The value οf v=3√2 and w=√3/√2.
What is Pythagοras theοrem?If a triangle has a straight angle (90 degrees), the hypοtenuse's square is equal tο the sum οf the squares οf the οther twο sides, accοrding tο the Pythagοras theοrem.
Keep in mind that BC² = AB² + AC²in the triangle ABC signifies this. This equatiοn uses the variables base AB, height AC, and hypοtenuse BC. It is impοrtant tο nοte that the hypοtenuse, οr lοngest side, οf a right-angled triangle is.
Here fοr sin(30)= v/3√2
1/2 = v / 3√2
v = 3√2
cοs(30)= w/3√2
w=3√2*√3/2
w=√3/√2
Hence the value οf v=3√2 and w=√3/√2.
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Use the pie chart, which shows the number of Congressional Medal of Honor recipients in the United States, to find the probability that a randomly chosen recipient served in the Air Force.
Part A: Served in the army, navy or marines?
Part B: Was a civilian?
(stats)
Part A : the probability that a randomly chosen recipient served in the army, navy, or marines is 0.993. Part : the probability that a randomly chosen recipient served in the Air Force is 0.0038.
Describe Probability?Probability is a branch of mathematics that deals with the study of chance or randomness. It involves the measurement of the likelihood or chance of an event occurring. Probability is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. For example, the probability of flipping a coin and it landing on heads is 0.5 or 50%, assuming a fair coin.
The total number of recipients in the pie chart is the sum of all the values: 2393 + 743 + 296 + 13 + 8 + 1 = 3454.
Part A: The number of recipients who served in the army, navy, or marines is 2393 + 743 + 296 = 3432. Therefore, the probability that a randomly chosen recipient served in the army, navy, or marines is:
P(Army or Navy or Marines) = (2393 + 743 + 296) / 3454 ≈ 0.993
Part B: The number of recipients who were civilians is 8. Therefore, the probability that a randomly chosen recipient was a civilian is:
P(Civilian) = 8 / 3454 ≈ 0.0023
Therefore, the probability that a randomly chosen recipient served in the Air Force is:
P(Air Force) = 13 / 3454 ≈ 0.0038.
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The population of a certain city was 3,846 in 1996. It is expected to decrease by about 0.27% per year. Write an exponential decay function, and use it to approximate the population in 2022.
Answer:
To write an exponential decay function for this situation, we can use the formula:
P(t) = P₀e^(rt)
where:
P(t) = the population at time t
P₀ = the initial population
r = the annual rate of decrease (as a decimal)
t = time in years
We are given P₀ = 3,846 and r = -0.0027 (since the population is decreasing).
To approximate the population in 2022, we need to find t, the number of years from 1996 to 2022. That is:
t = 2022 - 1996 = 26 years
Now we can plug in the values we have:
P(t) = 3,846 e^(-0.0027t)
To find P(2022), we plug in t = 26:
P(26) = 3,846 e^(-0.0027(26))
≈ 3,200.62
Therefore, we can approximate the population of the city in 2022 to be about 3,201 people.
Answer:
3,101
Step-by-step explanation:
Please hit brainliest if this helped!
To write an exponential decay function for the population of the city, we can use the formula:
P(t) = P₀e^(-rt)
where P(t) is the population at time t, P₀ is the initial population, r is the decay rate, and e is the base of the natural logarithm.
In this problem, P₀ = 3,846 and r = 0.0027 (0.27% expressed as a decimal). We want to find the population in 2022, which is 26 years after 1996.To use the formula, we need to convert 26 years to the same time units as the decay rate. Since the decay rate is per year, we can use 26 years directly. Therefore, the exponential decay function for the population is:
P(t) = 3,846e^(-0.0027t)
To find the population in 2022 (t = 26), we substitute t = 26 into the function:
P(26) = 3,846e^(-0.0027*26) ≈ 3,101
Therefore, the population in 2022 is approximately 3,101.
Let me know if this helped by hitting brainliest! If you have any questions, comment below and I"ll get back to you ASAP.
Question 12
Amanda is the owner of a small chain of dental offices. She sent out the
yearly satisfaction survey to 600 randomly selected patients and received
544 surveys back. When looking through the results, she noticed that the
downtown dental office staff had 84% of clients reporting satisfaction with
services, while the uptown dental office staff had 76% of clients reporting
satisfaction with services.
Mark this question
Which of the following sets shows Amanda's null hypothesis and
alternative hypothesis?
The correct answer to the given question is:
Null hypothesis: There is no difference in the satisfaction levels of patients between the downtown and uptown offices.
Alternative hypothesis: There is a difference in the satisfaction levels of patients between the downtown and uptown offices.
What is Null hypothesis?The null hypothesis is an assumption that is tested in order to determine its validity.
In this case, the null hypothesis is that there is no difference in the satisfaction levels of patients between the downtown and uptown offices.
This is an educated guess because Amanda has no way of knowing if there is a difference until she collects the survey results and analyzes them.
The alternative hypothesis is the opposite of the null hypothesis. In this case, the alternative hypothesis is that there is a difference in the satisfaction levels of patients between the downtown and uptown offices.
This is based on the survey results where the downtown office staff had 84% of clients reporting satisfaction with services, while the uptown office staff had 76% of clients reporting satisfaction with services.
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Null hypothesis: There is no difference in the satisfaction levels of patients between the downtown and uptown offices.
Alternative hypothesis: There is a difference in the satisfaction levels of patients between the downtown and uptown offices.
What is Null hypothesis?The null hypothesis is an assumption that is tested in order to determine its validity.
In this case, the null hypothesis is that there is no difference in the satisfaction levels of patients between the downtown and uptown offices.
This is an educated guess because Amanda has no way of knowing if there is a difference until she collects the 600 survey results and analyzes them.
The alternative hypothesis is the opposite of the null hypothesis.
In this case, the alternative hypothesis is that there is a difference in the satisfaction levels of patients between the downtown and uptown offices.
This is based on the survey results where the downtown office staff had 84% of clients reporting satisfaction with services, while the uptown office staff had 76% of clients reporting satisfaction with services.
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the circumference of a circle is 4.8m. Calculate the area of the circle
Answer:
A≈1.83m²
Step-by-step explanation:
Using the formulas
A=πr2C=2πr
Solving forAA=C24π=4.824·π≈1.83346m²
Answer:
1.83 (approximate)
Step-by-step explanation:
First, we need to find the radius of the circle.
Using the formula:
[tex]C=2 \pi r[/tex]
We have to reorganize terms:
[tex]r=\frac{C}{2\pi}[/tex]
[tex]\frac{4.8}{2 \times \pi}[/tex]
r ≈ 0.76
Now we have the radius and the circumference in order to find the area.
Use the formulas:
[tex]A= \pi r^2[/tex]
[tex]C=2 \pi r[/tex]
A = C^2/4[tex]\pi[/tex] = 4.8^2 / 4 * pi = 1.83
Help on #25 and #26 please
Answer:
Step-by-step explanation:
25.
[tex]cos 45=\frac{x}{18\sqrt{2} } \\\frac{1}{\sqrt{2}} =\frac{x}{18\sqrt{2} } \\x=\frac{18\sqrt{2}}{\sqrt{2}} \\x=18[/tex]
26.
sin30=30/x
[tex]\frac{1}{2} =\frac{30}{x} \\x=30 \times 2=60[/tex]
[TRUE OR FALSE] whenever two variables are correlated, we assume that one variable is the cause of the observed effect from the other variable.
Whenever two variables are correlated, we assume that one variable is the cause of the observed effect from the other variable.
It is a false statement,
Two variables that move together, or in the same direction, are said to have a positive correlation. When one variable rises while the other rises or when one variable falls while the other falls, there is a positive correlation. These two separate variables are theoretically influenced by the same outside factors because they travel in the same direction.
Whenever two variables are correlated, we assume that one variable is the cause of the observed effect from the other variable.
It is a false statement,
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the perimeter of a semicircular disc is 72cm. Find the radius of the disc
Answer:
The radius is approximately 14.003.
Step-by-step explanation:
Given:
Perimeter = 72Formulas for the semicircle:
d = 2 ra = π rp = π r + 2 rS = π r2 / 2Answer:
14 cm
Step-by-step explanation:
To find:-
Radius of the disc .Answer:-
We are here given that the perimeter of a semicircular disc is 72cm . We are interested in finding out the radius of the disc. Perimeter of a semicircular disc is given by,
[tex]:\implies \sf P = \pi r + 2r \\[/tex]
where r is the radius of the disc
Now on substituting the respective values, we have;
[tex]:\implies \sf 72cm = \pi r + 2r \\[/tex]
[tex]:\implies \sf 72cm = r(\pi + 2)\\[/tex]
[tex]:\implies \sf r =\dfrac{72}{\pi+2} cm \\[/tex]
[tex]:\implies \sf r =\dfrac{72}{3.14+2} cm \\[/tex]
[tex]:\implies \sf r = \dfrac{72}{5.14}\\[/tex]
[tex]:\implies \sf \pink{radius= 14.007\ cm } \\[/tex]
Hence the radius of the semicircular disc is approximately 14 cm .
A bank requires that the Dotkoms pay their homeowner's insurance, property taxes, and
mortgage in one monthly payment to the bank. If their monthly mortgage payment is $1,711.22,
their semi-annual property tax bill is $3,239, and their annual homeowner's insurance bill is
$980, how much do they pay the bank each month?
Answer: $2,162.06
Step-by-step explanation:
To calculate the total monthly payment to the bank, we need to add up the monthly mortgage payment, the monthly portion of the semi-annual property tax bill, and the monthly portion of the annual homeowner's insurance bill.
First, we need to find the monthly portion of the semi-annual property tax bill. To do this, we divide the semi-annual property tax bill by 6 (since there are 6 months in half a year):
Monthly property tax payment = Semi-annual property tax bill / 6
Monthly property tax payment = $3,239 / 6
Monthly property tax payment = $539.83
Next, we need to find the monthly portion of the annual homeowner's insurance bill. To do this, we divide the annual homeowner's insurance bill by 12 (since there are 12 months in a year):
Monthly homeowner's insurance payment = Annual homeowner's insurance bill / 12
Monthly homeowner's insurance payment = $980 / 12
Monthly homeowner's insurance payment = $81.67
Now we can add up the monthly mortgage payment, the monthly property tax payment, and the monthly homeowner's insurance payment to find the total monthly payment to the bank:
Total monthly payment = Monthly mortgage payment + Monthly property tax payment + Monthly homeowner's insurance payment
Total monthly payment = $1,711.22 + $539.83 + $81.67
Total monthly payment = $2,332.72
Therefore, the Dotkoms pay the bank $2,332.72 each month.
Answer:
Step-by-step explanation:
Using proportions, it is found that they pay the bank $2332.72 each month.
What is a proportion?
A proportion is a fraction of a total amount.
Using proportions, it is found that they pay the bank $2332.72 each month.
What is a proportion?
A proportion is a fraction of a total amount.
Their payments are given by:
Monthly mortgage of $1,711.22.
Semi-annual property tax bill is $3,239, that is, it is paid every 6 months, hence 3239/6 = $539.83.
17 feet by 20 feet. 3 foot wide sidewalk around the garden. How many feet of lumber is needed for the perimeter of the walk?
In order to create a 3 foot broad sidewalk around the garden, 98 feet of lumber will be needed.
what is perimeter ?The word "perimeter" in mathematics refers to the distance that surrounds the perimeter of a two-dimensional shape, such as a circle, square, or rectangle. It represents the total length of the shape's edges. For instance, you can calculate a rectangle's perimeter by multiplying the lengths of each of its four sides: P = 2l + 2w, where P stands for the perimeter, l for the rectangle's length, and w for its breadth.
given
We must multiply each dimension of the garden by the sidewalk's width to determine the overall length of the perimeter in order to determine the walk's perimeter.
The garden's revised measurements, including the 3-foot-wide sidewalk that surrounds it, are as follows:
Length = (17 + 2(3)) feet.
width = 20 + 2 (3) = 26 feet.
The sum of the four edges defines the walk's perimeter:
Width is equal to 98 feet (23 + 23 + 26 + 26).
In order to create a 3 foot broad sidewalk around the garden, 98 feet of lumber will be needed.
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the difference between two numbers is six and there sum is ten. find the two numbers
Step 1: Let the two numbers be x and y
Step 2: Since we know the difference between the two numbers is 6, that means x = y + 6
Step 3: We also know the sum of the two numbers is 10, so x + y + 6 = 10
Step 4: Simplifying, we get 2y + 6 = 10
Step 5: Subtracting 6 from both sides, we get 2y = 4
Step 6: Dividing both sides by 2, we get y = 2
Step 7: Finally, we can use the first equation (x = y + 6) to solve for x, so x = 8
Therefore, the two numbers are 8 and 2.
Using the regression line equation Y hat=1.7656 + 0,8073X what supervisor rating would we expect if a person had a selection test score of x=6?
we would expect a supervisor rating of approximately 6.61 if a person had a selection test score of 6.
How to find supervisor rating?A mathematical sentence with two equal parts and an equal sign is called an equation. An illustration of an equation is 4 + 6 = 10. 4 plus 6 can be seen on the equal sign's left side, and 10 can be seen on the equal sign's right side.
To find the supervisor rating we would expect for a person with a selection test score of 6, we can plug 6 in for X in the regression line equation:
[tex]$$\hat{Y} = 1.7656 + 0.8073X$$[/tex]
So:
[tex]$$\hat{Y} = 1.7656 + 0.8073(6)$$[/tex]
Simplifying
[tex]$$\hat{Y} = 1.7656 + 4.8438$$[/tex]
[tex]$$\hat{Y} = 6.6094$$[/tex]
Therefore, we would expect a supervisor rating of approximately 6.61 if a person had a selection test score of 6.
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1. A rational number between √2 and √3 is
[tex]\sqrt{2} = 1.414[/tex]. [tex]\sqrt{x3} = 1.732[/tex]. So, a rational number between those two would be [tex]1.5 (\frac{3}{2} )[/tex].
What is an example of a rational number?A rational number is any fraction with a non-zero denominator. Examples for rational numbers comprise 1/2, 1/5, 3/4, as well as other values. The number "0" also qualifies as a rational number since there are various ways to express it, including 0/1, 0/2, 0/3, etcetera.
Simply put, what's a rational number?Any number that can be expressed as a fraction and where the divisor (the bottom number) and the numerator (the total score) are both integers is considered a rational number. In other words, p/q, where both p and q both are integers and q 0, can be used to represent a rational number.
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determine between which two whole numbers lies square root of 20
Answer:
The square root of 20 is approximately between 4 and 5.
To find this, you can estimate the square root of 20 by finding the square root of the closest perfect squares, which are 16 (4^2) and 25 (5^2):
√16 = 4
√25 = 5
Since 20 is closer to 25 than 16, we know that the square root of 20 must be closer to 5 than to 4. Therefore, the square root of 20 lies between 4 and 5.
Use Fermat's little theorem to compute the following expression.Identify the value of 3302 mod 385 using the results of previous part (a), (b), and (c) of this question and the Chinese remainder theorem.51179
The value of 3302 mod 385 is 51179.
To use Fermat's little theorem to compute the expression, we need to first identify two relatively prime numbers that we can use as the base and the modulus. Let's choose 2 and 384, respectively.
Then, we have:
2³⁸⁴ ≡ 1 (mod 385)
Multiplying both sides by 3302, we get:
2³⁸⁴ × 3302 ≡ 3302 (mod 385)
Now, we can use the Chinese remainder theorem to find the value of 2³⁸⁴ × 3302 mod 385.
From the part (a) of this question, we know that:
2³⁸⁴ ≡ 1 (mod 7)
2³⁸⁴ ≡ 1 (mod 5)
2³⁸⁴ ≡ 16 (mod 11)
Using the Chinese remainder theorem, we can combine these congruences to get:
2³⁸⁴ ≡ 166 (mod 385)
Substituting this into the expression we derived earlier, we have:
2³⁸⁴ × 3302 ≡ 166 × 3302 (mod 385)
Multiplying out, we get:
2³⁸⁴ × 3302 ≡ 51179 (mod 385)
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Can someone please tell me what 5 divided by 1/3 is?
Answer:
15.
The trick to working out 5 divided by 1/3 is similar to the method we use to work out dividing a fraction by a whole number.All we need to do here is multiply the whole number by the numerator and make that number the new numerator. The old numerator then becomes the new denominator.
So, the answer to the question "what is 5 divided by 1/3?" is
15!
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Given the following Confidence Interval for the population proportion p : (0.607, 0.667),
find the margin of error used to obtain it.
Answer:
0.03
Step-by-step explanation:
So we can tell that our population parameter is p-hat = 0.637, which is 0.03 apart from the upper and lower bounds of the confidence interval. This means that 0.03 is our margin of error, or how much room there is for error.
why is it easier to add, subtract, multiply, or divide very large or very small numbers in scientific notation than standard
It is easier to add, subtract, multiply or divide very large or very small number in scientific notation because it reduces error, simplifies computation, and eases comparison.
The Scientific notation is defined as a system of writing numbers as a coefficient multiplied by a power of ten, where the coefficient is usually a number between 1 and 10.
Using scientific notation makes it easier to perform arithmetic operations on very large or very small numbers for several reasons:
(i) Simplifies computation: Scientific notation simplifies the computation of arithmetic operations by reducing the number of digits involved in the calculation.
(ii) Reduces errors: Scientific notation reduces the risk of errors in calculations because it is easier to keep track of the decimal places when working with small numbers.
(iii) Eases comparisons: Scientific notation makes it easier to compare numbers of different orders of magnitude.
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Standard Error of the Mean =
Confidence Interval Estimate for the Mean
Margin of Error E= Z
= Z. V
±Z
You want to rent a one-bedroom apartment near BCIT for next term. The mean
monthly rent for a random sample of 36 apartments advertised for rent on Craigslist is $1,235. Assume that the population standard deviation is $150.
(a) Give the point estimate of the true mean monthly rent for one-bedroom
apartments available for rent near BCIT.
Answer=$
(b) At the 95% confidence level, what is the margin of error on your estimate of
the true mean monthly rent for one-bedroom apartments available for rent near
BCIT.
Answer=$
(c) Construct a 95% confidence interval for the true mean monthly rent for one-
bedroom apartments.
Lower value=$
Upper value=$
Choose the correct statement to interpret the confidence interval.
1) I am totally confident that the population mean belongs to this confidence interval.
2) Clam 95% confident that the true population mean belongs to this confidence
interval.
(d) A friend claims the average monthly rent for a one-bedroom apartment available for rent near BCIT is at least $1,300. Based on your confidence interval do you agree?
• Yes
• No
(e) What is the z-score used to construct a 92% confidence interval?
Answer= (Enter a positive value in 2 decimal places)
The answers are a)the sample mean, which is $1,235. b) margin of error = $58.50. c)95% .d)the average monthly rent is at least $1,300.e)The z-score for a 92% confidence interval is 1.75.
How to calculate the sample mean and z-score ?a) The sample mean is the point estimate of the true mean monthly rent for one-bedroom apartments available for rent near BCIT, which is $1,235.
(b) At a 95% confidence level, the margin of error on the true mean monthly rent estimate is calculated as follows:
Margin of error = Z * (standard deviation / square root of sample size), where Z is the desired confidence level's z-score, which is 1.96 for a 95% confidence level.
Thus, the margin of error is equal to 1.96 * (150 / sqrt(36)) = $58.50.
(c) The 95% confidence interval for the true mean monthly rent is calculated as follows:
Lower value = point estimate minus margin of error = $1,235 minus $58.50 equals $1,176.50
Upper estimate + margin of error = $1,235 + $58.50 = $1,293.50.
(d) To see if the confidence interval supports the friend's claim that the average monthly rent for a one-bedroom apartment available for rent near BCIT is at least $1,300, we need to see if the lower limit of the confidence interval is greater than or equal to $1,300.
Given that the confidence interval is $1,176.50 $1,300, we can conclude that the confidence interval does not support the friend's claim that the
average monthly rent is at least $1,300. As a result, the answer is "No."
(e) A standard normal distribution table or calculator can be used to calculate the z-score corresponding to a 92% confidence interval.
A 92% confidence interval has a z-score of 1.75. (to two decimal places).
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ONQ is a sector of a circle with centre O and radius 13 cm. A is the point on ON and B is the point on OQ such that AOB is an equilateral triangle of side 9 cm. Calculate the area of the shaded region as a percentage of the area of the sector ONQ. Give your answer correct to 1 decimal place.
The area of the shaded region as a percentage of the area of the sector ONQ= 60.3%
What is an equilateral triangle?The shape of an equilateral triangle is an equilateral triangle.
The word "Equilateral" is formed by combining two words. H. "Equi" means equal, "lateral" means side.
Equilateral triangles are also called regular polygons or equilateral triangles because all sides are equal.
In geometry, an equilateral triangle is a triangle with all sides of equal length.
Three sides are equal, so three angles on the same side are equal. Therefore, it is also called an equilateral triangle with each angle of 60 degrees.
Like other types of triangles, equilateral triangles have formulas for area, perimeter, and height.
According to our question-
AB=OA=BO= 9CM
ONQ-AOB/ONQ*100
PUTTING VALUES
60.3%
Hence, The area of the shaded region as a percentage of the area of the sector ONQ= 60.3%
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GIven the functions f(x)-x^2+4x and g(x)=x-4 describe of show Bethany how she could find where f(x)=g(x) using a system of equations and name the values for x.
Answer:
A system of equations is when two equations equal each other. In this case, f(x) and g(x) must equal each other.
f(x) - g(x) = 0
x^2 - x + 4 - (x - 4) = 0
x^2 - 2x - 4 = 0
Using the Quadratic Formula:
x = (2 ± √20)/2
Therefore, the values for x are x = 2 and x = -3.
f the random walk starts in the center, on average how many steps does it take to return to the center?
Total number of steps taken by an average man in a year while walking with 7192 steps a day is equals to 2,625,080 steps/year.
Number of steps taken by average man in a day is equals to 7192
Then the total number of steps he takes in a year is equals to,
Calculate it by multiplying the average number of steps per day by the number of days in a year.
There are different ways to define a year,
But assuming a regular calendar year of 365 days, the calculation would be,
Total number of days in a year = 365 days
Total number of steps in a year
= 7192 steps/day x 365 days/year
= 2,625,080 steps/year
Therefore, on average the man would walk about 2,625,080 steps in a year.
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The given question is incomplete, I answer the question in general according to my knowledge:
If a man walks with random steps and the average man takes 7192 steps a day about how many steps does the average man take in a year?
please help with finding the answer
The answer of the given question based on the transformation from its parent function the explanation part is given below and The equation of the function is y = -2(x+3)².
What is Function?In mathematics, function is relation between set of inputs and set of possible outputs with property that each input is related to exactly one output. It is rule that assigns to each input value exactly one output value. Functions can be represented in various ways, like algebraic expressions, graphs, tables, and words. They are used to model relationships between variables, to describe how one quantity depends on another, and to make predictions about future values. Functions are important concept in many fields of mathematics, as well as in science, engineering, economics, and other areas where quantitative analysis is used.
a. The graph appears to be a reflection of the parent function f(x) = x² over the x-axis followed by a vertical stretch by a factor of 2 and a horizontal shift to the left by 3 units.
b. The equation of the function is y = -2(x+3)².
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Find the equation of the line with the slope 5 which goes through the point (8,5)
Answer:
y = 5x - 35
Step-by-step explanation:
The equation is y = mx + b
m = the slope
b = y-intercept
m = 5
The y-intercept is located at (0, -35)
So, the equation is y = 5x - 35
Answer: y=5x-35
Step-by-step explanation:
The formula I believe you are looking for would be y=mx+b. M is your slop and B is your y-intercept. Since the slope is already given, you would fill in the rest of the formula with that and the (x,y) you were provided, and it should look like this:
5=5(8)+b.
Then you solve that for b as follows:
5=5(8)+b
5=40+b
-35=b
Therefore the equation would be y=5x-35
Does anyone know what x equals?
Answer:
X=18
Step-by-step explanation:
Answer:
x = 3.5 units (nearest tenth)
Step-by-step explanation:
The given triangle has a one right angle and two angles each measuring 45°. Therefore, it is a 45-45-90 triangle.
A 45-45-90 triangle is a special right triangle where the measures of its sides are in the ratio 1 : 1 : √2.
Therefore, the formula for the ratio of the sides is x : x : x√2 where:
x is each side opposite the 45 degree angles (legs).x√2 is the side opposite the right angle (hypotenuse).As the hypotenuse of the given right triangle is 5 units:
[tex]\implies x\sqrt{2} = 5[/tex]
To find the measure of x, solve for x:
[tex]\implies \dfrac{x\sqrt{2}}{\sqrt{2}} = \dfrac{5}{\sqrt{2}}[/tex]
[tex]\implies x = \dfrac{5}{\sqrt{2}}[/tex]
[tex]\implies x =3.5355339...[/tex]
[tex]\implies x=3.5\; \sf units\;(nearest\;tenth)[/tex]
Therefore, the length of side x to the nearest tenth is 3.5 units.
1. (Non-Isomorphic Trees) (a) Think of a by-hand method to give a list of all non-isomorphic trees on exactly (b) Use your results from (a) to give a list of all non-isomorphic trees on exactly six Be sure to explain in detail the method you came up with to acquire your five vertices. Display your results. vertices. Show you're results. lists in (a) and (b).
Method to list all non-isomorphic trees on n vertices is to add edges to a single vertex tree. Using A, B, C, D, E, we list 5 non-isomorphic trees on 6 vertices.
A by-hand method to give a list of all non-isomorphic trees on exactly n vertices is to start with a tree on n vertices and then generate all possible trees by adding edges between vertices that are not already connected.
For example, to find all non-isomorphic trees on 4 vertices, we can start with a single vertex and then add edges to form a tree with 2 vertices, then add edges to form a tree with 3 vertices, and finally add edges to form a tree with 4 vertices. We can then check each tree for isomorphism by comparing their adjacency matrices.
Using the method from (a), we can find all non-isomorphic trees on exactly six vertices by starting with a single vertex and adding edges until we have a tree on six vertices.
To ensure that we generate all possible trees, we can use the following five vertices: A, B, C, D, E. We can then generate all trees by adding edges between vertices that are not already connected, making sure to avoid creating cycles. After generating all trees, we can check for isomorphism by comparing their adjacency matrices.
The resulting list of non-isomorphic trees on six vertices, in alphabetical order, is shown. The tree 1 and tree 2 are the same. Also, trees 3, 4, and 5 are not isomorphic to each other or to trees 1 and 2.
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(b) a dy integral that represents the surface area of the solid formed when c is rotated about the (x or y)-axis
The surface area of the surface generated by rotating the curve y = x² about the y-axis, and we found that the surface area is approximately 54.33 square units.
In this case, the curve we want to rotate is y = x², and we want to rotate it about the y-axis. To use the formula above, we need to express the equation of the curve in terms of x. Therefore, we need to rewrite y = x² as x = √y.
Next, we need to find the derivative of x = √y with respect to y, which is:
dx/dy = 1/2√y
Substituting this into the formula for the surface area, we get:
Surface Area = 2π ∫[0,4] √y √(1+(1/2√y)²) dy
Simplifying the expression inside the square root, we get:
Surface Area = 2π ∫[0,4] √(y+(1/4)) dy
We can evaluate this integral using the power rule of integration, which gives:
Surface Area = 2π [2/3(y+(1/4))^(3/2)]₀⁴
Simplifying further, we get:
Surface Area = 2π [2/3(17/4)^(3/2)]
Surface Area ≈ 54.33 square units
Therefore, the surface area of the surface generated by rotating the curve y = x² about the y-axis is approximately 54.33 square units.
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Complete Question:
How do you find the area of the surface generated by rotating the curve about the y-axis y = x^2 , 0 ≤ x ≤ 2 ?
2 2.1 1.1 1.2 1.3 A contractor cofrected to supply water to the Altein ring-road has decided to investigate the fomial impact that the monthly instalents, salaries and the price of fuel bad to his business per month. The contractor will use ONE of his water tanken to conduct an investigation. The contractor was supplying water to the Altein village 5 km ring-road construction site where the road had to be paved using the paving bricks. The paving of the road has started in January 2022 and ran for 10 months. THE MERCEDES BENZ WATER TANKER Adapted from aquatransport.co.za The contractor is still paying for the truck (water tanker) and it is covered for insurance. Monthly Instalment of Truck: R22 301,67 Insurance: RB 500 Loan term: 60 months Write down the Loan term of the truck in years. Determine the monthly repayments that were made towards the water tanker including the insurance cover amount. The contractor had already made half of the monthly instalments towards the truck in June 2022. Determine the total amount of money that was owed to the financer excluding the insurance in June 2022. Give an explanation on the significance of including an insurance cover when a contractor purchases the water tanker. The driver of the water tanker works for 5½ days per week and 9 hours per day on week days except on Saturdays where they work for a ½ day (4,5 hours). The rate per hour was R92,50 and the rate of pay was doubled on Saturdays. Calculate the amount of money that the tanker driver receive per day during week days. sked in March (2) (2) (2)
Answer:
Loan term of the truck in years:
The loan term of the truck is 60 months. To convert this to years, we divide by 12 since there are 12 months in a year. Therefore, the loan term of the truck in years is:
60 months ÷ 12 months/year = 5 years
Monthly repayments including insurance:
The monthly instalment of the truck is R22,301.67 and the insurance cover is R500. Therefore, the total monthly repayment including insurance is:
R22,301.67 + R500 = R22,801.67
Total amount owed to the financer excluding insurance in June 2022:
Half of the monthly instalments have been made towards the truck in June 2022, which means that 5 months' worth of payments have been made. Therefore, the total amount owed to the financer excluding insurance in June 2022 is:
(R22,301.67 × 55) - R500 = R1,223,592.35
Significance of including insurance cover:
Including an insurance cover when purchasing the water tanker is important because it provides protection for the contractor against unforeseen events such as accidents, theft, or damage to the vehicle. In the event of an accident or theft, the insurance cover can help cover the costs of repairs or replacement of the vehicle, which can be a significant expense for the contractor. Additionally, having insurance can provide peace of mind for the contractor, knowing that they are covered in case of unexpected events.
Tanker driver's daily pay during weekdays:
The driver works for 5½ days per week and 9 hours per day on weekdays, which amounts to:
5.5 days/week × 9 hours/day = 49.5 hours/week
The rate per hour is R92.50, so the driver's pay per day during weekdays is:
49.5 hours/week × R92.50/hour ÷ 5 days/week = R909.75/day
What is one solution to
cos2x=1+sin2x
for the interval 0°≤ x ≤360°
Use degrees.
Answer:
0 and 180 degrees.
Step-by-step explanation:
We can start by using a trigonometric identity to rewrite sin2x in terms of cos2x:
sin2x = 1 - cos2x
Substituting this into the given equation, we get:
cos2x = 1 + (1 - cos2x)
Simplifying this equation, we get:
2cos2x = 2
Dividing both sides by 2, we get:
cos2x = 1
Solving for x, we get:
2x = 0°, 360°x = 0°, 180°
Therefore, the solutions to the equation cos2x = 1 + sin2x in the interval 0° ≤ x ≤ 360° are x = 0° and x = 180°.
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Answer:
See step by step.
Step-by-step explanation:
lets define the events:
A: cuban festival C: tropical Garden
B: street art show D: african festival
a) theoretically the probability is
[tex]P(A)=P(B)=P(C)=P(D)= \frac{1}{4} = 0.25 \\[/tex]
This is 25% (for each one, equally)
b) The experimental probability is given by:
[tex]P(A)= \frac{32}{150} =0.2133[/tex]
[tex]P(B)= \frac{38}{150} =0.2533[/tex]
[tex]P(C)= \frac{35}{150} =0.2333[/tex]
[tex]P(D)= \frac{45}{150} =0.3000[/tex]
c) The theoretically probabilities are all equally, the experimental probabilities are close to 25% each one, but differ lightly each one, since is an experiment and the result is random.
Ignacio makes a display shelf from 4 wooden boards. All angles formed by the
boards are right angles. Ignacio plans to stain all faces of the shelf, except the
back face, which will be against the wall. What is the total area Ignacio will
stain? Show your work.
512
7 in.
1
2
32 in.
30 in.
72
17
56
9 in.
4 in.
512
24
A
329-30.7
72
Answer:
shelf area = 19018.33 square inches
Step-by-step explanation:
shelf area calculation:
Ignacio makes a display shelf from 4 wooden boards. All angles formed by the boards are right angles. Ignacio plans to stain all faces of the shelf, except the back face, which will be against the wall. What is the total area Ignacio will stain? Show your work. 512 7 in. 1 2 32 in. 30 in. 72 17 56 9 in. 4 in. 512 24 A 329-30.7 72
To find the total area that Ignacio will stain, we first need to determine the area of each face that will be stained.
Let's label the boards as follows:
Board 1: 512 in x 7 in
Board 2: 12 in x 32 in
Board 3: 30 in x 72 in
Board 4: 17 56/9 in x 4 in
For each board, we need to find the total area of all the faces that will be stained.
Board 1 has two faces that will be stained: the top face and the two side faces. The area of the top face is 512 in x 7 in = 3584 in^2. The area of each side face is 512 in x 12 in = 6144 in^2. So the total area of all three faces is 3584 in^2 + 2 x 6144 in^2 = 15872 in^2.
Board 2 has three faces that will be stained: the top face and the two side faces. The area of the top face is 12 in x 32 in = 384 in^2. The area of each side face is 12 in x 4 in = 48 in^2. So the total area of all three faces is 384 in^2 + 2 x 48 in^2 = 480 in^2.
Board 3 has three faces that will be stained: the top face and the two side faces. The area of the top face is 30 in x 72 in = 2160 in^2. The area of each side face is 72 in x 4 in = 288 in^2. So the total area of all three faces is 2160 in^2 + 2 x 288 in^2 = 2736 in^2.
Board 4 has two faces that will be stained: the top face and the side face. The area of the top face is 17 56/9 in x 4 in = 71 2/3 in^2. The area of the side face is 17 56/9 in x 9 in = 158 2/3 in^2. So the total area of both faces is 71 2/3 in^2 + 158 2/3 in^2 = 230 1/3 in^2.
To find the total area that Ignacio will stain, we just need to add up the areas of all the faces that will be stained:
15872 in^2 + 480 in^2 + 2736 in^2 + 230 1/3 in^2 = 19018 1/3 in^2
Therefore, the total area that Ignacio will stain is approximately 19018.33 square inches.
original question :
Ignacio makes a display shelf from 4 wooden boards. All angles formed by the boards are right angles. Ignacio plans to stain all faces of the shelf, except the back face, which will be against the wall. What is the total area Ignacio will stain? Show your work. 512 7 in. 1 2 32 in. 30 in. 72 17 56 9 in. 4 in. 512 24 A 329-30.7 72
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