Final answer:
In the context of a folding chair, as angle 1 (between the backrest and the seat) increases, the distance between the back of the chair and the front leg correspondingly increases due to the lever-like movement of the backrest.
Explanation:
When considering the geometry of a folding chair and the angles formed by its parts, it's important to visualize the chair as a system of linked levers. As angle 1 increases, which is the angle between the backrest of the chair and the seat, the relationship between the back of the chair and the front leg changes. If we assume that the front leg stays still and the back of the chair moves backward to increase the angle, the distance between the back of the chair and the front leg increases. This movement can be seen as the backrest acting like a lever, where increasing the angle effectively moves the lever away from the pivot point at the front leg.
Therefore, the correct answer in the context of a folding chair is: A. As the measure of angle 1 increases, the distance between the back of the chair and the front leg of the chair increases.
Show that each property of matrices is true for all 2 by 2 matrices scalar distributive
A computer password consists of 3 letters followed by two digits. none of the letters or digits repeat. how many different passwords can be created
Answer:
67,600
Step-by-step explanation:
A $360,000 building is depreciated by its owner. the value y of the building after x months is: y = 360,000 – 1,500 x. how many months will it take until it is completely depreciated
To find when the building will be completely depreciated, you solve for x in the equation y = 360,000 - 1,500x by setting y to 0. The solution is x = 240, meaning the building will be totally depreciated after 240 months or 20 years.
Explanation:In this case, you are looking to find the value of x (the number of months) when the value of the building (y) becomes 0. The equation given is y = 360,000 - 1,500x. Set y = 0 and solve for x
First, replace y with 0 in the given equation: 0 = 360,000 - 1,500x. Next, move the term with x to the other side by adding 1,500x to both sides, which gives: 1,500x = 360,000.Finally, solve for x by dividing both sides of the equation by 1,500. This gives you: x = 360,000 / 1,500 = 240.So, the building will be completely depreciated after 240 months or 20 years.
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The sides of an equilateral triangle are increasing at a rate of 10 cm/min. at what rate is the area of the triangle increasing when the sides are 30 cm long?
Use the conversion factor 4 quarts / 1 gallon to convert 5.25 gallons to quarts
Answer: 21 quarts
Step-by-step explanation: In this problem, we are asked to convert 5.25 gallons into quarts. To convert gallons into quarts, we use the conversion factor for gallons and quarts.
Conversion factor ⇒ 4 quarts = 1 gallon
Next, notice that we are going from a larger unit "gallons" to a smaller unit "quarts" and when we go from a larger unit to a smaller unit we multiply.
We will multiply 5.25 by the conversion factor which is 4 to get 21 quarts.
Therefore, 5.25 gallons is equal to 21 quarts.
What is (-3+2i)(-6-8i)
what is the equation of the line x-3y = 18 in slope-intercept form ?
Which value of x makes the numerical sentence true? 25^ 1/2 × 5 ^–3 = 5 ^x
Which symbol creates a true sentence when x equals 3?
8•3-4x_7(10-x)
A.<
B.=
C.>
Convert 5460 feet per minute to miles per hour. Round to the nearest whole number
Write a 10 digit number such that the first digit tells how many zeros
A solution containing 30 percent juice is mixed with a solution containing 10 percent juice to make 100 gallons of a 12 percent juice mixture. how much of the 30 percent juice solution was used
10 gallons of 30% juice was mixed with 90 gallons of 10% juice to make 100 gallons of 12% juice.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the amount of 30% juice and y represent the amount of 10% juice, hence:
x + y = 100 (1)
Also:
0.3x + 0.1y = 0.12(100) (2)
From eqn 1 and 2:
x = 10, y = 90
10 gallons of 30% juice was mixed with 90 gallons of 10% juice to make 100 gallons of 12% juice.
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What proportion of a normal distribution corresponds to z scores greater than 1.04?
Final answer:
The proportion of a normal distribution for z scores greater than 1.04 is 0.1492, which is found by subtracting the area to the left (0.8508) from the total area under the curve (1).
Explanation:
To find the proportion of a normal distribution that corresponds to z scores greater than 1.04, we must look up the area to the left of the z-score using a z-table or a standard normal distribution table. Once we have the area to the left, we can calculate the area to the right by subtracting this value from 1 (since the total area under the curve is 1). For a z-score of 1.04, the z-table shows that the area to the left is approximately 0.8508. Therefore, the proportion that is greater than a z-score of 1.04 is 1 - 0.8508, which equals 0.1492.
The standard normal distribution (Z~N(0,1)) has a total area of 1 under the curve, and it is symmetric about the mean, which is 0. Z-scores give us a way to determine how many standard deviations an observation is from the mean. Additionally, common z-scores used to determine confidence intervals or the proportion of observations within a certain range are tied to the percentage areas under the curve. For example, a z-score of ±1 encompasses approximately 68% of the data, ±2 about 95%, and ±3 approximately 99.7%.
I conceived on september 27 when will the test show the results
Which of the following expressions is a polynomial?
4a3+3a2+5a-9
32
y-3
x2-4x-2
I need help with a math question on my quick check. 0.24 x 13 A. 3.12 B. 4.62 C. 4.12 D. 3.10
This problem is simply a multiplication problem. All we have to do in this case is to multiply 0.24 by 13, or the other way around multiply 13 by 0.24. We can do this in the calculator which gives us:
13 x 0.24 = 3.12
Answer:
A. 3.12
What is the value of x? (7x-8) (6x+11)
Answer:
[tex]x=-\dfrac{11}{6},\dfrac{8}{7}[/tex]
Step-by-step explanation:
Given: [tex](7x-8)(6x+11)[/tex]
Set the expression to 0 to solve for x
[tex](7x-8)(6x+11)=0[/tex]
Set each factor to 0 and solve for x
7x-8 = 0 or 6x+11 = 0
7x = 8 or 6x = -11
[tex]x=\dfrac{8}{7}[/tex] or [tex]x=-\dfrac{11}{6}[/tex]
hence, The values of x are [tex]x=-\dfrac{11}{6},\dfrac{8}{7}[/tex]
Rearrange the formula v = GM r for r.
The correct formula for [tex]\( r \)[/tex] rearranged from [tex]\( v = \frac{GM}{r} \) is \( r = \frac{GM}{v} \)[/tex].
To rearrange the formula [tex]\( v = \frac{GM}{r} \)[/tex] to solve for [tex]\( r \)[/tex], follow these steps:
1. Start with the given formula:
[tex]\[ v = \frac{GM}{r} \][/tex]
2. Multiply both sides of the equation by [tex]\( r \)[/tex] to get rid of the denominator:
[tex]\[ vr = GM \][/tex]
3. Divide both sides of the equation by [tex]\( v \)[/tex] to isolate [tex]\( r \)[/tex]:
[tex]\[ r = \frac{GM}{v} \][/tex]
This gives us the rearranged formula for [tex]\( r \)[/tex] in terms of [tex]\( G \), \( M \), and \( v \)[/tex]
wich of the following is the correct graph of solution to the inequality -8 >-5x+2>-38
If f(x)=x^2+3x+5 what is f(3+h) ?
a person mailing postcards earns a fixed amount for each postcard he mails yesterday his hourly wage was $14 an hour if he worked 5 hours yesterday and mailed 300 postcards how much does he earn for each postcard mailed? show you work
For each postcard person gets $14/60 or $0.2333.
What is ratio?Ratio is basically compares quantities, that means it show value of one quantity with respect to other quantity.
If a and b are two values, there ratio will be a:b .
Given that,
Wage for 1 hour = $14,
Since,
The person mailed 300 postcards in 5 hours,
therefore, in 1 hour 60 postcards will be mailed.
Person gets $14 for 60 postcards ,
So for 1 postcard person will get $14/60 or $0.2333 .
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Ria is an Indian student who was admitted to a US university. Her annual tuition is $42,000. She has to pay her tuition fees in US dollars. She needs to calculate how many Indian rupees she will need to buy one dollar. The dollar to rupee exchange rate is 63.76 and rupee to dollar exchange rate is 0.015. How many Indian rupees will Ria need to buy one dollar?
50.00 rupees
56.00 rupees
63.76 rupees
76.63 rupees
Ria will need 2677920 Rupees to pay her tuition fees
Data;
Tuition fee = $42,000$1 = 63.76 rupees$1 rupees = $0.015How Many Rupees will she need to buy a Dollar?We need to convert the currency from dollars to rupees
From the data given in the question, $1 is equivalent to 63.7 Rupees.
This information can further be used to determine how many Rupees she needs to pay her Tuition fees.
[tex]\$1 = 63.76 Rupees\\\$42,000 = x\\x = 42000 * 63.76\\x = 2677920[/tex]
Ria will need 2677920 Rupees to pay her tuition fees
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find the value of v......
A sample of n = 9 scores is obtained from a population with m = 70 and s = 18. if the sample mean is m = 76, then what is the z-score for the sample mean?
in a simple random sample of 48 men, the mean wrist circumference of the men is 19.3 centimeters with a standard deviation of 1.2 centimeters. Round your answer to the nearest hundredth.
Which interval is the 95% confidence interval for the mean wrist circumference for all men?
18.99,19.61
18.96, 19.64
12.85, 19.75
19.14, 19.46
The 95% confidence interval for the mean wrist circumference for all men is 18.91 to 19.69 centimeters.
Explanation:To calculate the confidence interval for the mean wrist circumference, we can use the formula: CI = x ± t(s/√n), where CI is the confidence interval, x is the sample mean, t is the t-value corresponding to the desired confidence level, s is the sample standard deviation, and n is the sample size.
In this case, the sample mean is 19.3 centimeters, the sample standard deviation is 1.2 centimeters, and the sample size is 48. We can find the t-value for a 95% confidence level using a t-table or calculator. Assuming a normal distribution, the t-value is approximately 1.96. Plugging in these values into the formula, we get:
CI = 19.3 ± 1.96(1.2/√48) = 19.3 ± 0.3956
Therefore, the 95% confidence interval for the mean wrist circumference is approximately 18.91 to 19.69 centimeters.
If (a+b)^2=25, and a^2+b^2=17, then what is a*b equal to? Thanks.
20 points! If u can provide an explanation that would be great if not just tell me how certain that's the answer. Thanks a bunch
If 5kg more than 3 times mac’s mass is decreased by twice his mass the result is 60 kg. What is mac’s mass?
Mac's mass can be found by setting up the equation 3m + 5kg - 2m = 60kg, simplifying to m + 5kg = 60kg, and solving for m to get m = 55kg. Therefore, Mac's mass is 55kg.
The equation, according to the problem statement, is: 3m + 5kg - 2m = 60kg. This simplifies to m + 5kg = 60kg, from which we can subtract 5kg from both sides resulting in m = 55kg. So, Mac's mass is 55kg.
Steps to solve the problem:
Let m represent Mac's mass.
Write the equation according to the problem statement: 3m + 5kg - 2m = 60kg.
Simplify the equation: m + 5kg = 60kg.
Subtract 5kg from both sides: m = 55kg.
Conclude that Mac's mass is 55kg.
find the greatest common factor of 15x^2y^3 and -20x^3yz
The greatest common factor of [tex]\(15x^2y^3\)[/tex] and [tex]\(-20x^3yz\)[/tex] is [tex]\(5x^2y\)[/tex].
To find the greatest common factor (GCF) of [tex]\(15x^2y^3\)[/tex] and [tex]\(-20x^3yz\)[/tex], we need to identify the highest power of each common factor that both terms share.
List the prime factors of each term:
[tex]\(15x^2y^3 = 3 \times 5 \times x^2 \times y^3\)[/tex]
[tex]\(-20x^3yz = -1 \times 2 \times 2 \times 5 \times x^3 \times y \times z\)[/tex]
Identify the common factors:
Common factors: [tex]\(5\), \(x^2\), \(y\)[/tex]
Find the lowest exponent for each common factor:
For (5), it appears in both terms, so we use the smaller exponent, which is [tex]\(5^1\)[/tex].
For [tex]\(x^2\)[/tex], it appears in both terms, so we use the smaller exponent, which is [tex]\(x^2\)[/tex].
For (y), it appears in both terms, so we use the smaller exponent, which is [tex]\(y^1\)[/tex].
Multiply the common factors:
[tex]\(GCF = 5 \times x^2 \times y = 5x^2y\).[/tex]
So, the greatest common factor of [tex]\(15x^2y^3\)[/tex] and [tex]\(-20x^3yz\)[/tex] is [tex]\(5x^2y\)[/tex].
Option 1: $30 per month and $100 membership fee. Option 2: $25 per month and $150 membership fee.
Michael is trying to determine which tennis club to join. If Michael chooses option 2, for which month will his total cost for option 2 be less than his total cost for option 1? A) month 8 B) month 9 C) month 10 D) month 11
Let us say that m is the number of months. So that the equations for option 1 (O1) and option 2 (O2) are:
O1 = 30 m + 100
O2 = 25 m + 150
TO determine this, we equate O1 and O2 so that:
30 m + 100 = 25 m + 150
5 m = 50
m = 10
So at the 10th month, the cost for both options are equal. So we select month 11.
Answer:
D) month 11