-generating activities.
Hence , the solution is frequency table
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Brooklyn needs to earn $14 more dollars to have $32. How much money does Brooklyn have now?
Identify the steps needed to write and solve an equation to solve the word problem. Select all that apply.
The variable, m, is equal to the amount of money Brooklyn has now.
The variable, m, is equal to the amount of money Brooklyn needs to earn.
The correct equation is 14 + m = 32.
The correct equation is 14m = 32.
To solve the equation, subtract 14 from both sides.
To solve the equation, divide 14 on both sides.
Answer:
A,C,E
Step-by-step explanation:
Answer:
a and c and e
Step-by-step explanation:
got it right on my home work
find the height of right triangular prism
The side x of the triangular base prism is 0.4 centimetres.
How to find the side of a triangle prism?The diagram above is a triangular prism. The triangular base of the prism is a right triangle. Therefore, the unknown side x can be found using Pythagoras's theorem,
c²= a² + b²
where
a and b are the other legsc is the hypotenuse sideTherefore,
x² = 0.5² - 0.3²
x² = 0.25 - 0.09
x = √0.16
x = 0.4 cm
Therefore,
x = 0.4 centimetres.
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the dilation of the figure is 45,000cm3 what is the scale factor of the dilation
The scale factor of the dilation is 30:1.
We have,
A superhero action figure has a volume of 1500 cm³.
The volume of the dilated figure is 45,000 cm³
Now, the scale factor should be
= 45000/ 1500
= 30 /1
Thus, the scale factor of the dilation is 30:1.
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