Answer:
(18, -14), 7
Step-by-step explanation:
y - (y-intercept) = slope (x - (x-intercept))
If o=12, find the sample size to estimate the mean with an error of +4 and 95 percent confidence (rounded to the next higher integer).
Multiple Choice
75
35
58
113
URGENT
We need to round up to the next higher integer, the sample size required to estimate the mean with an error of +4 and 95 Percent confidence is 170.
To find the sample size to estimate the mean with an error of +4 and 95 percent confidence, we need to use the formula:
n = [(z*sigma)/E]^2
Where:
n = sample size
z = z-score for 95% confidence level (which is 1.96)
sigma = standard deviation (unknown in this case)
E = maximum allowable error (which is +4 in this case)
We are given that o=12, which is the population standard deviation. Since we do not have any information about the sample standard deviation, we can use the population standard deviation as an estimate. Therefore, we can substitute o=12 in the above formula to get:
n = [(1.96*12)/4]^2
n = 169.64
Since we need to round up to the next higher integer, the sample size required to estimate the mean with an error of +4 and 95 percent confidence is 170.
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Bus A stops at a certain bus stop every 25 minutes. Bus B stops at the same stop every 40 minutes. If both buses are at the bus stop at 9:30 a.m., when is the next time they will be there together again?
A. 12:20 p.m.
B. 12:50 p.m.
C. 1:10 p.m.
D. 1:30 p.m.
SHOW YOUR WORK!!
Answer:
B
Step-by-step explanation:
Bus A
1. 9:55
2. 10:20
3.10:45
4.11:10
5.11:35
6.12:00
7.12:25
8.12:50
Bus B
1. 10:10
2.10:50
311:30
4. 12:10
5. 12:50
Ten years into your 15-year $600,000 mortgage begun in October 2015, you inherit your rich uncle's estate and decide to pay off the outstanding principal on your mortgage. What is that amount? (Do not round the payment amount to the nearest cent. Round the final outstanding principal to the nearest cent.)
You need to pay mortgages of $6370 monthly.
What is mortgage?A mοrtgage is an agreement between yοu and a lender that gives the lender the right tο take yοur prοperty if yοu fail tο repay the mοney yοu've bοrrοwed plus interest. Mοrtgage lοans are used tο buy a hοme οr tο bοrrοw mοney against the value οf a hοme yοu already οwn
In this case,
P = $600000
r = 13.10 % = 0.131 [Credit card rate fοr Octοber 2015]
t = 15years
n = 12 [Cοmpοunded mοnthly]
Monthly payment = [tex]$ \rm \frac{r \times P}{n} \times \left[1 - (1 +\frac{r}{n}) - nt \right][/tex]
= [tex]$ \rm \frac{0.131 \times 600000}{12} \times \left[1 - (1 +\frac{0.131}{12}) - 12 \times 15 \right][/tex]
= 6550 - 180
= 6550 - 180
= 6370
Thus, You need to pay mortgages of $6370 monthly.
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High temperatures in a certain city for the month of August follow a uniform distribution over the interval 65°F to 87°F. What is the probability that a randomly selected August day has a high temperature that exceeded 70°F?
Probability that a randomly selected August day has a high temperature that exceeds 70°F is approximately 0.7727, or 77.27%.
Assuming that the range of high temperatures in a specific city throughout the month of August is uniform, the probability density function (pdf) of the distribution is as follows:
[tex]f(x) = 1 / (b - a) = 1 / (87 - 65) = 1 / 22[/tex]
where the temperature interval's lower and higher bounds are set at 65 and 87, respectively.
We must determine the area under the pdf curve to the right of x = 70°F in order to determine the likelihood that a randomly chosen August day will have a high temperature that is higher than 70°F. This can be done by integrating the pdf from 70 to 87:
[tex]P(x > 70) = ∫(70 to 87) (70 to 87) f(x) dx = ∫(70 to 87) (70 to 87) 1/22 dx = [1/22 * (x)] (70 to 87) = (1/22) * (87 - 70) = 0.7727[/tex]
As a result, there is a 77.27% probability that an August day chosen at random would have a high temperature above 70 degrees Fahrenheit. This suggests that out of 100 randomly selected August days, we may expect roughly 77 days to have a high temperature surpassing 70°F.
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Mark was working on the long jump
competition, and he was able to
jump 9 3
4 feet. Chris jumped 7
8
as far as Mark. Write and solve the
equation that will help you figure
out how far Chris jumped.
Explain the steps you took to solve
Chris has jumped 85/8 feet.
What is the distance?
Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. The distance can refer to a physical length in physics or an estimate based on other factors in common usage.
Here, we have
Given: Mark was working on the long jump competition, and he was able to jump 9 3/4 feet. Chris jumped 7/8 as far as Mark.
The distance jumped by Mark = 9 3/4 feet
The distance jumped by Chris = 9 3/4 + 7/8
The total distance covered by Chris would be:
= 9 3/4 + 7/8
= 7/8 + 39/4
= 85/8
Hence, Chris has jumped 85/8 feet.
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A ship traveled 25° South of West. After 250 miles changed direction to 70° East of South. After it traveled 45 miles further, find the distance and direction of the ship from its starting point.
We can approach this problem by breaking down the two displacements of the ship into their respective x- and y-components and then adding them together to find the net displacement.
For the first displacement, the ship traveled 25° South of West for 250 miles. This can be broken down into an x-component and a y-component as follows:
x = 250 cos(25°) (to the west) y = -250 sin(25°) (to the south)
For the second displacement, the ship changed direction to 70° East of South and traveled 45 miles further. This can also be broken down into an x-component and a y-component:
x = 45 cos(70°) (to the east) y = -45 sin(70°) (to the south)
To find the net displacement, we can add the x-components and y-components separately:
total x = 250 cos(25°) + 45 cos(70°) total y = -250 sin(25°) - 45 sin(70°)
We can use these values to find the distance of the ship from its starting point by using the Pythagorean theorem:
distance = sqrt((total x)^2 + (total y)^2)
Substituting the values from above and evaluating:
distance = sqrt((250 cos(25°) + 45 cos(70°))^2 + (-250 sin(25°) - 45 sin(70°))^2)
distance ≈ 272.8 miles
To find the direction of the ship from its starting point, we can use the inverse tangent function to find the angle:
angle = atan(total y / total x)
Substituting the values from above and evaluating:
angle ≈ -65.1°
Since the angle is negative, we know that the direction is to the west of south. Therefore, the ship is approximately 272.8 miles away from its starting point in a direction that is 65.1° west of south.
There are 37 erasers in the receptacle. Each day the students loose 3 erasers. How many erasers are in the receptacle for each of the first 6 days
There will be 34,31,28,25,22,19 erasers after Day 1,2,3,4,5,6respectively.
Define daysDays are units of time that are used to measure the duration of a complete rotation of the Earth on its axis. One day is defined as the time it takes for the Earth to complete one full rotation on its axis, which is approximately 24 hours long.
Starting with 37 erasers, if 3 erasers are lost each day, then the number of erasers in the receptacle for each of the first 6 days can be calculated as follows:
After Day 1: 37 - 3 = 34 erasers
After Day 2: 34 - 3 = 31 erasers
After Day 3: 31 - 3 = 28 erasers
After Day 4: 28 - 3 = 25 erasers
After Day 5: 25 - 3 = 22 erasers
After Day 6: 22 - 3 = 19 erasers
Therefore, there will be 34 erasers after Day 1, 31 erasers after Day 2, 28 erasers after Day 3, 25 erasers after Day 4, 22 erasers after Day 5, and 19 erasers after Day 6.
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WILL GIVE BRAINLIEST
Defense mechanisms
please just check my work, see if u can spot out any errors… thanks :)
Answer:
the is no error in your work
Which pair of ratios does NOT form a proportion? (1
03 24
5 40
-30 15
10
S
3
The pair of ratios that does not form a proportion is 103/24 and 5/40.
To check if two ratios form a proportion, we need to simplify them to their simplest form and compare them. If the two ratios are equal after simplification, then they form a proportion.
In this question, we are given five ratios: 103/24, 5/40, -30/15, 10/5, and 3/S.
To simplify the first ratio, we can divide both the numerator and denominator by their greatest common factor, which is 1. Therefore, the simplified form of 103/24 is 4.29 (rounded to two decimal places).
To simplify the second ratio, we can also divide both the numerator and denominator by their greatest common factor, which is 5. Therefore, the simplified form of 5/40 is 0.125.
When we compare these two simplified ratios, we can see that they are not equal. Therefore, the pair of ratios that does not form a proportion is 103/24 and 5/40.
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Which pair of ratios does NOT form a proportion?
103 24
5 40
-30 15
10 5
3 S
the product of a number and -6 amounts to five times the sum of that number and 33. Find the number.
By setting up the equation and solving for the unknown variable, we find that the number in question is -15. The answer provides a step-by-step method for solving an equation that represents a word problem.
Let's start by translating the given problem into an equation.
"The product of a number and -6" can be written as "-6x", where "x" is the unknown number. "Five times the sum of that number and 33" can be written as "5(x+33)".
Putting these together, we get:
-6x = 5(x+33)
Now we can solve for "x":
-6x = 5x + 165
-11x = 165
x = -15
Therefore, the number we're looking for is -15.
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A bank has fixed the rate of interest 10% p.a. semi-annually compound interest in account A and 12% per annum annually compound interest in account B. If you are going to deposit Rs. 30,000 for 2 years in the same bank in which account will you deposit and why? Give your reason with calculation.
As the calculations show, account B will yield a bigger total sum after two interest years than account A. As a result, we should deposit our funds in account B.
what is interest ?In mathematics, interest is the amount of money earned or payable on an original investment or loan. You can use either simple or compound interest. Simple interest is calculated as a percentage of the initial amount, whereas compound interest is calculated on the principal amount plus any previously earned interest. If you invest $100 at a 5% annual simple interest rate, you will get $5 in interest every year for three years, for a total of $15.
Account A: Semi-annual interest rate = 10% divided by two equals 5%.
2 years multiplied by 2 equals 4 compounding periods.
Total interest earned Equals Rs. 30,000 multiplied by (1 + 5%/2).
4 - Rs. 30,000 = Rs. 6,380.
13 After two years, the total sum is Rs. 30,000 plus Rs. 6,380.
13 = Rs. 36,380.
13
About Account B:
12% annual interest rate
The number of compounding periods is equal to two.
Total interest earned = Rs. 30,000 multiplied by (1 + 12%)
2 - Rs. 30,000 = Rs. 7,440
After two years, the total payment is Rs. 30,000 + Rs. 7,440 = Rs. 37,440.
As the calculations show, account B will yield a bigger total sum after two years than account A. As a result, we should deposit our funds in account B.
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Enterprise A is considering a new production line project with 100% equity financing. The expected operational life of the project is 6 years. Investment value in equipment is 1,500 million VND, which is paid once in 0. Working capital is spent 2 times in the first 2 years of the project (year 0 and year 1), with the amount respectively 300 million VND and 100 million VND. Working capital is fully recovered once at the end of the project (year 6). The production line is depreciated evenly over 6 years, with negligible liquidation value.
Year
1
2
3
4
5
6
Revenue
860
920
1.050
1.200
880
820
Million VND
Variable costs are 40% of net sales. Fixed costs (excluding depreciation of fixed assets) are VND 250 million/year. The corporate income tax rate is 20%. Corporate discount rate is 15%/year. Determine the NPV of the project. If the project is selected according to NPV criteria, will the project be approved?
To calculate the NPV of the project, we need to find the cash inflows and outflows for each year and discount them back to their present value using the corporate discount rate of 15%.
Year 0:
Initial investment = 1,500 million VND
Working capital = -300 million VND
Year 1:
Revenue = 860 million VND
Variable costs = -344 million VND (40% of net sales)
Fixed costs = -250 million VND
Depreciation = -250 million VND (1,500 million VND / 6)
Operating income before taxes = 16 million VND (860 - 344 - 250 - 250)
Taxes = -3.2 million VND (20% of operating income before taxes)
Operating income after taxes = 12.8 million VND (16 - 3.2)
Add back depreciation = 250 million VND
Net cash flow = 262.8 million VND
Discounted cash flow = 228 million VND (262.8 / 1.15)
Year 2:
Revenue = 920 million VND
Variable costs = -368 million VND (40% of net sales)
Fixed costs = -250 million VND
Depreciation = -250 million VND (1,500 million VND / 6)
Operating income before taxes = 52 million VND (920 - 368 - 250 - 250)
Taxes = -10.4 million VND (20% of operating income before taxes)
Operating income after taxes = 41.6 million VND (52 - 10.4)
Add back depreciation = 250 million VND
Net cash flow = 291.6 million VND
Discounted cash flow = 231.9 million VND (291.6 / 1.15^2)
Year 3:
Revenue = 1,050 million VND
Variable costs = -420 million VND (40% of net sales)
Fixed costs = -250 million VND
Depreciation = -250 million VND (1,500 million VND / 6)
Operating income before taxes = 130 million VND (1,050 - 420 - 250 - 250)
Taxes = -26 million VND (20% of operating income before taxes)
Operating income after taxes = 104 million VND (130 - 26)
Add back depreciation = 250 million VND
Net cash flow = 354 million VND
Discounted cash flow = 255.3 million VND (354 / 1.15^3)
Year 4:
Revenue = 1,200 million VND
Variable costs = -480 million VND (40% of net sales)
Fixed costs = -250 million VND
Depreciation = -250 million VND (1,500 million VND / 6)
Operating income before taxes = 220 million VND (1,200 - 480 - 250 - 250)
Taxes = -44 million VND (20% of operating income before taxes)
Operating income after taxes = 176 million VND (220 - 44)
Add back depreciation = 250 million VND
Net cash flow = 426 million VND
Discounted cash flow = 286.6 million VND (426 / 1.15^4)
Year 5:
Revenue = 880 million VND
Variable costs = -352 million VND (40% of net sales)
Fixed costs = -250 million VND
Depreciation = -250 million VND (1,500 million VND / 6)
Operating income before taxes = 28 million VND
fMr. Dieter wants to tile the family room in his basement. He has selected a pattern of square tiles that measure 9 inches by 9 inches each. The.shape of the floor to be tiled is shown below. (3 points for each part)
(a) The area of the family room is 146 square feet .
(b) 21.6 tiles of the 9 inches by 9 inches tiles will take to cover the floor.
(c) total number of boxes that Mr. Dieter will buy for the room is 1.8 boxes.
The area of the rectangle is on its side. Basically, the formula for the area is equal to the product of the length and width of a rectangle. And when we talk about the perimeter of a rectangle, it is equal to all four of its sides.
(a) the area of the family room can be determined by calculating the area of each of the shapes and adding the 3 areas together
area of a rectangle = length x breadth
⇒ 16 x 7 = 112 ft²
Area of a triangle = 1/2 x base x height
Area of the smaller triangle = (1/2) x 4 x 3 = 6 ft²
Area of the bigger triangle = (1/2) x 8 x 7 = 28 ft²
Some of the areas = 112 + 6 + 28 = 146 ft²
(b)
1. First convert the area of the room to inches
⇒ 1 ft = 12 in
⇒ 146 x 12 = 1752 in²
2. the next step is to determine the area of the tile
area of a square = length²
⇒ 9² = 81 in²
3. Divide the area of the room by the area of the tile
⇒ 1752 / 81 = 21.6 tiles
(c)
total number of boxes that would be bought = 21.6 /12 = 1.8 boxes.
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The entire group of individuals we want information about is called the sample.
The statement is False. The entire group of individuals we want information about is called the population, not sample.
What is sample?In statistics, a sample is a subset of individuals or observations taken from a larger population, which is used to estimate characteristics or parameters of the population.
The goal of statistical analysis is often to make inferences about a population based on information gathered from a representative sample. Therefore, it is important to carefully select a sample that is truly representative of the population of interest.
The sample is a subset of the population that is selected for analysis in order to make inferences about the population.
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The complete question is : The entire group of individuals we want information about is called the sample.
a. True
b. False
A bookstore manager will randomly select 1 of 5 newly
arrived fiction books and 1 of 4 newly arrived nonfiction
books for a window display. What is the probability that
the manager will select the shortest of the newly arrived
fiction books and the longest of the newly arrived
nonfiction books?
A. 5%
B. 10%
C. 20%
D. 45%
Answer:
Step-by-step explanation:
number of books are 5 so you will have to do 5 by hundred which will lead to twenty percent
The likelihood that the manager will choose the longest just-received nonfiction book and the shortest recently arrived fiction book is 1/20, or 5%.
What is percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
The probability of selecting the shortest fiction book is 1/5 and the probability of selecting the longest nonfiction book is 1/4. Since these events are independent, we can multiply their probabilities to find the probability of both events happening:
P(shortest fiction book and longest nonfiction book) = P(shortest fiction book) x P(longest nonfiction book) = 1/5 x 1/4 = 1/20
So the probability that the manager will select the shortest of the newly arrived fiction books and the longest of the newly arrived nonfiction books is 1/20, which is equivalent to 5%.
Therefore, the answer is option A.
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1. Find the critical points for the graph of
y = 2x² +22x + 48
Write your answers as ordered pairs (x, y).
y-intercept(s):
x-intercept(s):
vertex:
Answer:
X-intercept(s): (-3,0), (-8,0)
Y-intercept(s): (0,48)
Vertex: (-11/2,-25/2)
Step-by-step explanation:
X-intercepts: When you are finding the x-intercepts, there are two ways to find your x-intercepts like you can find in the Quadratic Formula or plug the equation into your calculator and see it on the graph/ table. If you like the quadratic formula, you need plug into the a, b, and c and it will look like x= -22±√(22^2)-4(2)(48))/2(2). It will be the same answer. on the another hand, if you like the calculator way, you get your calculator that need be TI-84 plus CE or TI-84 then go on y= then put your equation like 2x^2+22x+48 after that you click on graph. if you cant find the x-intercepts on the graph, you can do 2nd then above the graph buttom you can see it in the table. When you looking at the table, look for the 0s in the y table.
Y-intercept: When you are finding the y-intercepts, there are two ways to find your y-intercepts like you need plug in 0 for x or plug the equation into your calculator and see it on the graph/ table. If you like the quadratic formula, you need plug in 0 for x and it will look like y=2(0)^2 +22(0)+48. it would the get the same answer. if you like the calculator way, you get your calculator that need be TI-84 plus CE or TI-84 then go on y= then put your equation like 2x^2+22x+48 after that you click on graph. if you cant find the x-intercepts on the graph, you can do 2nd then above the graph buttom you can see it in the table. When you looking at the table, look for the 0s in the x table.
Vertex:
1. Get your equation in the form like this y=ax^2+bx+c
2. Calculate -b/2a. This is the x-coordinate of the vertex.
3. To find the y- coordinate of the vertex, simply plug the x to the quadratic equation and solve for y.
Comment if i am right or wrong
HElp plsssssssssssssss
can somebody please help me with this asap!!
The relative frequency of music downloads that were regional, either tropic or urban, were not urban are 42%,16% and 89% respectively.
What is relative frequency?Relative frequency is a statistical concept that refers to the proportion or percentage of times a particular event or category occurs in relation to the total number of events or categories. It is calculated by dividing the frequency of the event or category by the total number of events or categories
Equation:(a) The relative frequency of music downloads that were regional is:
230/550 = 0.42 or 42%
(b) The relative frequency of music downloads that were either tropical or urban is:
(80+10)/550 = 0.16 or 16%
(c) The relative frequency of music downloads that were not urban is:
(230+170+80)/550 = 0.89 or 89%
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a right triangle has sides 8,15, and 17 Use these lengths to find tanL, sinL, and cosL
The cosine of an angle in a right triangle is defined as the ratio of the length of the leg adjacent to the angle to the length of the hypotenuse.
[tex]tanL = 15/8[/tex][tex]sinL = 15/17[/tex][tex]cosL = 8/17[/tex]
What are the properties of a right triangle?In a right triangle, the side opposite the right angle is called the hypotenuse (in this case, it's the side with length 17).
The other two sides are called the legs. We can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs:
hypotenuse^2 [tex]= leg1^2 + leg2^2[/tex]
For this triangle, we have:
[tex]17^2 = 8^2 + 15^2[/tex]
Simplifying this equation, we get:
[tex]289 = 64 + 225[/tex]
Therefore, the equation is true, and we have verified that this is a right triangle.
Now, we can use the trigonometric ratios to find the values of tanL, sinL, and cosL, where L is the angle opposite the leg with length 8.
The tangent of an angle in a right triangle is defined as the ratio of the length of the leg opposite the angle to the length of the leg adjacent to the angle. Therefore, we have:
tanL = opposite/adjacent [tex]= 15/8[/tex]
The sine of an angle in a right triangle is defined as the ratio of the length of the leg opposite the angle to the length of the hypotenuse. Therefore, we have:
sinL = opposite/hypotenuse [tex]= 15/17[/tex]
The cosine of an angle in a right triangle is defined as the ratio of the length of the leg adjacent to the angle to the length of the hypotenuse. Therefore, we have:
cosL = adjacent/hypotenuse = 8/17
Therefore, , the values we found are:
[tex]tanL = 15/8[/tex]
[tex]sinL = 15/17[/tex]
[tex]cosL = 8/17[/tex]
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A bus travelled for 3 3⁄4 hours at an average speed of 48 km per hour. What is the total distance
covered by the bus?
Answer:
distance = 180 km
Step-by-step explanation:
To find the total distance, we use this formula:
distance = speed * time
where speed is 48 km/hour and time is 3 [tex]\frac{3}{4}[/tex] hours.
inserting the value we get
distance = 48 km/hour × 3.75 hours
distance = 180 km
What is the additive inverse of the polynomial?
The additive inverse of the polynomial -7y² + x²y -3xy - 7x² include the following: A. 7y² - x²y + 3xy + 7x².
What is an additive inverse?In Mathematics and Geometry, an additive inverse can be defined as a number (n) which when added to another number (a) makes it equal to zero (0). This ultimately implies that, an additive inverse is the opposite of another number (a).
Mathematically, an additive inverse can be represented by the following equations:
a + n = 0
a = -n
-7y² + x²y - 3xy - 7x² = -(-7y² + x²y - 3xy - 7x²)
-7y² + x²y - 3xy - 7x² = 7y² - x²y + 3xy + 7x²)
In this context, we can reasonably infer and logically deduce that an additive inverse of -7y² + x²y -3xy - 7x² is 7y² - x²y + 3xy + 7x².
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Choose all of the expressions that are equal to 61.
a. |−61|
b. the distance from zero to −61
c. the opposite of 61
d. −(−61)
e. the opposite of −61
f. −|−61|
g. −|61|
Answer:
a mode of negative number again gives the positive value
d. -(-61) =61 by multiplication sign rule
e. opposite of -61 =61
Answer: e
Step-by-step explanation:
the opposite is 61
PLSSS HELP NEED THIS ASAP
Answer:
Step-by-step explanation:
[tex]\frac{e^2\times e^3}{e^6}=\frac{e^{2+3}}{e^6}[/tex]
[tex]=\frac{e^5}{e^6}[/tex]
[tex]=e^{5-6}[/tex]
[tex]=e^{-1}[/tex]
Solution: (C)
how do i find these I’m so confused
Triangles BIG and MOP are similar so, the values of v, w, x, y are 36 cm, 156°, 46.7°, 43.2° respectively.
Describe Triangles?A triangle is a two-dimensional geometric shape that is formed by three line segments that connect three non-collinear points in a plane. These points are called the vertices of the triangle, and the line segments connecting them are called sides.
Triangles are characterized by several properties, including their side lengths, angles, and areas. Based on the lengths of their sides, triangles can be classified into three types:
Scalene triangle: A triangle in which all three sides have different lengths.
Isosceles triangle: A triangle in which two sides have the same length.
Equilateral triangle: A triangle in which all three sides have the same length.
Since triangles BIG and MOP are similar, we know that their corresponding angles are equal and their corresponding sides are proportional.
Let's first find the value of w in triangle BIG. We know that the sum of angles in a triangle is 180 degrees. Therefore, we can find angle BIG as follows:
angle BIG = 180 - angle BGI
= 180 - 24
= 156 degrees
Now we can use the fact that the corresponding sides of similar triangles are proportional to set up the following ratios:
v/42 = 48/v (since BI/IG = GB/BI)
v^2 = 4248
v = sqrt(4248)
v = 36
In triangle MOP, we can use the law of cosines to find the value of angle MOP:
cos(MOP) = (60^2 + 72^2 - y^2) / (26072)
cos(MOP) = (3600 + 5184 - y^2) / 8640
cos(MOP) = (8784 - y^2) / 8640
MOP = acos((8784 - y^2) / 8640)
MOP = 46.7 degrees (approximately)
Now we can use the fact that the corresponding sides of similar triangles are proportional to set up the following ratios:
v/60 = y/72 (since BI/MO = IG/MP)
y = (v/60)*72
y = (36/60)*72
y = 43.2 cm
Lastly, we can use the fact that the sum of angles in a triangle is 180 degrees to find the value of angle POM in triangle MOP:
angle POM = 180 - angle MOP - 126
= 180 - 46.7 - 126
= 7.3 degrees (approximately)
Therefore, we have:
v = 36 cm
w = 156 degrees
x = 46.7 degrees (approximately)
y = 43.2 cm
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A fast-food restaurant promotes certain food items by giving a game piece with each item.
Advertisements proclaim that "25% of the game pieces are Instant Winners!" To test this claim, a frequent diner collects 20 game pieces and gets only 3 instant winners.
1. Identify the population, the parameter, the sample, and the statistic in this context.
The correct answer of population is all the game pieces and sample is 20.
How to find the percentage of winners?
As we know that a fast-food restaurant promotes certain food items by giving a game piece with each item, and proclaims that 25% of the game pieces are instant winners.
Population is all the game pieces.
Parameter is true proportion of all the game pieces that are winner.
Sample is 20, the game pieces that is collected.
Statistics is the proportion of the sample that are winners i.e. [tex]\frac{3}{20}[/tex]
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sample is the 20 and the statistic is 3/20 .
What is sample space ?A random experiment's sample space is the collection of all possible outcomes. A portion of the sample space is an event that is associated with a random experiment. Any outcome has a probability that is between 0 and 1. All outcomes have probabilities that add up to 1.
he population is all the game pieces that the fast-food restaurant produces.
The parameter is the proportion of game pieces that are instant winners in the population.
The sample is the 20 game pieces that the frequent diner collected.
The statistic is the proportion of instant winners in the sample. In this case, the statistic is 3/20 or 0.15 (15%).
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Given that a function, g, has a domain of -1 ≤ x ≤ 4 and a range of 0 ≤ g(x) ≤ 18 and that g(-1) = 2 and g(2) = 8, select the statement that could be true for g. HEEEELP
Answer:
The answer to your problem is, g(3) = 18
Step-by-step explanation:
Given that the function, g, has a domain of -1 ≤ x ≤ 4 and a range of - 0 ≤ g(x) ≤ 18 and that g(-1) = 2 and g(2) = 8
Listed in order 1 - 4
The value(s) of x must be between -1 and 4The values of g(x) must be between 0 and 18.g(-1)=2g(2)=9A. The value of x=5. This contradicts property 1 stated above. Therefore, it is not true.
B. The value of g(x)=-2. This contradicts property 2 stated above. Therefore, it is not true.
C. The value of g(2)=4. However by property 4 stated above, g(2)=9. Therefore, it is not true.
D. This statement can be true as its domain is in between -1 and 4 and its range is in between 0 and 18.
Thus the answer to your problem is, D. g(3) = 18
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(36^5-6^9)(38^9-38^8) is divisible by 30 and 37 but the answer is _ x 30 x 37
it is true that the expression (36⁴−6⁹)(38⁹−38⁸) is divisible by 30 and 37
Carl Friedrich Gauss introduced the fundamental principle of number theory in 1801, which states that any integer higher than one can be expressed as the product of prime numbers only in one way. Number theory is also referred to as arithmetic. Addition, subtraction, multiplication, and division are the four foundational operations in mathematics. Below, a quick discussion of all these operations is provided.
The expression is given as:
(36⁴−6⁹)(38⁹−38⁸)
Express 36 as 6²
(36⁴ - 6⁹) = (6²)⁴ - 6⁹
= 6⁸ - 6⁹
= 6⁷(6 - 6²)
= 6⁷(6 - 36)
= 6⁷(-30)
=(38⁹ - 38⁸)
= 38⁸(38 - 1)
= 38⁸(37)
=(36⁴−6⁹)(38⁹−38⁸)
=6⁷(-30) × 38⁸(37)
=(30)(37)(-6⁷)(38⁸)
Clearly, 30 and 37 are factors, so divisible by them.
The complete question is-
Prove that the value of the expression: b (36^5−6^9)(38^9−38^8) is divisible by 30 and 37.
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A company had inventory of 5 units at a cost of $20 each on November 1. On November 2, it purchased 10 units at $22 each. On November 6 it purchased 6 units at $25 each. On November 8, it sold 18 units for $54 each. Using the LIFO perpetual inventory method, what was the cost of the 18 units sold?
Using the LIFO perpetual inventory method, the cost of the 18 units sold is $420.
The perpetual inventory strategy known as LIFO (Last In, First Out) is predicated on the idea that the most recent inventory purchases are sold first.
In order to account for the number of units sold, we use this method to count backward from the most recent inventory acquisition.
The business sold 18 units on November 8, which is more than its most recent purchase of 6 units on November 6. Therefore, starting with a total of 18 units, we first use the 10 units from the November 2 purchase and the 8 units from the November 6 buy.
10 units were bought on November 2 for a total of $220, or $22 each unit. The 8 pieces that were bought on November 6 cost $25 apiece, for a total of $200. Hence, $220 plus $200 equals $420 for the 18 units that were sold.
The cost of the 18 sold units, calculated using the LIFO perpetual inventory approach, is $420.
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A store sells 12 oranges for 4 dollars how many oranges can you buy for 1 dollar?
A) 2 B) 3 c) 4 D) 6
Answer:
B) 3
Step-by-step explanation:
Divide 12 and 4 then you will get 3 as your answer.
Answer:
You can Buy 3 oranges from 1 dollar.
Given- A Store sells 12 Oranges for 4 dollars
let dollar = x (equation 1)
Now,
12 oranges = 4x (Equation 1)
Taking 4 to the other side of equals sign, it divides 12 : -
12/4 oranges = x
3 oranges = x
Thus we get the value of x which is 3 oranges. As we know that x = dollar, we get to know that each dollar will get us 3 oranges.
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Use compensation to add or subtract
499+599+699
Answer: 1,797
Step-by-step explanation:
Step 1: Round Numbers Up:
500+600+700 = 1,800
Step 2: Subtract 3 to get answer (-1 for every number rounded up)
1,800-3 = 1,797
Addition using compensation method : 1800
Subtraction using compensation method : 1797
Given,
499+599+699
Here,
Compensation : Round off to the nearest number so that the calculation of addition and subtraction becomes more easy .
So,
Firstly addition,
499 + 599 + 699
Add 3 adding one to each, we get,
500 + 600 + 700 = 1800
Now,
Subtracting 3, 1800 - 3 = 1797
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