Answer: 81
Step-by-step explanation:
\(v=\sqrt{2gh}\\\\g=32, v=72\\\\\implies 72=\sqrt{2(32)h}\\\\5184=64h\\\\h=81\)
Felipe made $168 for 8 hours of work. At the same rate, how much would he make for 18 hours of work?
Answer: $378
Step-by-step explanation: 18/8=2.25
Multiply 2.25 and 168 to get 378
Find the slope of the line given the graph. Write your answer in the format m-#.
Answer:
It has a slope of 0
m-0
Step-by-step explanation:
. If m angle TUV = (9x + 1)° , m angle TUW = (7x – 9)°, and m angle WUV = (5x - 11)°, find the value of x.
For the real-valued functions f(x)=√(3x+15) and g(x)= x-1, find the composition f of g and specify it's domain using interval notation.
the domain of the composition f(g(x)) is x ≥ -4, expressed in interval notation as (-4, ∞).
To find the composition f of g, we substitute the function g(x) into the function f(x). The composition is denoted as f(g(x)).
f(g(x)) = f(x - 1)
Replacing x in the function f(x) with (x - 1), we have:
f(g(x)) = √(3(x - 1) + 15)
Simplifying the expression inside the square root:
f(g(x)) = √(3x - 3 + 15)
f(g(x)) = √(3x + 12)
The composition of f(g(x)) is √(3x + 12).
To specify the domain of the composition, we consider the domain of g(x), which is all real numbers. However, since the function f(x) contains a square root, the argument inside the square root must be non-negative to ensure a real-valued result. Therefore, we set the expression inside the square root greater than or equal to zero:
3x + 12 ≥ 0
Solving this inequality, we have:
3x ≥ -12
x ≥ -4
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Light sample A has a frequency of 4.30×1015 Hz and light sample B has a frequency of 8.70×1018 Hz. What is the wavelength of light sample A in meters? Light sample A has a frequency of 4.30×1015 Hz and light sample B has a frequency of 8.70×1018 Hz. What is the wavelength of light sample B in meters? Light sample A has a frequency of 4.30 ×1015 Hz and light sample B has a frequency of 8.70×1018 Hz. Based on frequency, which set gives the most correct description of the types of light for samples A and B respectively? Light sample A has a frequency of 4.30 ×1015 Hz and light sample B has a frequency of 8.70×1018 Hz. Based on frequency, which set gives the most correct description of the types of light for samples A and B respectively?
1) The wavelength of A is equal to 6.98 × \(10^{-8}\)meters
2) The wavelength of B is equal to 3.45 × \(10^{-11}\) meters
Since we know that the wavelength = speed of light / frequency
The speed of light is 3.00 × \(10^8\) meters per second.
For light sample A with a frequency of 4.30 × 10^15 Hz can be calculated as;
wavelength of A = (3.00 × \(10^8\) m/s) / (4.30 × 10^15 Hz)
wavelength of A = 6.98 × \(10^{-8}\) meters
For light sample B with a frequency of 8.70 × \(10^18\) Hz can be calculated as;
wavelength of B = (3.00 × \(10^8\) m/s) / (8.70 ×\(10^18\) Hz)
wavelength of B = 3.45 × \(10^{-11}\) meters
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Find the slope of the line through each pair of points. (-17,-5), (15.-13)
write an equation of a line passing through the point (4,-9) and parallel to the line 3x-6y=30
The equation of a line in the slope intercept form is expressed as
y = mx + c
Where
m represents slope
c represents y intercept
The equation of the given line is expressed as
3x - 6y = 30
Rearranging it so that it will look like the slope intercept form, it becomes
6y = 3x - 30
Dividing both sides by 6, it becomes
6y/6 = 3x/6 - 30/6
y = x/2 - 5
Looking at the equation, slope, m = 1/2
If two lines are parallel, it means that they have equal slope. This means that the slope of the line parallel to the given line is 1/2
To determine the y intercept, c of the line passing through the point (4, - 9), we would substitute
x = 4, y = - 9 and m = 1/2 into the slope intercept equation. It becomes
- 9 = 1/2 * 4 + c
- 9 = 2 + c
c = - 9 - 2
c = - 11
By substtuting m = 1/2 and c = - 11 into the slope intercept equation, the equation of the line would be
y = x/2 - 11
what is the probability of rolling two numbers that sum to 4 after two rolls of the six-sided die (the sum of the two numbers from each roll equals 6)?
The probability of rolling two numbers that sum to 4 after two rolls of a six-sided die is 1/9 or approximately 0.1111. This means that out of all possible combinations, there is a 1 in 9 chance of obtaining a sum of 4.
To calculate the probability, we need to consider all possible outcomes of two dice rolls and determine the favorable outcomes where the sum of the two numbers equals 4.
Let's analyze the possible combinations for the first roll:
1 + 3 = 4
2 + 2 = 4
3 + 1 = 4
Out of these three combinations, only one of them results in a sum of 4.
For the second roll, we have the same possible combinations as the first roll. Again, only one combination gives a sum of 4.
Since the rolls are independent events, we can multiply the probabilities of each roll to find the probability of both events occurring. Therefore, the probability of rolling two numbers that sum to 4 is:
(1/6) * (1/6) = 1/36
However, we rolled the dice twice, so we need to account for the order in which these combinations can occur. We have two favorable outcomes: (1 + 3) and (3 + 1). Therefore, the probability becomes:
2 * (1/36) = 1/18
However, there are two possible ways to achieve a sum of 4: (1 + 3) and (3 + 1). Thus, we need to multiply by 2 again:
2 * (1/18) = 1/9
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Suppose a simple random sample of five hospitals is to be drawn from a population of 20 hospitals. There are 15,504 different samples of size 5 that can be drawn. The relative frequency distribution of the values of the mean of these 15,504 different samples would specify the ________ of the mean. Group of answer choices sampling distribution confidence level confidence interval normal distribution
The relative frequency distribution of the values of the mean of these 15,504 different samples would specify the sampling distribution of the mean.
What does the relative frequency distribution of the values of the mean of the 15,504 different samples specify?The sampling distribution of the mean refers to the distribution of sample means obtained from repeated sampling from the same population.
In this case, we have 15,504 different samples of size 5 drawn from a population of 20 hospitals.
Each sample has its own sample mean. The relative frequency distribution of these sample means would specify the sampling distribution of the mean.
The sampling distribution of the mean is important in statistics because it allows us to make inferences about the population mean based on the distribution of sample means.
It helps us understand the variability of sample means and provides a basis for constructing confidence intervals and conducting hypothesis tests.
Therefore, the relative frequency distribution of the mean values from the different samples would describe the characteristics of the sampling distribution of the mean..
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Khadija is trying to pick out an outfit for the first day of school. she can choose from 2 pairs of pants, 2 t-shirts, and 6 pairs of shoes. how many different outfits does khadija have to choose from?
Using the Fundamental Counting Theorem, it is found that Samantha has 24 different outfits to choose from.
What is the Fundamental Counting Theorem?
It is a theorem that states that if there are n things, each with n1 ,n2 , n3, ..... nn ways to be done, each thing independent of the other, the number of ways they can be done is:
N= n1*n2*n3.....nn
In this problem:
For the pants, there are 2 options, hence n1=2 .
For the t-shirts, there are 2 outcomes, hence n2=2.
For the shoes, there are 9 outcomes, hence n3=6.
Thus, the total number of outfits is given by:
N = 2 x 2 x 6 = 24.
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a total of $7000 is invested: part at 6% and the remainder at 10%. How much is invested at each rate if the annual interest is $470?
Answer:
680
Step-by-step explanation:
g. Substitute x back into one of the equation to solve for y. 5x+2y=7 3x-y=2
Answer: Substitute x back into one of the equations to solve for y.
Step-by-step explanation:
the great pyramid of king khufu was built of limestone in egypt over a 20-year time period from 2580 bc to 2560 bc. its base is a square with side length 756 ft and its height when built was 481 ft. (it was the tallest man-made structure in the world for more than 3800 years.) the density of the limestone is about . (a) estimate the total work done in building the pyramid. (b) if each laborer worked 10 hours a day for 20 years, for 340 days a year, and did of work in lifting the limestone blocks into place, about how many labor?ers were needed to construct the pyramid
Volume = (571,536 sq ft × 481 ft) / 3 = 91,227,792 cubic ft
What is Limestone?
Calcium carbonate is one of the most commonly found materials in limestone rocks. Composition of calcium and magnesium as commonly produced from fossils, shells and debris.
(a) To estimate the total work done in building the pyramid, we need to calculate the gravitational potential energy of the pyramid. Gravitational potential energy is given by the formula:
Potential Energy = Mass × Gravity × Height
To calculate the weight of the pyramid, we need to determine its volume and density. The volume of a square pyramid is given by:
Volume = (base area x height) / 3
The base area of the pyramid is given by:
Area of base = length of side × length of side
Let's calculate the values step by step:
Base area = 756 feet x 756 feet = 571,536 square feet
Volume = (571,536 square feet × 481 feet) / 3 = 91,227,792 cubic feet
Next, we need to convert volume to mass using density. However, the given information lacks the density of limestone. Could you please provide the density of the limestone so I can proceed with the calculation?
(b) Once we have the density of the limestone, we can estimate the number of workers needed to build the pyramid.
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CAN SOMEBODY PLEASE HELP ME WITH THIS QUESTION!!!!
Answer:
nope sorryyyyyy
Step-by-step explanation:
Ms Gegory had $300 to purchase sports equipment for summer camp she bought 6 soccer balls . Each basketball cost $16.98, and each soccer ball cost 13.79 how mush money did she have left after these purchases?
Answer: $217.26
Step-by-step explanation:
13.79 x 6 = 82.74
300 - 82.74 = 217.26
Ms. Gregory has $217.26 left.
Pls answer fast I will give brainliest!
Write an expression for the measure of ∠DBC. Justify your expression.
Write an expression for the measure of ∠BDC. Justify your expression.
Write an expression for the measure of ∠ADH. Justify your expression.
Write an equation that can be used to determine the value of x from triangle △DAB. Justify your equation. What does x equal?
What are the measures of ∠DBC, ∠BDC, ∠ADH, and ∠EBG?
Answer:
in triangle ABD
x+6+2x-3+90=180(sum of interior angle of triangle) (since each angle of rectangle=90)
3x+3=180-90
3x=90-3
x=87/3=29°
<DBC=<ADB{ALTERNATE ANGLE)=2x-3=2×29-3=55°
<BDC=ABD(ALTERNATE ANGLE)=x+6=29+6=35°
<ADH=180-<ADB{LINEAR PAIR)=180-2x-3=180-2×29-3=180-58-3=119°
<EBG=<DBC(VERTICALLY OPPOSITE ANGLE)=55°
NEED HELP ASAP WITH WORK
so I can use the work for the questions later on
The width of the rectangular garden is 21 feet.
What is a rectangle?A rectangle is a plane shape that have pair of opposite sides equal and parallel.
To calculate the width of the rectangle, we use the formula below
Formula:
w = 3P/20...................... Equation 1Where:
w = Width of the rectangleP = Perimeter of the rectangleFrom the question,
Given:
P = 140 feetSubstitute into equation 1
w = 3×140/20w = 21 feetHence, the right option is D. 21 feet.
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Triangle ABC is an isosceles triangle.
AB = BC
mB = 34°
What is mA?
A. 34°
B. 56°
C. 73°
D. 112°
Answer:
C. 73
Step-by-step explanation:
angles A and C will be the same because their sides are the same length!
so to solve this, let's set up an equation
34 + 2x = 180 let x represent the missing anglenow let's solve!
2x = 146x = 73angle A = 73
let me know if you have any questions :)
Answer:
C!
Step-by-step explanation:
a car radiator contains 5 liters of a 25% solution of antifreeze. how many liters must be removed and then replaced bya 75% antifreeze solution to leave the radiator filled with a 55% sltuion
To leave the radiator filled with a 55% antifreeze solution, 3 liters of the 25% solution of antifreeze must be removed and replaced with 3 liters of a 75% antifreeze solution.
We start by calculating the amount of antifreeze in the initial solution. Since the solution is 25% antifreeze, the amount of antifreeze in the solution is 25% of 5 liters, or 1.25 liters.
Let x be the amount of 75% antifreeze solution that must be added. We can set up the equation for the amount of antifreeze in the final solution as follows:
1.25 - 0.25(3) + 0.75x = 0.55(5)
Simplifying and solving for x, we get:
x = 3
Therefore, 3 liters of the 25% antifreeze solution must be removed from the radiator and replaced with 3 liters of the 75% antifreeze solution to leave the radiator filled with a 55% antifreeze solution.
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plz I need help!!! will give brainlyyyyy
what statement does not apply to a debit card
Answer:
payment fees
Step-by-step explanation:
2. Solve for y.
A 10.5
B 9
C 13.5
D 12
In one month, the median home price in the west fell from $203,400 to $192,300. Find the percent decrease
Mi. 1. John starts driving along the border of Libya and the Mediterranean Sea at an average speed of 45 John is traveling hr from the capital of Libya, Tripoli, to the city of Surt. The distance between these two cities is 230 miles. His distance from Surt is given by the equation y= 230 – 45x, where y is the distance from Surt in miles and x is the time in hours. Complete the table in the attached worksheet (the green column) of data for John's drive.
Here is the completed table:
Time (x) Distance from Surt (y)
0 230
1 185
2 140
3 95
4 50
5 5
To complete the table for John's drive, we need to substitute different values of x into the equation y = 230 - 45x to calculate the corresponding distances from Surt (y) at different times (x).
In this table, the time (x) represents the number of hours John has been driving, and the distance from Surt (y) represents the corresponding distance he has covered from Surt in miles.
For example, when John starts driving (x = 0), he is 230 miles away from Surt. As time progresses, the distance from Surt decreases by 45 miles for every hour of driving, according to the equation y = 230 - 45x.
By substituting different values of x into the equation, we can determine the distance from Surt at various points in John's drive.
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The answer appears incorrect, please help me correct it :)
Every line on the graph is 1/2 unit.
When y = 0, x would be -0.25 and 1.25
When y = 2, x would be -0.5 and 1.5
Complete this item. Identify 1 and 2. Select all that apply of the following terms: acute , right , obtuse , adjacent , vertical , complementary , supplementary. obtuse adjacent vertical supplementary acute right complementary
∠1 and ∠2 are right angles because the measure of both angles is 90 and supplementary angles because the sum of both angles is 180°.
What is the triangle?Triangle is a polygon that has three sides and three angles and the sum of the angle of the triangle is 180 degrees.
The figure is attached in the picture, please refer to the attached picture.
Given that:
An Angle in the figure is a right angle.
Its measure = 90°
So,∠2 = 90° ( vertically opposite angles are equal )
∠1 + ∠2 = 180° ( Linear Pair )
∠1 = 180 - 90
∠1 = 90°
∠1 = ∠2 = 90°
So, ∠1 and ∠2 are right angles because measure of both angles is 90°.
Adjacent angles because both a common arm and a common vertex.
Thus, ∠1 and ∠2 are right angles because the measure of both angles is 90 and supplementary angles because the sum of both angles is 180°.
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Complete the equivalent ratios to find 60% of $600
The value of 60 percent of $600 will be $360.
What is a percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
In this case, 60% of $600 will be illustrated thus:
= 60% × $600
= 60/100 × $600
= 0.6 × $600
= $360
Therefore, the value is $360.
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(Y to the eighth power)(y to the second power) simpified
Answer:
y^10
multiplication of exponents is like addition, you just add exponents
Latoya builds a border for her strawberry plot, which is shaped like a square. All the sides measure 5 feet. How many feet of border does she need to buy?
The amount of feet of border that she needs to purchase is given as follows:
20 feet.
How to obtain the perimeter of a square?The perimeter of a square of side length s is given by the multiplication of four and the side length s, as follows:
P = 4s.
All the sides measure 5 feet, hence the parameter s is given as follows:
s = 5.
Then the perimeter of the square plot is given as follows:
P = 4 x 5
P = 20 feet.
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Ian has $6,000.00 to invest for 2 years. The table shows information about two investments Ian can make.
Ian makes no additional deposits or withdrawals. Which investment earns the greater amount of interest over a period of 2 years?
Investment X earns the greater amount of interest over a period of 2 years.
What is simple interest?Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. It is calculated with the help of the formula,
SI = PRT
where SI is the simple interest, P is the principal amount, R is the rate of interest, and T is the time period.
Let's consider that Ian invests in X, then:
Principle amount, P = $6,000
Time, T = 2 Years
Rate of Interest, R = 4.5% at simple Interest = 0.045
The interest earned is:
Interest = PRT = $6,000 × 0.045 × 2 = $540
Now, consider that Ian invests in Y, then:
Principle amount, P = $6,000
Time, n = 2 Years
Rate of Interest, R = 4% at Compound Interest = 0.04
The interest earned is:
Interest = P(1+R)ⁿ - P
= $6,000(1+0.04)² - $6,000
= $489.6
Since $540>$489.6, therefore, Investment X earns the greater amount of interest over a period of 2 years.
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