Answer:
If the larger bottle of shampoo gives 25% more for the same price, then it must contain 1.25 times the amount of shampoo in the smaller bottle. Let's represent the size of the smaller bottle as x ounces.
Thus, we can set up the following equation:
x * 1.25 = 6.7
Solving for x, we get:
x = 6.7 / 1.25
x ≈ 5.36
Therefore, the size of the original smaller bottle of shampoo is approximately 5.4 ounces (rounded to the nearest tenth).
Order the angles from greatest to least
The side opposite to angle Y is the longest, and angle Y is the largest angle in triangle XYZ. So, the angles can be ordered from greatest to least as follows:
angle Y > angle Z > angle X.
What is triangle ?
A triangle is a three-sided polygon, or a closed two-dimensional shape with three straight sides and three angles. The sum of the angles in a triangle always adds up to 180 degrees. The sides of a triangle can be of different lengths, and the angles can be acute (less than 90 degrees), right (equal to 90 degrees), or obtuse (greater than 90 degrees).
To order the angles from greatest to least in triangle XYZ, we need to determine which side is the longest. By the Law of Cosines, we know that:
[tex]c^2 = a^2 + b^2 - 2ab*cos(C)[/tex]
where c is the side opposite to angle C, and a and b are the other two sides.
So, let's calculate [tex]c^2[/tex] for each angle:
For angle X: [tex]c^2 = 25^2 + 27^2 - 2(25)(27)*cos(X)[/tex] ≈ 173.65
For angle Y: [tex]c^2 = 24^2 + 27^2 - 2(24)(27)*cos(Y)[/tex] ≈ 267.43
For angle Z: [tex]c^2 = 24^2 + 25^2 - 2(24)(25)*cos(Z)[/tex] ≈ 121.97
Therefore, the side opposite to angle Y is the longest, and angle Y is the largest angle in triangle XYZ. So, the angles can be ordered from greatest to least as follows:
angle Y > angle Z > angle X
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johnny read 30 pageson monday. opn tuesday he read 1/8 of the book. on wednesday he read the remaining 1/4. how many pages
Johnny read 30 pages on Monday. On Tuesday he read 1/8 of the book. On Wednesday he read the remaining 1/4. How many pages did he read in total?To find out how many pages Johnny read in total, we need to first determine the total number of pages in the book. We know that he read 1/8 of the book on Tuesday and the remaining 1/4 on Wednesday. So we can add these two fractions to find out the total fraction of the book that he read:1/8 + 1/4 = 3/8Now we know that Johnny read 3/8 of the book. We can use this information to set up a proportion to find out how many pages he read in total:3/8 = x/total number of pagesTo solve for x, we can cross-multiply and simplify:3/8 * total number of pages = xMultiply both sides by 8/3:total number of pages = x * 8/3Now we need to find out what x is. We know that Johnny read 30 pages on Monday, which is 1/8 of the total number of pages. So we can use this information to set up another proportion:1/8 = 30/total number of pagesTo solve for the total number of pages, we can cross-multiply and simplify:1/8 * total number of pages = 30Multiply both sides by 8:total number of pages = 240Now we can substitute this value for the total number of pages in our previous equation to find out how many pages Johnny read in total:total number of pages = x * 8/3240 = x * 8/3Multiply both sides by 3/8:x = 90Therefore, Johnny read a total of 30 + 90 = 120 pages.
How much will a new TV be worth now if it depreciates by 9% each month, and you bought it new 8 months ago for $2740?
Give your answer to two decimal places.
How much it's worth after 8 months =$
Answer:
To find out how much the TV is worth now, we need to apply the depreciation rate of 9% to the original price for 8 months:
First, let's calculate the value after the first month:
Value after 1 month = $2740 - (9% of $2740) = $2501.40
Now, let's calculate the value after 2 months:
Value after 2 months = $2501.40 - (9% of $2501.40) = $2275.80
We can continue this process for 8 months to find the current value:
Value after 3 months = $2071.67
Value after 4 months = $1888.81
Value after 5 months = $1725.10
Value after 6 months = $1579.92
Value after 7 months = $1452.16
Value after 8 months = $1339.53
Therefore, the TV is worth $1,339.53 now.
Solve the compound inequality. Graph the two inequalities on the first two number lines and the solution set on the third number line.
As a result, the compound inequality has the following solution: -1 ≤ x < 28/9
what is inequality ?An inequality in mathematics is a claim that two values or expressions are not equivalent to one another. A spectrum of potential values for a variable can be described by an inequality, which can also be used to compare the values of two quantities. There are various kinds of inequality, such as: Inequalities involving linear expressions or formulae are referred to as linear inequalities. An illustration of a linear inequality is 2x + 3 7. Inequalities involving quadratic expressions or formulae are known as quadratic inequalities. x2 - 4x + 3 > 0 is an illustration of a quadratic equation.
given
The compound inequality is as follows:
-4 ≤ 3x - 1 < 8
This can be resolved by splitting it into two distinct inequalities:
-4 <= 3x - 1 and 3x - 1 < 8
By adding 1 to both sides and dividing by 3, we can solve the first equation for x:
-4 + 1 ≤ 3x - 1 + 1/3
-3/3 ≤ x
-1 ≤ x
Solving the second inequality for x, we add 1 to both sides and split by 3:
3x - 1 + 1/3 < 8 + 1/3
3x < 9 + 1/3
3x < 28/3
x < 28/9
As a result, the compound inequality has the following solution: -1 ≤ x < 28/9
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Alex used his grandmother’s recipe to make 11 3/7 pounds of granola. If he fills as many bags as he can with 2 2/3 pounds of granola in each bag, how many pounds will he have left over?
A 16/21 pound
B 2 20/21 pounds
C 4 2/7 pounds
D 8 16/21 pounds
The number of pounds that he will have left over from 11 3/7 pounds is 4 2/7
How many pounds will he have left over?To find out how many bags of granola Alex can fill, we need to divide the total amount of granola he made by the amount of granola in each bag.
We can convert 11 3/7 pounds to an improper fraction:
11 3/7 pounds = 80/7 pounds
Also, we have
2 2/3 pounds = 8/3 pounds
Now we can divide the total amount of granola by the amount in each bag:
(80/7) ÷ (8/3)
To divide fractions, we invert the second fraction (change it to its reciprocal) and multiply:
(80/7) × (3/8)
Simplifying, we get:
(80 x 3) / (7 x 8) = 30/7
Divide
(80 x 3) / (7 x 8) = 4 2/7
Hence, the bags is 4 2/7
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6. One hundred twenty-five townspeople were interviewed at random. Forty of the interviewed townspeople were from the middle school. The middle school has 800 students. Estimate the size of the town.
Answer:
See below, please.
Step-by-step explanation:
To estimate the size of the town, we can use a proportion.
Number of middle school students / Total town population = Number of interviewed middle schoolers / Total number of interviewed townspeople
Let x be the total town population. Then we have:
800 / x = 40 / 125
Simplifying this proportion, we get:
40x = 800×125
40x = 100000
x = 100000 / 40
x = 2500
Therefore, the estimated size of the town is 2500.End of unit 4 assessment right triangle trigonometry
End of unit 4 assessment on right triangle trigonometry is an evaluation of a student's understanding of the basic concepts and applications of trigonometry involving right triangles.
This assessment may cover topics such as the trigonometric functions, Pythagorean theorem, special right triangles, and solving right triangles.
Trigonometry is the study of the relationships between the angles and sides of triangles, particularly right triangles. It is a branch of mathematics that has numerous applications in fields such as physics, engineering, and astronomy.
The trigonometric functions are sine, cosine, and tangent, which are ratios of the sides of a right triangle. These functions can be used to solve problems involving angles and sides of right triangles, such as finding the missing side or angle.
The Pythagorean theorem is another fundamental concept in right triangle trigonometry. It states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
Special right triangles, such as the 30-60-90 triangle and the 45-45-90 triangle, have specific ratios of their side lengths that can be used to solve problems more easily.
Solving right triangles involves finding the measures of all the angles and sides of a right triangle given certain information, such as the length of one side and the measure of one angle.
In conclusion, the end of unit 4 assessment on right triangle trigonometry evaluates a student's understanding of the basic concepts and applications of trigonometry involving right triangles. This assessment is important for students to demonstrate their mastery of the subject and to prepare them for further studies in mathematics and related fields.
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End of unit 4 assessment right triangle trigonometry describe the importance of Side ratios in right triangles as a function of the angles ?
juan owns 7 pairs of pants, 5 shirts, 6 ties, and 8 jackets. how many different outfits can he wear to school if he must wear one of each item?
Answer: I believe he could wear 768 outfits
Step-by-step explanation: I had a similar question consisting of the same numbers.
one-tailed two-tailed a) a pharmacist wants to test whether the effect of a placebo is different from zero. b) holdem motors wants to test whether the mean time to assemble a car is less than 24 hours. c) ihi insurance wants to test whether the mean time to process a claim is less than 7 days
The appropriate type of test for each scenario is a) a two-tailed test, b) a one-tailed test, and c) a one-tailed test.
a) This would be a two-tailed test as the pharmacist is testing for a difference, rather than a specific direction of effect.
b) This would be a one-tailed test as Holdem Motors is specifically testing whether the mean time to assemble a car is less than 24 hours, rather than testing for a difference in either direction.
c) This would be a one-tailed test as IHI Insurance is specifically testing whether the mean time to process a claim is less than 7 days, rather than testing for a difference in either direction.
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Solve for x,
using the secant lines.
6 cm
3 cm
x = [?] cm
X
15 cm
Remember a b = c d
W
Enter
Answer: 3
Step-by-step explanation:
Thus, the values of x for the given secant lines on the circle is found to be: x = 3 cm.
Explain about the secant lines?A straight line connecting two points on such a function is known as a secant line. The average change rate or just the slope across two locations can also be used to describe it.
The slope between two points and the average rate of shift in a function among two points are interchangeable terms.
Given data:
AE = 6 cm, AB = 3 cm, ED = x cm, BC = 15 cm
Now,
AD = AE + ED
AD = 6 + x ...eq 1
AC = AB + BC
AC = 3 + 15
AC = 18 ....2
As the given two chords are intersecting internally,
AC x AB = AD x AE
18 x 3 = (6 + x) x 6
6 + x = 18 x 3 / 6
6 + x = 9
x = 3
Thus, the values of x for the given secant lines on the circle is found to be: x = 3 cm.
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Complete question:
Solve for x, using the secant lines.
AE = 6 cm, AB = 3 cm,ED = x = [?] cm, BC = 15 cm
Remember a.b = c.d
The diagram is attached.
using the rule of 72, how long will it take $100,000 to equal $200,000 if you can earn 14% annually? question 40 options: 5.1429 years 4.1529 years 2.78 years 1.38 years
The Rule of 72 is a simple mathematical formula that allows investors to quickly estimate the number of years required for an investment to double in value.
To use this formula, we divide the number 72 by the annual interest rate earned on the investment.
The result is an estimate of the number of years it would take for the investment to double in value. For example, if an investment earns an annual interest rate of 8%, it would take approximately nine years for the investment to double in value (72 divided by 8 equals 9).The Rule of 72 is a useful tool for investors who want to quickly estimate the potential growth of their investments.However, it is important to note that this formula provides only an estimate, and the actual time required for an investment to double in value will depend on a variety of factors, such as market conditions, investment fees, and taxes.
Nevertheless, the Rule of 72 can be a helpful starting point for investors who want to set realistic expectations for their investments.
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Above, a right triangle is removed from a rectangle. What is the area of the remaining figure?
O 48 in²
O 136 in²
O 140 in²
O 160 in2
The correct option is (b) i.e. The area of the remaining figure is 136 in².
What is Right angled triangle?
A right angled triangle, also known as a right triangle, is a triangle in which one of the interior angles measures 90 degrees (a right angle). The side opposite the right angle is called the hypotenuse, and the other two sides are called the legs or the adjacent and opposite sides. The length of the hypotenuse can be found using the Pythagorean theorem, which states that the sum of the squares of the two legs is equal to the square of the hypotenuse.
Given : length = 20 and breadth = 8
The area of given rectangle = l × b
= 20 × 8
= 160 in²
Similarly, area of right angled triangle = 1/2 × b × h
= 1/2 × (20-8) × 4
= 1/2 × 12 × 4
= 24 in²
Hence, The area of remaining figure :
= The area of given rectangle - area of right angled triangle
= 160 - 24
= 136 in²
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find 3 consecutive odd integers such that 3 times the sum of the first and second equals 13 less than the third
Three consecutive odd integers are -3, -1, and 1.
A detailed explanation of the answer.
To find 3 consecutive odd integers such that 3 times the sum of the first and second equals 13 less than the third, we can follow these steps:
Let's assume that the first odd integer is x.Thus, the second odd integer will be x + 2, and the third odd integer will be x + 4.The sum of the first and second odd integers is x + (x + 2) = 2x + 2.Three times the sum of the first and second odd integers is 3(2x + 2) = 6x + 6.Thirteen less than the third odd integer is (x + 4) - 13 = x - 9.Thus, the equation can be written as 6x + 6 = x - 9. Solving for x gives us x = -3.Then, the three consecutive odd integers are x, x + 2, and x + 4, which are -3, -1, and 1, respectively.Therefore, the three consecutive odd integers are -3, -1, and 1.
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you spin the spinner once.
what is p(less than 4)?
write your answer as a fraction or whole number
The equation used to obtain the probability of a number less than 4 on the spinner is given as follows:
P(less than 4) = number of regions with numbers that are less than 4/ total number of regions in the spinner.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
The outcomes for this problem are given as follows:
Desired: number of regions with numbers that are less than 4.Total: total number of regions.Hence the probability is calculated as follows:
P(less than 4) = number of regions with numbers that are less than 4/ total number of regions in the spinner.
Missing InformationThe problem asks for the probability of spinning a number less than 4 on the spinner.
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pizzas are sized by diameter. what percent increase in area results if chantel's pizza increases from a 10-inch pizza to a 12-inch pizza?
Step-by-step explanation:
Area of circle = pi r^2
10 inch = pi (5)^2 = 25 pi
12 inch = pi (6)^2 = 36 pi
12 inch is 11pi bigger
percentage: 11 pi is what percentage of 25 pi ?
11 pi / 25 pi x 100% = 44 % bigger
The area of a pizza increases with the square of the diameter. Therefore, a 10-inch pizza has an area of [tex]π*(10/2)^2= 78.54[/tex] square inches, and a 12-inch pizza has an area of [tex]π*(12/2)^2 = 113.10[/tex] square inches. This is an increase of 113.10 - 78.54 = 34.56 square inches, or an increase of 44.2%.
To explain further, the diameter of a pizza is measured from one side to the other through the center of the pizza. As the diameter of the pizza increases, the area of the pizza increases. This is because the area of a pizza is calculated as [tex]π*(d/2)^2[/tex], where d is the diameter. So, if the diameter increases, the area increases as well.
For example, if a 10-inch pizza has an area of 78.54 square inches, a 12-inch pizza would have an area of 113.10 square inches. This is an increase of 113.10 - 78.54 = 34.56 square inches, or an increase of 44.2%. This is because the diameter of the pizza has increased by 2 inches (10 inches to 12 inches), and the area has increased by 44.2%.
It is important to note that increasing the diameter of the pizza does not just increase the circumference of the pizza, but also the area. The increase in area is directly related to the increase in diameter, and can be calculated by taking the difference between the areas of the two pizzas.
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how mang triangles are possible given the following side maesurment: 3 feet , 5 feet, 4 feet
The answer is: 1 triangle is possible given the following side maesurment: 3 feet , 5 feet, 4 feet.
To determine how many triangles are possible with these side measurements, we can use the triangle inequality theorem, which states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side.
What is inequality theorem?
In this case, we have three side measurements: 3 feet, 5 feet, and 4 feet. Let's call these sides a, b, and c, respectively. Using the triangle inequality theorem, we can see that:
a + b > c
a + c > b
b + c > a
Substituting in the values of a, b, and c, we get:
3 + 5 > 4
3 + 4 > 5
4 + 5 > 3
All three of these inequalities are true, so it is possible to form a triangle with these side measurements.
To determine how many distinct triangles are possible, we can use the fact that any two triangles are distinct if and only if they have at least one side with a different length. In this case, all three sides have different lengths, so there is only one distinct triangle that can be formed with these side measurements.
Therefore, the answer is: 1 triangle.
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Complete question is: 1 triangle is possible given the following side maesurment: 3 feet , 5 feet, 4 feet.
your cousin says that if two fractions have the same numerator,then the fraction with the greater denominator is the greater fraction. is your cousin correct explain
It is not always true that if two fractions have the same numerator, then the fraction with the greater denominator is the greater fraction.
The statement that if two fractions have the same numerator, then the fraction with the greater denominator is the greater fraction is not always correct. This is because the value of a fraction is determined by both its numerator and denominator, and if the denominators of two fractions with the same numerator are different, then the fractions are not directly comparable.
Consider the fractions 3/4 and 3/5. Both have a numerator of 3, but the denominator of the first fraction is greater than the denominator of the second fraction. However, 3/5 is actually the greater fraction because it represents a larger portion of the whole.Consider the fractions 5/7 and 5/9. Both have a numerator of 5, but the denominator of the second fraction is smaller than the denominator of the first fraction. Therefore, 5/7 is the greater fraction because it represents a larger portion of the whole.
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Enola has x quarters and y dimes. She has a minimum of 18 coins worth at most $3.60 combined. Solve this system of inequalities graphically and determine one possible solution.
Answer: Let's start by setting up the system of inequalities:
x + y ≥ 18 (Enola has at least 18 coins)
0.25x + 0.10y ≤ 3.60 (The total value of her coins is at most $3.60)
To graph this system of inequalities, we can start by graphing the line x + y = 18 (the boundary for the first inequality). This line represents all the possible combinations of x and y that would give Enola exactly 18 coins. To graph this line, we can plot two points on it and connect them with a straight line. For example, if x = 0, then y = 18, and if y = 0, then x = 18. So the line passes through the points (0, 18) and (18, 0).
Next, we need to shade the region that satisfies the second inequality. To do this, we can rearrange the inequality to get:
y ≤ (3.60 - 0.25x) / 0.10
This inequality represents all the possible combinations of x and y that would give Enola a total value of coins at most $3.60. We can graph this inequality by shading the region below the line y = (3.60 - 0.25x) / 0.10.
Putting both of these graphs together, we get:
Graph of system of inequalities
One possible solution to this system of inequalities is (x, y) = (10, 8). This corresponds to Enola having 10 quarters and 8 dimes, for a total of 18 coins. The total value of her coins is:
0.25(10) + 0.10(8) = 2.50 + 0.80 = 3.30
Since 3.30 is at most $3.60, this solution satisfies both inequalities. Note that there may be other possible solutions as well.
Step-by-step explanation:
The system of inequalities is solved by plotting the inequalities in the xy-plane and finding the overlapping region. One possible solution for the number of quarters (x) and dimes (y) Enola could have that meets the conditions is x = 8 and y = 10.
Explanation:The subject of this question is inequalities. Enola has x quarters and y dimes. Each quarter is worth $0.25 and each dime is worth $0.10. Therefore, the total amount of money she has is $0.25x + $0.10y. Since she has at least 18 coins, we have the inequality x + y >=18. Since the total money is at most $3.60, we have the inequality $0.25x + $0.10y <= 3.60. Because we are dealing with a whole number of coins, x and y should be integers. The solution of this system of inequalities can be found graphically by plotting these inequalities in the xy-plane and finding the overlapping region. One possible solution is x = 8 and y = 10.
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help i will give alot of points
According to the information, the surface area of the prism is 3200 square meters.
How to find surface area of the prism?To find the surface area of the prism, we need to add up the areas of all its faces.
The prism has 2 triangle sides with a height of 15m and a base of 40m. The area of each triangle can be calculated using the formula A = 1/2 × b × h, where b is the base and h is the height of the triangle. So, the total area of these two triangles is:
A = 2 × 1/2 × 40m × 15mA = 600m^2The prism also has 2 triangle sides with a height of 25m and a base of 40m. The total area of these two triangles is:
A = 2 × 1/2 × 40m × 25mA = 1000m^2Finally, the prism has 2 rectangular sides with a height of 40m and a base of 40m. The area of each rectangle is simply the product of its height and base, so the total area of these two rectangles is:
A = 2 × 40m × 40mA = 1600m^2To find the total surface area of the prism, we add up the areas of all its faces:
Total surface area = 600m^2 + 1000m^2 + 1600m^2Total surface area = 3200m^2Therefore, the surface area of the prism is 3200 square meters.
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Book I, Problem 18. Find three numbers such that the sum of any pair exceeds the third by a given amount; say the given excesses are 20, 30, and 40. (Hint: Let the sum of all three numbers be 2x. Add number (3) to both sides of the equation (1) + (2) = (3) + 20 to get (3) = x – 10. Obtain expressions for (1) and (2) similarly.]
a = 5, b = 25, c = 0
step by step explanation:
Let the three numbers be a, b, and c. Then, we have the following system of equations:
a + b = c + 20 (1)
a + c = b + 30 (2)
b + c = a + 40 (3)
Adding all three equations together, we get:
2(a + b + c) = 90
Simplifying, we get:
a + b + c = 45
Now, using the hint given in the problem, we can write:
c = x - 10
b = a + 20
a + (a + 20) = (x - 10) + 30
Simplifying this equation, we get:
2a + 20 = x + 20
Solving for x, we get:
x = 2a
Substituting this value of x in the equation c = x - 10, we get:
c = 2a - 10
Now we can express b and c in terms of a:
b = a + 20
c = 2a - 10
Therefore, three numbers that satisfy the given conditions are:
a = 5, b = 25, c = 0
We can verify that the sum of any pair exceeds the third by the given amounts:
a + b = 30 > c + 20 = 20
a + c = 5 > b + 30 = 25
b + c = 15 > a + 40 = 45
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Find the volume of the triangular prism below
We can claim that after answering the above question, the As a result, the triangular prism has a volume of 240 cubic centimetres.
what is prism?A prism is a polyhedron with an n-sided polygonal basis, a second base that is a shifted copy of the first base, and n extra faces (necessarily all parallelograms), with two connecting the corresponding sides of the base. All cross sections that are parallel to the base are translations of it. A prism is a two-sided, solid, three-dimensional object with two faces. It has the same cross-sections, flat sides, and similar bases. Faces of a prism are parallelograms or rectangles with no bases. A prism is a refracting item that is homogeneous, solid, and transparent, contained by two planes that are obliquely oriented to one another. A typical prism has two triangular faces and three parallel rectangular faces. They are made of either glass or metal.
To calculate the volume of a triangular prism, multiply the area of the triangular base by the prism's height.
Triangle area = 1/2 * base * height
Triangle area = 1/2 * 8 cm * 6 cm
Triangle area = 24 cm2
We must now determine the prism's height. The diagram shows that the prism has a height of 10 cm.
Finally, the volume of the triangular prism can be calculated by multiplying the area of the triangle base by the prism's height:
Prism volume = base area * The prism's height
Prism volume = 24 cm2 * 10 cm
Prism volume = 240 cm3
As a result, the triangular prism has a volume of 240 cubic centimeters.
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Evelyn buys bracelets thats cost $6 each and three purses that cost $12 each. The cost of evelyns total purchase is $60. Write and equation thar can be used to find n, the number of bracelets that evelyn buys
b + 2p = 10 ,we have an equation that relates the number of bracelets to the number of purses and the total cost of the purchase. if Evelyn buys two purses, she also buys six bracelets.
Let's start by defining our variables. We'll let "b" represent the number of bracelets that Evelyn buys and "p" represent the number of purses she buys.
We know that each bracelet costs $6 and each purse costs $12. We also know that her total purchase is $60.
Using this information, we can create an equation:
6b + 12p = 60
Now we want to solve for "b", which represents the number of bracelets. To do this, we need to isolate "b" on one side of the equation. We can start by simplifying the equation by dividing both sides by 6:
b + 2p = 10
Now we have an equation that relates the number of bracelets to the number of purses and the total cost of the purchase. We can use this equation to find the value of "b" given any value of "p". For example, if Evelyn buys two purses, we can substitute "p = 2" into the equation and solve for "b":
b + 2(2) = 10
b + 4 = 10
b = 6
So if Evelyn buys two purses, she also buys six bracelets.
In general, we can see that the equation tells us that for every two purses that Evelyn buys, she buys one less bracelet. This makes sense because purses are more expensive than bracelets, so as she buys more purses, she can afford fewer bracelets.
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Korey and I have been working with a financial planner named Stephen for years. He's been so good to us in explaining things like retirement, high yield savings, life insurance and college planning. This last time that we met with Stephen he explained to us that our money for the kids college savings account could be modeled with an equation to help my math brain see the big picture.
Currently, our savings account for the kids college is modeled by A of x equals 20000 times 1.05 raised to the x minus 1 power .
He explained that with inflation that we really needed to have a steady increase in our savings to be able to pay for both kids college funds. Stephen suggested that we look at how much money we would have if we didn't deposit any more money in our savings account and just relied on the interest to build based on this equation. He gave us a random number of 5% for the interest rate as shown in the model above and x is the number of years.
A) Is this sequence arithmetic, geometric, or neither?
B) Break apart the equation -Tell me what each of those terms represent above in the A(x) equation.
C) How much money would we have if we only did interest on this account in 11 years when Kolton starts college?
SHOW ALL MATH WORK AND EXPLANATIONS FOR THIS FROM START TO FINISH! IT'S A 10 POINT PROBLEM!
Answer:
A) This sequence is geometric.
B) In the equation A(x) = 20000(1.05)^(x-1):
A(x) represents the amount of money in the savings account after x years.
20000 represents the initial amount of money in the savings account.
1.05 represents the interest rate, which is compounded annually.
(x-1) represents the number of compounding periods, which is one less than the number of years because the initial amount is not compounded.
C) To find out how much money we would have in the savings account in 11 years when Kolton starts college, we can substitute x = 11 into the equation and simplify:
A(11) = 20000(1.05)^(11-1)
A(11) = 20000(1.05)^10
A(11) ≈ 35,123.58
Therefore, if we only relied on the interest to build our savings for 11 years, we would have approximately $35,123.58 in the savings account when Kolton starts college. However, this amount may not be enough to cover the total cost of college, so it is important to continue making regular deposits to the savings account.
what is the volume of a sphere with a height and diameter of 6 inches
Answer:
Step-by-step explanation:
6cm×6cm≈36cm²H + i3 where i = 1 and h = 19 caculate please
Answer: 22
Step-by-step explanation:
Substitude 1 for i and 19 for H.
19+1(3) = 19+3 = 22
Problem 2 Write an equation for the nth term of the arithmetic sequence −26,−15,−4,7,...,
please answer asap
Answer:
5.9
Step-by-step explanation:
find the comma different
Colleen paid $13.70 to download 12 songs from an online music service. Some of the songs were on sale and cost $0.99 each. The rest were regularly priced at $1.25 per song. Let x represent the number of sale priced songs, and let y represent the number of regularly priced songs. This situation can be represented by the system x+y=12 and 0.99x+1.25y=13.7 . How many of each type of song did Colleen purchase?
Using equations, we can find that the number of sale-priced songs is 5 and the number of regularly priced songs is 7.
What exactly is an equation system?Equations are mathematical statements with the equals (=) symbol and two algebraic expressions on either side. This illustrates the equality of the relationship between the expressions printed on the left and right sides. The formula LHS = RHS (left hand side equals right hand side) is utilised in all mathematical equations. To determine the value of an unknown variable that represents an unknown quantity, you can solve equations. A statement is not regarded as an equation if it has no "equal to" symbol.
As per the question, equation given are:
x + y = 12
x = 12 - y
Now, substituting the value in:
0.99x+1.25y = 13.7
= 0.99(12-y) +1.25y = 13.7
= 11.88 - 0.99y + 1.25y = 13.7
= 0.26y = 13.7 - 11.88
0.26y = 1.82
y = 1.82/0.26
y = 7
Now, substitute this value,
x = 12 - 7
x = 5
As a result, there are 5 songs on sale and 7 songs that are regularly priced.
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Hello can you find the absolute value?
-3 2/3=
Answer:
Yes, I can find the absolute value of -3 2/3.
The absolute value of a number is the distance of the number from zero on the number line. It is always a positive number.
To find the absolute value of -3 2/3, we need to ignore the negative sign and just look at the magnitude of the number.
So, the absolute value of -3 2/3 is:
|-3 2/3| = 3 2/3
Therefore, the absolute value of -3 2/3 is 3 2/3.
PLEASE HELP AND PLEASE SHOW ALL STEPS IT WOULD BE VERY MUCH APPRECIATED!!
Answer:
I got to #1 and #3 but I didn't finish in time and I have to leave before I can finish the other ones, my apologies. The solve and steps for 1 and 3 are below. If no one has answered the other two I can probably solve the other two later tonight!
Hope this helps!
Jason worked for 14/3 hours on Monday, and his friends Sheldon worked for 25/6 hours.How many more hours did Jason work than Sheldon?
Answer:
Step-by-step explanation:
To find out how many more hours Jason worked than Sheldon, we need to subtract the number of hours Sheldon worked from the number of hours Jason worked:
Jason's hours = 14/3
Sheldon's hours = 25/6
Jason's hours - Sheldon's hours = (14/3) - (25/6)
To subtract fractions, we need to have a common denominator, which in this case would be 6:
(14/3) - (25/6) = (28/6) - (25/6) = 3/6
Simplifying the result, we get:
3/6 = 1/2
Therefore, Jason worked 1/2 more hours than Sheldon.
Jason worked 1/3 more hours than Sheldon.
To find out how many more hours Jason worked than Sheldon, we need to subtract the number of hours Sheldon worked from the number of hours Jason worked.
Jason worked for 14/3 hours, which can be simplified to 4 and 2/3 hours. Sheldon worked for 25/6 hours, which can be simplified to 4 and 1/6 hours.
Subtracting the hours Sheldon worked from the hours Jason worked, we get: 4 and 2/3 - 4 and 1/6 = 2/3 - 1/6 = 1/3.
Therefore, Jason worked 1/3 more hours than Sheldon.
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