The points where the tangent line is vertical are (13/16, -5/16) and (-13/16, 5/16) and The slope of the tangent line is positive on the intervals t < -1 and t > 1, and negative on the interval -1 < t < 1.
How can we analyzing the properties of a parametric curve?(a) To find where the tangent line is horizontal, we need to find values of t where the derivative of y with respect to x (dy/dx) is equal to 0.
We have:
dy/dx = (dy/dt)/(dx/dt) = (5t^4 - 5)/(12t^2 - 3)
Setting dy/dx = 0, we get:
5t^4 - 5 = 0
t^4 = 1
t = ±1 or t = ±i
Substituting t = 1 into the parametric equations gives us the point (1,-4). Substituting t = -1 gives us the point (-1,4). Substituting t = i or t = -i gives us points on the imaginary axis, which are not part of the real plane.
Therefore, the points where the tangent line is horizontal are (1,-4) and (-1,4).
To find where the tangent line is vertical, we need to find values of t where dx/dt is equal to 0.
We have:
dx/dt = 12t^2 - 3
Setting dx/dt = 0, we get:
t^2 = 1/4
t = ±1/2
Substituting t = 1/2 into the parametric equations gives us the point (13/16, -5/16). Substituting t = -1/2 gives us the point (-13/16, 5/16).
Therefore, the points where the tangent line is vertical are (13/16, -5/16) and (-13/16, 5/16).
(b) To determine the intervals where the slope of the tangent line is positive or negative, we need to examine the sign of the derivative dy/dx.
From part (a), we know that dy/dx is equal to:
dy/dx = (5t^4 - 5)/(12t^2 - 3)
The denominator is always positive, so the sign of dy/dx is determined by the numerator.
For t < -1, we have 5t^4 - 5 > 0, so dy/dx > 0.
For -1 < t < 1, we have 5t^4 - 5 < 0, so dy/dx < 0.
For t > 1, we have 5t^4 - 5 > 0, so dy/dx > 0.
Therefore, the slope of the tangent line is positive on the intervals t < -1 and t > 1, and negative on the interval -1 < t < 1.
(c) To determine the intervals where the curve is concave upward or downward, we need to examine the sign of the second derivative d^2y/dx^2.
We have:
d^2y/dx^2 = ((d^2y/dt^2)(dx/dt) - (dy/dt)(d^2x/dt^2)) / (dx/dt)^3
Calculating the second derivatives, we get:
d^2y/dt^2 = 20t^3
d^2x/dt^2 = 24t
Substituting these into the expression for d^2y/dx^2, we get:
d^2y/dx^2 = (20t^3)(12t^2 - 3) - (5t^4 - 5)(24t) / (12t^2 - 3)^3
Simplifying this expression, we get:
d^2
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Use the equation in the example to find the number of
cups of water you need if you have 12 cups of flour.
Answer: 2.5
Step-by-step explanation:
Given the equation: f = 2.5w
The constant of proportionality is 2.5.
This means that the ration of the cups of flour to the cups of water used in the recipe is 2.5
If the simple interest on 5000 dollars for 5 years is 2000 dollars the what is the interest rate
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$ 2000\\ P=\textit{original amount deposited}\dotfill & \$5000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &5 \end{cases} \\\\\\ 2000 = (5000)(\frac{r}{100})(5) \implies 2000=250r\implies \cfrac{2000}{250}=r\implies \stackrel{ \% }{8}=r[/tex]
a skateboarding ramp is 16 in. high and rises at an angle of 13 degrees. How long is the base of the ramp? Round to the nearest inch.
In the trigonometric function , the length of the base of the ramp is
3.69 in.
What is trigonometric function?
The functions of an angle in a triangle are known as trigonometric functions, commonly referred to as circular functions. In other words, these trig functions provide the relationship between a triangle's angles and sides. There are five fundamental trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.
Here Height of ramp = 16in , angle = 13 degrees.
Now The skateboard ramp arrangement looks like a right angled triangle,
then using trigonometric ratio ,
=> tan 13° = opposite/adjacent
=> tan 13° = 16/x
=> x = 16/tan 13°
=> x = 3.69 in
Hence the length of the base of the ramp is 3.69 in.
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suppose the cpa practice advisor reports that the mean preparation fee for 2017 federal income tax returns was $273. use this price as the population mean and assume the population standard deviation of preparation fees is $100. (a) what is the probability that the mean price for a sample of 40 federal income tax returns is within $16 of the population mean? (round your answer to four decimal places.) (b) what is the probability that the mean price for a sample of 60 federal income tax returns is within $16 of the population mean? (round your answer to four decimal places.) (c) what is the probability that the mean price for a sample of 81 federal income tax returns is within $16 of the population mean?(round your answer to four decimal places.) (d) which, if any, of the sample sizes in parts (a), (b), and (c) would you recommend to ensure at least a 0.95 probability that the sample mean is within $16 of the population mean? (select all that apply.)
(a)The probability that the mean price for a sample of 40 federal income tax returns is within $16 of the population mean is 0.6884, (b)The probability that the mean price for a sample of 60 federal income tax returns is within $16 of the population mean is 0.7805. (c) The probability that the mean price for a sample of 81 federal income tax returns is within $16 of the population mean is 0.8502. (d) The best sample sizes are 153, and 154 so that at least a 0.95 probability that the sample mean is within $16 of the population mean
The solution to the given problem is as follows:A) For sample size of 40 Sample size, n=40Sample Mean, x = $273 Standard deviation of the population, σ= $100. Sampling Error = Standard error of mean = σ/√n = 100/√40 = $15.8114 therefore, the required probability is P(273-16 < x < 273+16) = P(256.99 < x < 289.0 1)Using the Central Limit Theorem, the standard normal distribution can be used for solving the problem.The required probability is given by;P(Z < (289.01 - 273)/15.81) - P(Z < (256.99 - 273)/15.81)P(Z < 1.012) - P(Z > -1.012) = 0.8453 - 0.1569 = 0.6884. (B) For sample size of 60, sample size, n=60 sample Mean, x = $273 standard deviation of the population, σ= $100 sampling Error = Standard error of mean = σ/√n = 100/√60 = $12.9155. therefore, the required probability is P(273-16 < x < 273+16) = P(256.99 < x < 289.01). Using the Central Limit Theorem, the standard normal distribution can be used for solving the problem.The required probability is given by;P(Z < (289.01 - 273)/12.92) - P(Z < (256.99 - 273)/12.92)P(Z < 1.2389) - P(Z > -1.2389) = 0.8907 - 0.1102 = 0.7805.
C) For sample size of 81Sample size, n=81, sample Mean, x = $273 standard deviation of the population, σ= $100 sampling Error = Standard error of mean = σ/√n = 100/√81 = $11.111. Therefore, the required probability is P(273-16 < x < 273+16) = P(256.99 < x < 289.01)Using the Central Limit Theorem, the standard normal distribution can be used for solving the problem.The required probability is given by;P(Z < (289.01 - 273)/11.11) - P(Z < (256.99 - 273)/11.11)P(Z < 1.4403) - P(Z > -1.4403) = 0.9251 - 0.0749 = 0.8502.D) To ensure that the sample mean is within $16 of the population mean with 95% confidence, we need to find out the sample size that has a probability of 0.95.Probability is given by;P(-1.96 < Z < 1.96) = 0.95The Z-scores are obtained from the standard normal distribution table or calculator. Here, the probability of Z being less than -1.96 is equal to the probability of Z being greater than 1.96. The Z-score for a 95% confidence interval is 1.96. Therefore,1.96 = (289.01 - 273)/σnFor n = 152.94For n = 153, 1.96 = (289.01 - 273)/σ√153The best sample sizes are 153, and 154 so that at least a 0.95 probability that the sample mean is within $16 of the population mean.
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What are the coefficients?
Answer: a numerical or constant quantity placed before and multiplying the variable in an algebraic expression (4 in 4xy)
Step-by-step explanation: the coefficient is the number or digit that is being multiplied and it is placed before a constant quantity
Lines BC and DE are both vertical.
What is the length of AD?
Answer:
The answer is 6
help my math please help
Answer:
Step-by-step explanation:
Strap in man I can only do so much with 5000 characters:
1) 8 outcomes
2) Fried rice - chicken adobo - pineapple juice
Fried rice - pinakbet - pineapple juice
Steamed rice - chicken adobo - pineapple juice
Steamed rice - pinakbet - pineapple juice
3) 4
4) 2
5) 2
6) 2
7) 4/8 or 1/2 or 50%
8) 2/8 or 1/4 or 25%
9) 2/8 or 1/4 or 25%
10)2/8 or 1/4 or 25%
That's it! I hope this helps you out. Got any questions. I'll uh...be here :)
If triangle ABC has points A(2, -4) B(-3, 1) C(-2, -6) and you perform the following transformations, where will B' be?
Reflection over the y-axis, rotation 90° clockwise, and translation (x + 2, y - 1)
B'( , )
Therefore, the coordinates of the image point B' are (3, -4) when a triangle ABC has points A(2, -4) B(-3, 1) C(-2, -6).
To find the image of point B after performing the given transformations, we need to apply them in sequence.
Reflection over the y-axis:
This transformation will change the sign of the x-coordinate of point B, while leaving the y-coordinate unchanged. Therefore, the image of point B after reflection over the y-axis is (-(-3), 1), which simplifies to (3, 1).
Rotation 90° clockwise:
This transformation will swap the x and y-coordinates of the point and then change the sign of the new x-coordinate. Therefore, the image of point B after rotation 90° clockwise is (1, -3).
Translation (x + 2, y - 1):
This transformation will shift the image of point B two units to the right and one unit down. Therefore, the final image of point B after all three transformations is (1 + 2, -3 - 1), which simplifies to (3, -4).
Therefore, the coordinates of the image point B' are (3, -4).
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Convert to polar form y=4x^2
One more than two-thirds of a number is no less than 25
One more than two-thirds of a number is no less than 25 is x = -30.
An equation is a mathematical expression that contains two algebraic expressions on either side of the "equals (=)" sign. It shows the equality between the words written to the left and the words written to the right. In all mathematics there is L.H.S = R.H.S (left side = right side). Equations can be solved to find the values of unknown variables that represent unknown quantities or numbers. If there is no "equals" sign in the expression, it means it is not equal. It will be treated as a guide.
let the no. be x
According to the question:-
2/3 × x = 1/2× (x-5)
⇒ 2x/3 = x/2- 5
⇒ 2x/3 - x/2 = -5
⇒ (4x- 3x)/6 = -5
⇒ x/6 = -5
⇒ x = -30.
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What is the quotient of 1.888×10 and 5.9×10 6 expressed in scientific notation?
The required quotient of 1.888 x 10 and [tex]5.9 x 10^6[/tex] expressed in scientific notation is [tex]$3.1966 \times 10^{-6}$[/tex].
How to find quotient in scientific notation?To express the quotient of 1.888 x 10 and [tex]5.9 x 10^6[/tex] in scientific notation, we can write:
[tex]$\frac{1.888 \times 10}{5.9 \times 10^6}$[/tex]
We can simplify the numerator by moving the decimal point one place to the left:
[tex]$\frac{0.1888 \times 10^1}{5.9 \times 10^6}$[/tex]
Now, we can divide the coefficients and subtract the exponents:
[tex]$\frac{0.1888}{5.9} \times 10^{2-6}$[/tex]
[tex]$= 0.031966 \times 10^{-4}$[/tex]
Finally, we can express the result in proper scientific notation by moving the decimal point one place to the right:
[tex]$= 3.1966 \times 10^{-6}$[/tex]
Therefore, the quotient of 1.888 x 10 and [tex]5.9 x 10^6[/tex] expressed in scientific notation is [tex]$3.1966 \times 10^{-6}$[/tex].
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You are looking for a way to improve reading glasses by adding mineral to the glass. It is known that without additives, people who use glasses, on average, read 25 pages per day
with a standard deviation of 2.4 pages per day. Now you are wondering if the addition of the mineral increases the number of pages read. You select 30 people for research and give them glasses with a mineral supplement. As you go through your research, you find that these thirty people read an average of 25.5 pages per day. Using z-test for a mean, with a 5% significance level, is it possible to conclude from
this result that the addition of the mineral is effective?Justify your answer by stating what is
(a) the null hypothesis and alternative hypothesis. Explain what test (left-tailed, right-tailed or two-tailed)
you are using. Also find
(b) critical z-value (not the p-value!)
(c) test value
According to the given information, We will use a right-tailed test. The critical [tex]$z$[/tex]-value is [tex]$z_\alpha = 1.645$[/tex] and the test value is 1.77.
What is right-tailed test?
A right-tailed test, also known as a one-tailed test, is a statistical hypothesis test where the alternative hypothesis is directional and is expressed as an inequality with the greater-than symbol (>), indicating that the parameter being tested is expected to be larger than a specified value.
(a) The null hypothesis [tex]($H_0$)[/tex] and alternative hypothesis [tex]($H_a$)[/tex] are:
[tex]$H_0: \mu = 25$[/tex] (the addition of the mineral does not increase the number of pages read per day)
[tex]$H_a: \mu > 25$[/tex] (the addition of the mineral increases the number of pages read per day)
We will use a right-tailed test because the alternative hypothesis is one-sided (i.e., [tex]$\mu$[/tex] is greater than the hypothesized value).
(b) The critical [tex]$z$[/tex]-value for a one-tailed test with a 5% significance level and 29 degrees of freedom ([tex]df=n-1$, where $n=30$[/tex]) is:
[tex]$z_\alpha = 1.645$[/tex] (from the standard normal distribution table or calculator)
(c) The test value ([tex]$z$[/tex]-value) can be calculated as:
[tex]$z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$$[/tex]
where [tex]$\bar{x}$[/tex] is the sample mean, [tex]$\mu$[/tex] is the hypothesized population mean, [tex]$\sigma$[/tex] is the population standard deviation, and [tex]$n$[/tex] is the sample size.
Plugging in the values, we get:
[tex]$z = \frac{25.5 - 25}{\frac{2.4}{\sqrt{30}}} \approx 1.77$$[/tex]
The test value (1.77) is greater than the critical [tex]$z$[/tex]-value (1.645), so we reject the null hypothesis and conclude that the addition of the mineral is effective in increasing the number of pages read per day.
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HELPPPP DUE TONIGHT!!!!!!!
Find the polynomial that multiplied to 32
is equal to −124 − 62
1a) Show your work below to demonstrate how to obtain the polynomial
PLEASE HELP I NEED TO PASS THIS
The missing number in the blank is -5. To find the polynomial that multiplied by 327 is equal to -12s^2 - 62, we need to factorize the expression. We can start by finding the factors of 327. We can see that 327 = 3 x 109. Now, we need to express -12s^2 - 62 in terms of these factors. We can write:
-12s^2 - 62 = -6 x 2 x (s^2 + 5)
Therefore, the polynomial that multiplied by 327 is equal to -12s^2 - 62 is:
(2)(-6)(s^2 + 5)
= -12s^2 - 60
So, the missing number in the blank 322 ( ) = 2st - 62 is -5. We can write the complete polynomial as:
(2)(-6)(s^2 + 5) = -12s^2 - 60
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I need help with one of my math problems. I need to simplify, not answer it
20 divided by(4-(10-8)
Answer:
Step-by-step explanation:
20 ➗ (4 * (10 - 8)
10 - 8 = 2 * 4 = 8
Then, 20 ➗ 8 = 2.5
4.5 Draw a diagram representing the scenario and find the requested value. A man is standing 270 feet from the base
of a statue. If he man looks up at an angle of 34 degrees to see the top of the statue, how tall is the statue. Please
round to the nearest whole foot.
Therefore, the height of the statue is approximately 192 feet.
What is height?Height is a measure of how tall or high something or someone is, typically referring to the vertical distance from the base of an object or person to its highest point. It can be measured in various units such as feet, inches, meters, centimeters, etc. Height is an important physical characteristic of living organisms and is often used as a parameter in many applications, such as architecture, construction, athletics, and medical assessments.
by the question.
let A be the top of the statue, B be the position of the man, and θ be the angle of elevation from the man to the top of the statue. Let AB = h be the height of the statue and let BC = 270 ft be the distance between the man and the base of the statue.
We can use the tangent function to find the height of the statue:
tan(θ) = opp/adj = h/BC
Solving for h, we get:
h = tan(θ) * BC
Substituting θ = 34 degrees and BC = 270 ft, we get:
h = tan (34) * 270
h ≈ 192 ft
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Read the following word problem. Solve and write your answer in a statement. Ex
solve the problem. Show all of your work.
Hank buys his dog food in bulk by
the bag. He uses a scoop that
holdscup of dog food and feeds
8
his dog one scoop a day.
If there are 5 cups of dog-food in
the bag, how many days can he
feed his dog?
Hank can feed his dog for 40 days with one bag of dog food.
Define fractionA fraction represents a part of a whole or a ratio between two quantities. It is a mathematical expression that consists of a numerator and a denominator separated by a horizontal line, also called a fraction bar or a vinculum.
To solve the problem, we need to find how many scoops of dog food are in the bag and divide that by the number of scoops used per day:
Number of scoops in bag = 5 cups ÷ 1/8 cup/scoop = 40 scoops
Number of days he can feed his dog = 40 scoops ÷ 1 scoop/day = 40 days
Therefore, Hank can feed his dog for 40 days with one bag of dog food.
Statement: Hank can feed his dog for 40 days with one bag of dog food.
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SOMEONE PLEASE HELP ME WITH THIS QUESTION
A) 56% of what number is $21.84?
Percent Proportion -
Percent Equation-
B) $495 is 55% of what number?
Percent Proportion -
Percent Equation-
C) 144 is what percent of 240?
Percent Proportion -
Percent Equation-
Answer:
A) 39
B) 900
C) 60%
A) proportion:
21.84 is 56% of x number
x number = 100%
If you want to calculate x you can use proportion. First of all make this kind of system..
x - 100%
21.84 - 56%
Then multiply numbers diagonally.
56x = 2184
Finally solve x
x = 2184/56
x = 39
steve is trying to earn $300 in interest for a new guitar. he puts $2500 in an account that earns 2% interest yearly (simple interest). how long will it take to earn $300?
The time required to earn $300 in interst on a principal of $2,500.00 at an interest rate of 2% per year is 6 years.
Steve puts $2500 in an account that earns 2% interest yearly.
This means principal P = $2500
And interest rate as percentage (R) = 2%
He is trying to earn $300 in interest
I = $300
so, the final amount A = P + I
A = $2800
Now we convert the rate of interest R percent to r a decimal:
r = R/100
r = 2%/100
r = 0.02 per year,
We need to find the number of years t:
We know that the formula for the simple interest is:
A = P(1 + rt)
So, t = (1/r)[A/P - 1]
t = (1/0.02)((2800/2500) - 1)
t = 6
Therefore, the time required to earn $300 in interst = 6 years
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a) Write the missing numbers.
50% of 60 =
5% of 60 =
1% of 60 =
b) Work out 56% of 60
You can use part (a) to help you.
38
3
0.6
The missing numbers 50% of 60 = 30
What are numbers?A number is a numerical unit of measurement and labeling in mathematics.
The natural numbers 1, 2, 3, 4, and so on are the first examples.
Number words are a linguistic way to express numbers.
Most commonly, specific numbers can be represented using symbols known as numerals; for instance, the numeral "5" stands in for the number five.
Basic numerals are frequently grouped in a numeral system, which is an ordered manner to represent any number, because only a small number of symbols can be learned.
The most widely used number system is the Hindu-Arabic number system, which enables the depiction of any number using a combination of 10 basic numerical symbols, or "digits."
50*60/100
30
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A rectangular poster has an area of 35 square feet. It is 5 ft. at its base. What is the
height of the poster?
The rectangular poster is 7 feet tall.
which has the form of a rectangle?The rectangular shape in two dimensions has four sides, four corners, and four right angles (90°). Equal and parallel opposing sides make form a rectangle. Being a two-dimensional form, a rectangle has length and breadth as its two dimensions.
The procedure for calculating a rectangle's area may be used to get the rectangular poster's height:
Area = length * width
In this case, we know that the area is 35 square feet and the width (or base) is 5 feet. So we can rearrange the formula to solve for the length (or height):
length = Area / width
Substituting the values we get:
length = 35 sq ft / 5 ft = 7 ft
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A machine fills 16 ounce coke bottles. It places coke in the bottles.
Not all bottles hold exactly 16 ounces. The volume of the coke is
normally distributed with a mean of 16.2 ounces and a standard
deviation of 0.3 ounces.
Make a curve to represent the distribution to help you answer the
following:
a. If you purchase a coke filled by the dispenser what is the
percentage it has less than 16.5 ounces?
b. If you purchase a coke filled by the dispenser what is the
percentage it has less than 15.9 ounces?
c. If you purchase a coke what is the percentage it has more than
15.3 ounces?
d. If you purchase a bag what is the percentage it has between 15.9
and 16.8 ounces?
Option B is best represents for the answer. A. 84.13%. B. 15.87%. 99.87%. D. 81.86%. To create the distribution curve, we can use the normal distribution formula: [tex]f(x) = (1/σ√(2π)) * e^(-0.5((x-μ)/σ)^2)[/tex]
where:
f(x) = probability density function at value x
μ = mean = 16.2
σ = standard deviation = 0.3
Using this formula, we can calculate the probabilities for the given scenarios:
a. Probability of a coke having less than 16.5 ounces:
We need to find P(X < 16.5), where X is the volume of the coke in ounces.
Using the z-score formula, we can standardize the value of 16.5:
z = (16.5 - 16.2) / 0.3 = 1
P(Z < 1) = 0.8413
Therefore, the probability of a coke having less than 16.5 ounces is 84.13%.
b. Probability of a coke having less than 15.9 ounces:
We need to find P(X < 15.9), where X is the volume of the coke in ounces.
Using the z-score formula, we can standardize the value of 15.9:
z = (15.9 - 16.2) / 0.3 = -1
P(Z < -1) = 0.1587
Therefore, the probability of a coke having less than 15.9 ounces is 15.87%.
c. Probability of a coke having more than 15.3 ounces:
We need to find P(X > 15.3), where X is the volume of the coke in ounces.
Using the z-score formula, we can standardize the value of 15.3:
z = (15.3 - 16.2) / 0.3 = -3
P(Z > -3) = 0.9987
Therefore, the probability of a coke having more than 15.3 ounces is 99.87%.
d. Probability of a bag having between 15.9 and 16.8 ounces:
We need to find P(15.9 < X < 16.8), where X is the volume of the coke in ounces.
Using the z-score formula, we can standardize the values of 15.9 and 16.8:
z1 = (15.9 - 16.2) / 0.3 = -1
z2 = (16.8 - 16.2) / 0.3 = 2
P(-1 < Z < 2) = 0.8186
Therefore, the probability of a coke having a volume between 15.9 and 16.8 ounces is 81.86%.
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A plan of a school compound is drawn to a scale of 1cm represent 5m. 1 find its length and breadth of the drawing. If the football field is 50m by 30m. 2 if the scale drawing of the hall is 7cm by 32cm rectangle, find its length and breadth
the length of the hall is 35 m and the breadth of the hall is 160 m.
To find the length and breadth of the drawing, we need to use the scale given. We know that 1 cm represents 5 m, so we can use this proportion to find the actual dimensions of the school compound:
1 cm : 5 m = x cm : y m
To find the length of the drawing, we can use the given dimensions of the football field, which are 50 m by 30 m:
Length of the drawing = 50 m / 5 m per cm = 10 cm
Breadth of the drawing = 30 m / 5 m per cm = 6 cm
Therefore, the length of the drawing is 10 cm and the breadth of the drawing is 6 cm.
To find the actual length and breadth of the hall, we need to use the scale given. We know that 7 cm represents the length and 32 cm represents the breadth:
Length of the hall = 7 cm x 5 m per cm = 35 m
Breadth of the hall = 32 cm x 5 m per cm = 160 m
Therefore, the length of the hall is 35 m and the breadth of the hall is 160 m.
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What is the LCM of 78 and 92?
Answer:
3588
Step-by-step explanation: prime factorize and find common factors, only count those once, take the rest and the common factors and multiply
the alpha level for a hypothesis test defines the critical region the alpha level for a hypothesis test defines the critical region true false
True. The alpha level for a hypothesis test defines the critical region.
A hypothesis test is a statistical technique that is used to test an assumption or hypothesis regarding a population parameter or distribution.
The critical region refers to the region of the sampling distribution that contains values that are unlikely to have occurred by chance if the null hypothesis is true.
The alpha level is the probability of committing a type I error, which is rejecting the null hypothesis when it is actually true.
The critical region is defined by the alpha level, which is the level of significance or the maximum probability of rejecting the null hypothesis when it is actually true. For example, if the alpha level is set at 0.05, the critical region will be the upper and lower 2.5% of the sampling distribution. If the test statistic falls within this region, the null hypothesis is rejected. On the other hand, if the test statistic falls outside this region, the null hypothesis is accepted.
Therefore, the alpha level plays a crucial role in determining the critical region and making decisions based on the results of the hypothesis test.
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What is 71% written as a fraction?
what is the probability that at least two of the six members of a family are not born in the fall? assume that all seasons have the same probability of containing the birthday of a person selected randomly.
The probability that at least two of the six members of a family are not born in the fall is approximately 0.66.
Since there are four seasons and each season has an equal probability of containing a randomly selected person's birthday, the probability that a person's birthday is not in the fall is 3/4. Therefore, the probability that all six family members are born in a season other than fall is (3/4)⁶, which is approximately 0.18.
The probability that only one family member is born in the fall is 6*(1/4)*(3/4)⁵, which is approximately 0.41. To find the probability that at least two family members are not born in the fall, we can subtract the probability that all six are born in the fall or only one is born in the fall from 1: 1 - 0.18 - 0.41 = 0.41.
In conclusion, the chance of having at least two out of the six family members not born in the fall is roughly 66%.
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-1/2(32x-40)+(20x-4)
Answer:
4x+16
Step-by-step explanation:
Distribute -1/2 to 32 and -40
That gets you -16x+20+20x-4
Combine -16x and 20x which gets you 4x+20-4
subtract 4 from 20
4x+16
someone help me please and asap
(a) GI side of right triangle GHI is the hypotenuse.
(b) GI is the side which is opposite to ∠H
(c) GH is the side that is adjacent to ∠G.
What is right angle Triangle?A right-angled triangle is a type οf triangle that has οne οf its angles equal tο 90 degrees. The οther twο angles sum up tο 90 degrees. The sides that include the right angle are perpendicular and the base οf the triangle. The third side is called the hypοtenuse, which is the lοngest side οf all three sides.
(a) GI side of right triangle GHI is the hypotenuse.
(b) GI is the side which is opposite to ∠H
(c) GH is the side that is adjacent to ∠G.
(d) HI is the side that is opposite to ∠G
(e) HI is the side that is adjacent to ∠I.
(f) GH is the side which is opposite to I.
(g) 5 : 12 is the numerical ratio of the length of the side opposite to G to the length of the side adjacent to ZG.
(h) 12 : 5 is the numerical ratio of the length of the side opposite to I to the length of the side adjacent to I.
(i) 5 : 13 is the numerical ratio of the length of the side opposite to G to the length of the hypotenuse.
(j) 12 : 13 is the numerical ratio of the length of the side adjacent to ZG to the length of the hypotenuse.
(k) 12 : 13 is the numerical ratio of the length of the side opposite to I to the length of the hypotenuse.
(H) 5 : 13 is the numerical ratio of the length of the side adjacent to I to the length of the hypotenuse.
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