Final answer:
The ratio of the areas of two similar triangles with heights of 6 and 10 meters is 9/25.
Explanation:
To find the ratio of the areas of two similar triangles, △ABC and △DEF, with heights 6 meters and 10 meters respectively, we use the knowledge that the areas of similar triangles are proportional to the squares of the corresponding linear dimensions, such as their heights. For these triangles, the ratio of their heights is 6/10 or 3/5. Thus, the ratio of their areas is (3/5)2 or 9/25.
Rosen 15 how many solutions are there to the equation x1 x2 x3 x4 x5
Simone is buying 10 bracelets for her friends. Each bracelet costs $8. Simone is also buying a necklace for her mother for $18. She believes that her total will be $98. Which expression could be used to estimate the reasonableness of Simone’s total? 8 × $8 + $10 8 × $8 + $18 10 × $8 + $20 10 × $10 + $10
Eighty percent of the dogs have completed obedience classes. How many of the dogs have completed obedience classes? Five dogs of different breeds 4 dogs 3 dogs 2 dogs 1 dog
A. 11 cm^3
B. 14 cm^3
C. 15 cm^3
D. 25 cm^3
1. A sine function has the following key features:
Frequency = 16π
Amplitude = 2
Midline: y = 3
y-intercept: (0, 3)
The function is not a reflection of its parent function over the x-axis.
Use the sine tool to graph the function. The first point must be on the midline and the second point must be a maximum or minimum value on the graph closest to the first point.
2. A sine function has the following key features:
Period = 12
Amplitude = 4
Midline: y = 1
y-intercept: (0, 1)
The function is not a reflection of its parent function over the x-axis.
Use the sine tool to graph the function. The first point must be on the midline and the second point must be a maximum or minimum value on the graph closest to the first point.
3. A sine function has the following key features:
Period = 4π
Amplitude = 2
Midline: y = 3
y-intercept: (0, 3)
The function is a reflection of its parent function over the x-axis.
Use the sine tool to graph the function. The first point must be on the midline and the second point must be a maximum or minimum value on the graph closest to the first point.
4. picture
5. picture
Answer:
1. Picture Below
2. Ordered Pair : (0,1) (3,5) (6,1) - Function: f(x)=4sin(pi/6x)+1
3. Ordered Pair : (0,3) (3.14,5) (6.27,3) - Function: f(x)= 2sin(1/2x)+3
4. I have no idea.
5. Plot the first point at (0, 20) and the second point at (2, 22)
Step-by-step explanation:
The height of a tree was 4.8m .After one year the height of the tree was increased by 12.5%.find its new height
The new height of the tree after it has increased by 12.5% is 5.4 meters
To find the new height of the tree after it has increased by 12.5%, we start by calculating the increase in height using the following equation
Increase = 12.5% of the original height
The original height is given as 4.8m. So, the formula can be expressed as follows
Increase = 12.5% * 4.8
Increase = 0.125 * 4.8
Increase = 0.6 meters
Add the increase to the original height
New height = Original height + Increase
The above equation can then be expressed as follows
New height = 4.8 + 0.6
New height = 5.4 meters
The owners want to hire a contractor to build a porch along side the parlor. The parlor is rectangular with width Of 32 feet and length of 50 feet. The porch will have the same width that on each side of the house. See design plans.
The width of the porch will be 32 feet, the same as the parlor. However, to calculate the amount of building materials needed, additional specifics are required such as the porch's length, location of posts, and number of boards.
Explanation:To answer the question related to designing a porch that matches the width of the parlor, we first understand that the parlor is of a rectangular shape with a width of 32 feet. Considering that the porch will have the same width, it means the porch will also have a width of 32 feet.
From this point, specifics such as the desired length of the porch, location of posts, number of boards or rails, and other related factors would come into play in the calculating of building materials needed for the construction. There may also be the need to consider factors like the ratio of width to length in the design, akin to the mathematical relation mentioned in the statement 'X = Y x 2 + 1'.
So, while we know the width of the porch because it matches the parlor, the exact amount of materials that will be required would depend on further specifics of the porch design, similar to the steps in a stoichiometry problem in chemistry where one calculates the amount of reactants or products in a chemical reaction based on known ratios.
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You are standing 40 feet away from a building that is 115 feet tall. What is the angle from the ground to the top of the building to the nearest degree?
A knife is 3 times the cost of the spoon 9 spoons and 12 knives costs £82.80 work out the cost of 1 knife
The cost of spoon is £1.84 and therefore the cost of one knife is £5.52.
Given :
A knife is 3 times the cost of the spoon.9 spoons and 12 knives costs £82.80.Solution :
This question is solve by creating a linear equation and linear equations are nothing but yet another subset of "equations". Linear calculations that requires more than one variable can be done with the help of linear equations.The standard form of a linear equation in one variable is ax + b = 0.Now let x be the cost of spoon. Than the cost knife is 3x. It is given that 9 spoons and 12 knives costs £82.80.
[tex]9x + 12\times(3x)= 82.80[/tex]
[tex]9x + 36x = 82.80[/tex]
[tex]45x =82.80[/tex]
[tex]x = 1.84[/tex]
Therefore the cost of 1 knife = [tex]1.84\times 3 = 5.52[/tex].
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How do I solve #21???? Please don't just give me the answer.... tell me how u got it... thanks!
Y= v^2/2a solve for v
Final answer:
To solve for v in the equation y = v²/2a, multiply both sides by 2a and then take the square root of both sides which gives v = √(2ay).
Explanation:
The question requires us to solve the equation y = v²/2a for the velocity v. To isolate v, we multiply both sides of the equation by 2a, then take the square root of both sides.
Multiply both sides of the equation by 2a: 2ay = v²Take the square root of both sides to solve for v: v = √(2ay)This mathematical process makes v the subject of the equation based on the given formula from kinematics. It's important to note that v will have two values, one positive and one negative, since taking the square root of a number yields both a positive and negative result.
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If the public debt of the United States in 2002 was $6,228,235,965,597.16 and the budget deficit in 2003 was $554,995,097,146.46, what was the public debt in 2003?
A. $11,778,186,937,061.76
B. $5,673,240,868,450.70
C. $5,549,950,971,464.60
D. $6,783,231,062,743.62
Based on the public debt in 2002 and the budget deficit incurred in 2003, the public debt in 2003 was D. $6,783,231,062,743.62.
The budget deficit refers to the amount that the government had to borrow in order to fund the budget of the country.
To find the public debt in 2003 therefore, you need to add the debt of the previous year to the deficit of the current year.
= 2002 Public debt + Budget deficit
= 6,228,235,965,597.16 + 554,995,097,146.46
= $6,783,231,062,743.62
In conclusion, the public debt in 2003 was $6,783,231,062,743.62.
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What is the measure of
A. Cannot be determined
B. 74
C. 16
D. 32
Three brothers have ages that are consecutive even integers. the product of the first and third boys' ages is 20 more than wice the second boy's age. find the age of each of the three boys.
The table shows different geologic time periods: Period Number of Years Ago Jurassic 2.08 ⋅ 108 Silurian 4.38 ⋅ 108 Tertiary 6.64 ⋅ 107 Triassic 2.45 ⋅ 108
Order the time periods from oldest to youngest. (4 points)
1. Tertiary, Jurassic, Triassic, Silurian
2.Jurassic, Triassic, Silurian, Tertiary
3.Silurian, Triassic, Jurassic, Tertiary
4.Triassic, Silurian, Jurassic, Tertiary
Select all of the potential solution(s) of the equation 2log5x=log54.
Given :[tex] 2log_{5} x^{2} =log_{5} 2^{2} [/tex]
To solve for x we use the logarithm rule for powers.
The log rule for powers states:
[tex] mlog_{a}n =log_{a} n^{m} [/tex]
We apply this rule to the left side of the equation.
[tex] log_{5} x^{2} =log_{5} 4
Both sides have log with same base so it can be eliminated.
Eliminating log from both sides we have:
[tex] x^{2} =4
To solve for x we take root of both sides
x=2,-2.
if 7(t-4)-2t=4(t-3), what is the value of t?
Find the average rate of change of the function over the given interval. f(x) = 3x − 2; [0, 5]
The average rate of change of the function over the given interval is 3.
Explanation:To find the average rate of change of the function over the given interval, we need to calculate the change in the function values and divide it by the change in the input values.
Step 1: Calculate the function values for the two endpoints of the interval.
f(0) = 3(0) - 2 = -2
f(5) = 3(5) - 2 = 13
Step 2: Calculate the change in the function values.
Change in function values = f(5) - f(0) = 13 - (-2) = 15
Step 3: Calculate the change in the input values.
Change in input values = 5 - 0 = 5
Step 4: Divide the change in function values by the change in input values.
Average rate of change = (Change in function values) / (Change in input values) = 15 / 5 = 3
The measure of angle x is 25 more than 4 times the measure of its complement. find the measure of x. x= degrees
.please help me thank you you will be given brainley
o valor da expressão a=1,67 . 10 + 3,95 . 10
Find the measure of “rst”
Answer: it is 110 bcs each section in 10° and there are 11 sections
What is the domain of the given function? {(3, –2), (6, 1), (–1, 4), (5, 9), (–4, 0)}
{x | x = –4, –1, 3, 5, 6} {y | y = –2, 0, 1, 4, 9} {x | x = –4, –2, –1, 0, 1, 3, 4, 5, 6, 9} {y | y = –4, –2, –1, 0, 1, 3, 4, 5, 6, 9}
The volumes of two similar solids are 53cm³ and 1113cm³. Which is the ratio of the corresponding sides?
A. 7
B. 21
C. √21
D. ³√21
Which of the following is equal to (2x/3 - 7) + 7
A. (2x - 7) + 21
B. 2x - 21/3
C. 3x/2
D. 2x/3
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I need help ASAP. I don't understand how to solve this
3. Your fixed expenses are $1,500.45/month. Your emergency fund has 4 month’s worth of coverage. You invest half in a savings account with an interest rate of 3.15% APR and the other half in a 45 day CD with an interest rate of 4.65% APR. How much is your total interest in 45 days?
4. If you had invested only 1 month’s worth of the emergency fund in the saving account at a 3.15% APR and the remainder in the 45 day CD at a 4.65% APR, what is the difference in the interest earned in 45 days when compared with question #3?
The total interest earned in 45 days when the emergency fund is evenly split between a savings account and a CD is approximately $29.17. If 1 month's worth of emergency funds were in the savings account and the rest in a CD, the total interest would be approximately $38.05. The difference between the two scenarios is approximately $8.88.
Calculating Interest for Emergency Funds in Savings and CDs
To answer the student's question about the interest earned in 45 days on the emergency fund invested half in a savings account and half in a 45-day CD, as well as the comparison with an alternative investment scenario, we need to perform several calculations using the given interest rates and time periods.
Answer to Question 3
Firstly, the student's fixed expenses are $1,500.45/month, so for a 4-month emergency fund coverage, the total amount saved would be $1,500.45 x 4 = $6,001.80.
Half of this amount goes into the savings account and the other half into the CD, so each gets $3,000.90.
The interest in the savings account with an APR of 3.15% for 45 days (1.5 months) would be calculated using the formula for simple interest: Interest = Principal x Rate x Time.
So the interest earned on the savings account would be: $3,000.90 x (3.15% per year / 12 months) x 1.5 months ≈ $11.85.
The interest in the 45-day CD with an APR of 4.65% would be calculated similarly: $3,000.90 x (4.65% per year / 12 months) x 1.5 months ≈ $17.32.
Therefore, the total interest earned in 45 days would be approximately $11.85 + $17.32 = $29.17.
Answer to Question 4
If only 1 month's worth of emergency fund ($1,500.45) was invested in the savings account and the remainder in the CD, the interest from the savings account would not change, but the interest from the CD would, as it would be calculated on a larger principal of $4,501.35.
The new interest for the CD investment would be $4,501.35 x (4.65% per year / 12 months) x 1.5 months ≈ $26.20.
So the new total interest would be $11.85 (from savings) + $26.20 (from CD) = $38.05.
The difference in interest between the two scenarios would be $38.05 - $29.17 = $8.88.
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What is the probability that a point chosen at random in the rectangle is also in the blue triangle
Answer:
The probability that a point chosen at random in the rectangle is also in the blue triangle is:
1/2
Step-by-step explanation:
We are given a figure
We have to find the probability that a point chosen at random in the rectangle is also in the blue triangle.
Area of rectangle= 4×5 sq. in.
= 20 sq. in.
The area of blue triangle=[tex]\dfrac{1}{2}\times 4\times 5[/tex]
= 10 sq. in.
P(that a point chosen at random in the rectangle is also in the blue triangle)
= area of blue triangle/whole area of the rectangle
= 10/20
= 1/2
Answer: the answer is 1/2
Step-by-step explanation:
The table shows the percentage of students in each of three grade levels who list soccer as their favorite sport. Soccer Sophomores (35%) 50%
Juniors (33%) 45%
Seniors (32%) 30%
Total (100%) (0.5)(0.35) + (0.45)(0.33) + (0.32)(0.3) = 0.4195 or about 42%
Find the probability that the student is a junior, given that soccer is the favorite sport listed.
P(junior | soccer) = ???%
The probability that the student is a junior, given that soccer is the favorite sport listed is 0.354.
How to calculate the probability?The percentage of student on Junior level who like soccer will be:
= 33% × 45%
= 0.1485
The total percentage of students who like soccer is 42%. Therefore, probability that the student is a junior, given that soccer is the favorite sport listed will be:
= 0.1485/0.42
= 0.354
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