Answer:
He took 3 3/4 hours to clean both rooms.
Step-by-step explanation:
1/2 = 2/4
3 1/4 + 2/4 = 3 3/4
Therefore, he took 3 3/4 hours.
A farmer ships oranges in wooden crates. Suppose each orange weighs the same amount. The total weight of a crate filled with g oranges is 24.5 pounds. Write an equation that represents the relationship between the weight of the crate and the number of oranges it contains.
Empty crate:15 ib
Orange:0.38 ib
24.5=___+___×___
What is the inverse of the function, f(x)=2x−1‾‾‾‾‾‾√3−3?
Responses
f−1(x)=(x+3)3−12
f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator open parentheses x plus 3 close parentheses cubed minus 1 over denominator 2 end fraction
f−1(x)=(x−3)3−12
f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator open parentheses x minus 3 close parentheses cubed minus 1 over denominator 2 end fraction
f−1(x)=(x−3)3+12
f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator open parentheses x minus 3 close parentheses cubed plus 1 over denominator 2 end fraction
f−1(x)=(x+3)3+12
Answer:
its the third please mark me as a brainliest
a bookshelf holds 24 mysteries, 12 nonfiction, and 4 biographies. what is the probability of selecting a mystery book, then without replacing it, selecting a non-fiction book?
The probability of selecting a mystery book, then without replacing it, selecting a nonfiction book is approximately 0.1462.
How to determine the probability of selecting a mystery book, then without replacing it, selecting a non-fiction bookOn the bookcase, there are 24 + 12 + 4 = 40 volumes.
The odds of picking a mystery book on the first draw are 24/40.
There are 39 books remaining after the first is drawn, including 12 nonfiction works. Because the initial book was never replaced, there are currently only 11 nonfiction volumes left.
Given that a mystery book was chosen without replacement in the first draw, the probability of selecting a nonfiction book in the second draw is 12/39.
When we multiply these probability together, we get:
P(nonfiction after mystery, not replacing) * P(mystery, not replacing) = (24/40) * (12/39) = 0.14615...
P(nonfiction after mystery, not replacing) * P(mystery, not replacing) = 0.1462
So, the probability of selecting a mystery book, followed by a nonfiction book without replacing it is roughly 0.1462.
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Suppose that prices of a certain model of new homes are normally distributed with a mean of $150,000. Use the 68-95-99.7 rule to find the percentage of buyers who paid:
between $150,000 and $156,000 if the standard deviation is $2000.
The percentage of buyers who paid between $150,000 and $156,000 if the standard deviation is $2000 is 49.9%
Calculating the percent of data of values from the the z-scoresFrom the question, we have the following parameters that can be used in our computation:
Mean = 150000
Standard deviation = 2000
Scores = from $150,000 and $156,000
So, we have
z = (150000 - 150000)/2000 = 0
z = (156000 - 150000)/2000 = 3
This means that it is between a z-score of 0 and a z-score of 3
This is represented as
Probability = (0 < z < 3)
Using a graphing calculator, we have
Probability = 0.49865
Express as percentage
Probability = 49.9%
Hence, the probability is 49.9%
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Winnie and Vanessa Co Ltd. borrowed an amount of money (P) from a rural bank in Miotso at i% p.a simply interest. The company paid A amount of money as well as the total amount of interest (I) to the bank at the end of n- years. Show that, p= A(1+in)-1
The amount of money borrowed by the company from the rural bank is:
P = [tex]A(1 + in)^{-1}[/tex]
What is Amount?
Amount is a term used to describe the total quantity or value of something. It can refer to a quantity of a physical substance or object, such as the amount of water in a bottle or the amount of money in a bank account.
Let P be the amount of money borrowed by Winnie and Vanessa Co Ltd from the rural bank at an interest rate of i% per annum.
The simple interest on this amount after n years will be:
I = P * i * n
The total amount to be paid by the company after n years will be:
A = P + I = P + P * i * n
We can simplify this expression by factoring out P:
A = P(1 + i * n)
Dividing both sides of this equation by (1 + i * n), we get:
P = A / (1 + i * n)
Therefore, the amount of money borrowed by the company from the rural bank is:
P = [tex]A(1 + in)^{-1}[/tex]
This is the desired result.
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In the diagram shown, ABCD is a square. Suppose AB = 6. Find:
17). AC
18). AO
19). BO
Suppose AO = 4. Find:
20). BO
21). Area of Δ AOB
22). Area of ABCD
Suppose DO = 5. Find:
23). DC
24). Area of Δ DOC
25). Area of ABCD
ABCD is square, AC = 6, AO = 3√2, BO = 3√2, BO = 4, DC = 6, OC = 2√13 and area is 36 square units.
To solve the problems, we can use the following properties of squares:
The diagonals of a square bisect each other and are equal in length.
The diagonals of a square form two congruent right triangles.
The center of a square is equidistant from all four vertices of the square.
Since ABCD is a square, we have AC = AB = 6.
Since O is the center of the square, AO is half the length of the diagonal of the square. Using the Pythagorean theorem, we can find the diagonal of the square:
diagonal² = AB² + BC²
= 6² + 6²
= 72
diagonal = √72 = 6√2
Therefore, AO = (1/2) diagonal = 3√2
Since O is the center of the square, BO is equal in length to AO, which we found in part (18). Therefore, BO = 3√2.
If AO = 4 and BO = AO, then BO = 4.
The area of ΔAOB is half the area of the square ABCD. The area of a square is given by side², so the area of ABCD is 6² = 36. Therefore, the area of ΔAOB is (1/2) × 36 = 18 square units.
The area of a square is given by side², so the area of ABCD is 6² = 36 square units.
Since the diagonals of a square bisect each other, DO is half the length of the diagonal of the square. Using the Pythagorean theorem, we can find the diagonal of the square:
diagonal² = AB² + BC²
= 6² + 6²
= 72
diagonal = √72 = 6√2
Therefore, DO = (1/2) diagonal = 3√2
Since ABCD is a square, DC = AB = 6.
The area of ΔDOC is half the area of the square ABCD. Using the Pythagorean theorem, we can find the length of OC:
OC² = AO² + AC²
= 4² + 6²
= 52
OC = √52 = 2√13
Therefore, the area of ΔDOC is (1/2) × 6 × 2√13 = 6√13 square units.
The area of a square is given by side², so the area of ABCD is 6² = 36 square units.
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Leslie deposits $1,600 into an account that earns 3.7% annual interest compounded quarterly. What will be
the total value of her investment after 4 years?
Answer:
A = $1853.96
Step-by-step explanation:
The formula for compound interest is
[tex]A(t)=P(1+r/n)^n^t[/tex], where A(t) is the amount, P is the principal (amount invested or deposited), r is the interest rate, n is the number of compound periods per year, and t is the time in years.
For the problem, our P value is $1600Our r value is 0.037 (we must convert the percent to a decimal)Our n value is 4 (quarterly means 4 so the money is compounded once every 3 months since there 3 months make up a quarter in a year)Our t value is 4We must solve for A(t)[tex]A(t)=1600(1+0.037/4)^(^4^*^4^)\\A(t)=1600(1.00925)^1^6\\A(t)=1853.958942\\A(t)=1853.96[/tex]
there are 105 days until basketball season starts. Melanie says the season starts in 15 weeks. Is this reasonable? Use estimation to justify your answer.
Answer:
Yes, Melanie's statement that the basketball season starts in 15 weeks is reasonable.
To see why, we can estimate the number of days in 15 weeks. Since 1 week is equal to 7 days, 15 weeks would be approximately equal to:
15 weeks x 7 days/week = 105 days
5x+3y=4 -2x-8y=6 Which strategy can you use to eliminate a variable.
The strategy that could be used to eliminate a variable is:
Multiply the first equation by 2 and multiply the second equation by 5. Then, add the resulting equations
Solving system of linear equations using the elimination method: Determining a strategy to eliminateFrom the question, we are to determine a strategy that could be used to eliminate a variable in the given system of equations
From the given information,
The system of linear equations is
5x + 3y = 4
-2x - 8y = 6
To eliminate the variable x, we can multiply the first equation by 2 and then multiply the second equation by 5. After that, we will add the resulting equations
2 × [ 5x + 3y = 4
5 × [-2x - 8y = 6
10x + 6y = 8
-10x - 40y = 30
Add the resulting equations
10x + 6y = 8
+ (-10x - 40y = 30
------------------------
-34y = 38
This way we have eliminated x
Hence,
The above strategy can be used to eliminate a variable
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A weather station on the top of a mountain reports that the temperature is currently -10*C and has been falling at a constant rate of 3*C per hour. If it continues to fall at this rate, find each indicated temperature.
What will the temperature be in 5 hours?
What was the temperature 8 hours ago?
PLEASE HELP ME!!!!
Answer:
The temperature in 5 hours will be -25°C.
The temperature 8 hours ago was 14°C.
Step-by-step explanation:
To find the temperature, y, in degrees Celsius at any given number of hours, x, from the current time, we can create a linear equation in the form y = mx + b, where m is the rate of change and b is the current temperature.
Given the current temperature is -10°C, then b = -10.
Given the temperature falls at a constant rate of 3°C per hour, then m = -3.
Substitute the values of m and b into the formula:
[tex]\boxed{y = -3x - 10}[/tex]
where:
y is the temperature in °C.x is the number of hours.To calculate the temperature in 5 hours time, substitute x = 5 into the equation:
[tex]\begin{aligned}\implies y&=-3(5)-10\\&=-15-10\\&=-25^{\circ}\text{C}\end{aligned}[/tex]
Therefore, the temperature in 5 hours will be -25°C.
To calculate the temperature 8 hours ago, substitute x = -8 into the equation. The value of x is negative since we want to find the temperature 8 hours before the current time.
[tex]\begin{aligned}\implies y&=-3(-8)-10\\&=24-10\\&=14^{\circ}\text{C}\end{aligned}[/tex]
Therefore, the temperature 8 hours ago was 14°C.
Aisha spent $120.94 to buy 2 wheelbarrows. The wheelbarrows both had the same price. How much did each wheelbarrow cost?
#9 75% of 1
#10 50% of 350 is
#11 What percent of 450 is 50
#9 75% of 1.
#10 50% of 350.
#11
To find out what percent of 450 is 50, we can set up a proportion
x/100 = 50/450
Simplifying the right-hand side of the equation by dividing both numerator and denominator by 50 gives
x/100 = 1/9
Multiplying both sides by 100 gives
x = 100/9
Hence, 50 is approximately 11.1% of 450.
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Eight cards with one letter on each card spell out the word SURPRISE. If you choose one card at random, what is the probability of this event?
P(R) =
given h(x)=2x^2-7x+4, find h(-7)
The output value of h(-7) in the function h(x) = 2x² - 7x + 4 is 151.
What is the output value of h(-7) in the given function?A function is simply a relationship that maps one input to one output.
Given the function in the question
h(x) = 2x² - 7x + 4,
Find h(-7)
To find h(-7), we substitute -7 for x in the equation of h(x) and simplify:
h(x) = 2x² - 7x + 4
Plug in x = -7
h(-7) = 2(-7)² - 7(-7) + 4
h(-7) = 2(49) + 49 + 4
h(-7) = 98 + 49 + 4
h(-7) = 151
Therefore,the output value of h(-7) is equal to 151.
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a skateboard ramp is 11 in high and raises at an angle of 22 in how long is the base of the ramp? Round to the nearest inch.
Answer: The length of the base of the ramp is approximately 27 inches when rounded to the nearest inch.
Step-by-step explanation:
We can use trigonometry to solve this problem.
Let's call the length of the base of the ramp "x". Then, we can use the tangent function to find x:
tan(22) = 11/x
To solve for x, we can multiply both sides by x and divide by tan(22):
x = 11 / tan(22)
Using a calculator, we can find that:
x ≈ 27 inches
Therefore, the length of the base of the ramp is approximately 27 inches when rounded to the nearest inch.
Greetings! ZenZebra at your service, hope it helps! <33
Let = {1, 2, 3, 4, 5} be a set. Consider the functions = {(1,3), (2,5), (3,3), (4,1), (5,2)} and = {(1,4), (2,1), (3,1), (4,2), (5,3)} From into . (i) Determine the range of and (ii) Find the composition functions ∘ and ∘ .
g ∘ f is the function {(1,2), (2,1), (4,2), (5,3)}. And the range of f is {1, 2, 3, 5}, and the range of g is {1, 2, 3, 4}.
How to solve the problem?
(i) To determine the range of a function, we need to find all the possible output values of the function. In other words, we need to find the set of all second elements in the ordered pairs of the function. For the function f, the set of all second elements is {3, 5, 1, 2}. For the function g, the set of all second elements is {4, 1, 2, 3}. Therefore, the range of f is {1, 2, 3, 5}, and the range of g is {1, 2, 3, 4}.
(ii) To find the composition functions f ∘ g and g ∘ f, we need to apply the functions in the correct order. The composition function f ∘ g means that we first apply g and then apply f to the result. The composition function g ∘ f means that we first apply f and then apply g to the result.
For f ∘ g:
First, we apply g to the domain of f.
(1,3) is mapped to (4,2) by g
(2,5) is mapped to (1,4) by g
(3,3) is mapped to (1,4) by g
(4,1) is mapped to (2,1) by g
(5,2) is mapped to (3,1) by g
Now we apply f to the result of g.
(4,2) is mapped to 2 by f
(1,4) is mapped to 4 by f
Therefore, f ∘ g is the function {(1,4), (4,2)}.
For g ∘ f:
First, we apply f to the domain of g.
(1,4) is mapped to 3 by f
(2,1) is mapped to 5 by f
(3,1) is mapped to 3 by f
(4,2) is mapped to 1 by f
(5,3) is mapped to 2 by f
Now we apply g to the result of f.
3 is mapped to (1,2) by g
5 is mapped to (2,1) by g
1 is mapped to (4,2) by g
2 is mapped to (5,3) by g
Therefore, g ∘ f is the function {(1,2), (2,1), (4,2), (5,3)}.
Note that the composition functions f ∘ g and g ∘ f are not the same. In general, composition of functions is not commutative, i.e., f ∘ g is not equal to g ∘ f.
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Is anyone here looking for a personal tutor?????
meAnswer: me
Step-by-step explanation: I need help
Callie spent 1 1/2 hours outside with her sister. They spent half of that time jumping on the trampoline. How long did they jump on the trampoline?
Answer:
45 Minutes
Step-by-step explanation:
1.5 Hours = 90 Minutes (1.5*60)
90/2 = 45
45 Minutes on the trampoline.
What is the meter reading, in ccf, indicated by each of the gas meters shown? cengage
The meter reading, in ccf, indicated by each of the gas meters would be 8.83 ccf.
Required to find the meter reading in ccf
Let x be [tex]m^{2}[/tex] - meter readings.
The readings in ccf is:
Reading = x/ 2.832
Now, Assume the value of x is 25; The readings will be:
Reading = 25/ 2.832 ccf
Reading = 8.83 ccf
The complete question is
Manuel works for the water company as a meter reader. The meter below is the Jansen's water meter. What is the reading, in ccf, on the meter shown?
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What is the surface area of this cylinder?
Use ≈ 3.14 and round your answer to the nearest hundredth.
10 mm
5 mm
square millimeters
The surface area of the cylinder is 471 mm².
Given is a cylinder of height 5 mm and radius 10 mm, we need to find the surface area of the cylinder,
So, the surface area of the cylinder is = 2π × r (h+r)
= 2 × 3.14 × 5 (5+10)
= 2 × 3.14 × 75
= 471 mm²
Hence, the surface area of the cylinder is 471 mm².
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The tractor will cost £64,950 the compound interest rate is 4% per annum. You will pay back the loan in 36 equal monthly payments. What will you pay each month?
Answer: You will pay £1,912.54 each month.
Step-by-step explanation:
We can use the formula for the monthly payment of a loan with compound interest:
monthly payment = (principal * monthly interest rate) / (1 - (1 + monthly interest rate)^(-n))
where principal is the amount borrowed, monthly interest rate is the annual interest rate divided by 12, and n is the total number of monthly payments.
In this case, the principal is £64,950, the annual interest rate is 4%, so the monthly interest rate is 4%/12 = 0.00333, and the number of monthly payments is 36.
Plugging in these values, we get:
monthly payment = (64950 * 0.00333) / (1 - (1 + 0.00333)^(-36)) = £1,912.54
Therefore, you will pay £1,912.54 each month.
$44,000 a 6% for 2 years for simple interest
The total interest that will accrue on the principal amount of $44,000 over a period of 2 years at a simple interest rate of 6% is $5,280.
The given problem involves calculating the amount of interest that will accrue on a principal amount of $44,000, which is invested at a simple interest rate of 6% for a period of 2 years.
To solve the problem, we can use the formula for simple interest, which is:
Interest = Principal x Rate x Time
In this case, the principal amount is $44,000, the rate of interest is 6%, and the time period is 2 years. So, plugging in these values, we get:
Interest = $44,000 x 0.06 x 2
Interest = $5,280
Unlike compound interest, simple interest is calculated only on the principal amount, and not on the accumulated interest. This means that the interest earned each year remains constant, which can make it easier to calculate and understand compared to compound interest.
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a tree in lamar’s backyard has been growing for 4 1/2 years. the tree is 4/5 meters tall. what is the unit rate in meters per year? write your answer as a fraction or pixies number in simplest form.
As the tree is 4/5 meters tall the unit rate in meters per year is 8/45 or approximately 0.177 meters per year.
To find the unit rate in meters per year, we need to divide the height of the tree by the time it took to grow.
Height of the tree = 4/5 meters
Time taken to grow = 4 1/2 years = 9/2 years
Unit rate = Height/Time = (4/5)/(9/2) meters per year
To divide by a fraction, we can multiply by its reciprocal:
Unit rate = (4/5) * (2/9) meters per year
Unit rate = 8/45 meters per year
Therefore, the unit rate of the tree in meters per year is 8/45 or approximately 0.177 meters per year.
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The body temperatures in degrees Fahrenheit of a sample of adults in one small town are:
98 97.9 99 97.3 98.9 99.6 97.8 99.8 99.1 98.4 98.7 97.6 96.5
Assume body temperatures of adults are normally distributed. Based on this data, find the 95% confidence
interval of the mean body temperature of adults in the town. Enter your answer as an open-interval (i.e.,
parentheses) accurate to 3 decimal places. Assume the data is from a normally distributed population.
95% C.I. =
The 95% confidence interval of the mean body temperature of adults in the town is (97.584, 98.876)°F (open-interval notation), accurate to 3 decimal places.
What is the 95% confidence interval of the mean body temperature of adults in the town?To find the 95% confidence interval (C.I.) of the mean body temperature, we need to use the formula:
C.I. = x ± z*(σ/√n)
Where:
x is the sample mean
σ is the population standard deviation (unknown, but we can estimate it using the sample standard deviation)
n is the sample size
z is the critical value for the desired confidence level (95% in this case)
First, we need to calculate the sample mean, sample standard deviation, and sample size:
x = (98 + 97.9 + 99 + 97.3 + 98.9 + 99.6 + 97.8 + 99.8 + 99.1 + 98.4 + 98.7 + 97.6 + 96.5) / 13 = 98.23
s = √((1/(n-1)) * Σ(xi - x)²)
s = 1.339
n = 13
Next, we need to find the critical value, z, for a 95% confidence level. We can look this up in a standard normal distribution table or use a calculator. For a 95% confidence level, z = 1.96.
Now we can plug in the values into the formula to get the 95% confidence interval:
C.I. = 98.23 ± 1.96*(1.339/√13) = (97.584, 98.876)
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Given this equation what is the value of y at the indicated point?
Answer:
y = 4
Step-by-step explanation:
given equation of line is
y = - 3x - 2 and (- 2, y ) is a point on the line, then substitute x = - 2 into the equation for y , that is
y = - 3(- 2) - 2 = 6 - 2 = 4
[64+{23-(-14+5x12/2-6)}]
Answer:
77
Step-by-step explanation:
First, let's simplify the expression inside the innermost parentheses:
5x12 = 60
60/2 = 30
-14 + 30 - 6 = 10
Now, we have:
[64 + {23 - 10}] = [64 + 13] = 77
Please help
Question in image
Answer:
C 86
Step-by-step explanation:
You want the measure of the angle marked x° where chords cross. The angle marked x° intercepts an arc of 104° and one that is unmarked. The remaining arcs of the circle are marked 111° and 77°.
Measure of xThe measure of angle x is half the sum of the arcs it intercepts. One of those is given as 104°. The other will be ...
360° -111° -104° -77° = 68°
Then the value of x is ...
(104 +68)/2 = 172/2 = 86
The value of x is 86, choice C.
<95141404393>
I need help plssss i domt get it
Answer:
V = 5747.02 ft^3
Step-by-step explanation:
We're given the general formula for volume (V) and we must use this general formula and the information we're given to find the volume of the hemisphere.r stands for radius, which is 1/2 the distance between the center of a circle and the edge. The 14 in the diagram represents the radiusIn the formula r^3 means that the radius is cubed and thus 14 must be multiplied by itself three times (14 * 14 * 14)
Therefore, to solve for volume, we plug in 14 for r in the general formula:
[tex]V=2/3\pi (14)^3\\V=2/3\pi (14)(14)(14)\\V=2/3\pi *2744\\V=5747.020161\\V=5747.02[/tex]
Lastly, volume is always in units cubed (e.g., ft^3 or mi^3 since volume deals with the three-dimensional space of an object
Please help with question #2
Answer:
50 in
Step-by-step explanation:
Split into 4 shapes. One on each side with 5 in x 2 in, one on the top with 12 in x 2 in, and one in the middle with 3 in x 2 in. We add all together:
2(5×2)+(12×2)+(3×2) = 50 in
A caterer made a sandwich 6' 6" long for a party. by request 3' 8" were added to the sandwich. what was the total length of the sandwich?
The total length of the sandwich, given the addition to the sandwich, would be 10. 17 feet.
How to find the length of the sandwich ?In order to accurately add lengths measured in feet and inches, it is necessary to transform the unit type prior to adding them together. As an example, take a sandwich that originally measured 6 feet 6 inches long with 3 feet 8 inches being added into it.
To combine these measurements, we must first convert inches to feet or vice versa for optimal results. Let's begin with transforming the inches to feet:
6 feet 6 inches = 6 + ( 6 / 12 ) feet = 6. 5 feet
3 feet 8 inches = 3 + ( 8 / 12 ) feet = 3. 67 feet
Then add the lengths to become :
6. 5 feet + 3. 67 feet = 10. 17 feet
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