Number of 50 g weigh balls = 12
And, Number of 120g weigh balls = 8
We have to given that;
There is a total of 20 balls. Some balls weigh 50g each and others weigh 120g each.
Let number of 50 g weigh balls = x
And, Number of 120g weigh balls = y
Hence, We can formulate;
x + y = 20 .. (i)
And, 50x + 120y = 1560
⇒ 5x + 12y = 156 .. (ii)
From (i);
x = 20 - y
Plug in (ii);
5 (20 - y) + 12y = 156
100 - 5y + 12y = 156
7y = 56
y = 8
From (i);
x = 20 - y
x = 20 - 8
x = 12
Thus, number of 50 g weigh balls = 12
And, Number of 120g weigh balls = 8
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when a 90% confidence interval for the mean of a normal population, given a random sample of 16 values with a mean and standard deviation of 100 and 10 respectively, what is the upper limit of the interval? round your answer to two decimal places.
The upper limit of the 90% confidence interval for the population mean is 104.11.
Using the formula for a 90% confidence interval for the population mean, we have:
Upper limit = mean + (z-value)*(standard deviation/square root of sample size)
where the z-value for a 90% confidence interval is 1.645.
Plugging in the values from the given information, we get:
Upper limit = 100 + (1.645)*(10/square root of 16)
Upper limit = 100 + 4.1125
Upper limit = 104.11 (rounded to two decimal places)
A 90% confidence interval is an interval that, with a 90% probability, contains the true value of the population mean. To find the upper limit of the interval, we need to use the formula that takes into account the sample mean, sample standard deviation, sample size, and the z-value corresponding to the desired confidence level.
Given a sample size of 16 with a mean and standard deviation of 100 and 10 respectively, the upper limit of the 90% confidence interval is calculated to be 104.11.
This means that we are 90% confident that the true value of the population mean lies between 100 and 104.11.
The upper limit of the 90% confidence interval for the population mean, given a random sample of 16 values with a mean and standard deviation of 100 and 10 respectively, is 104.11.
This means that we can be 90% confident that the true value of the population mean lies between 100 and 104.11.
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What determintes the rate of a molecules's migration through an electric field during electrophoresis?
The rate of a molecule's migration through an electric field during electrophoresis is determined by factors such as the molecule's size, shape, and charge, as well as the properties of the electric field and the medium through which the molecule is moving.
The rate of a molecule's migration through an electric field during electrophoresis is determined by several factors. The size and shape of the molecule play a significant role. Larger molecules will migrate more slowly than smaller molecules, and molecules with more complex shapes will also migrate more slowly due to increased resistance to movement through the gel or solution. Secondly, the charge of the molecule is also a determining factor. Molecules with a higher charge will migrate more quickly than those with a lower charge.
The strength of the electric field and the properties of the gel or solution used for electrophoresis can also affect the rate of migration. The rate of a molecule's migration through an electric field during electrophoresis is a complex process with multiple factors influencing the final outcome.
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The American Automobile Association (AAA) reported that families planning to travel over the Labor Day weekend would spend an average of $749 (The Associated Press, August 12, 2012). Assume that the amount spent is normally distributed with a standard deviation of $225.
a. What is the probability that family expenses for the weekend will be less than $400?
b. What is the probability that family expenses for the weekend will be $800 or more?
c. What is the probability that family expenses for the weekend will be between $500 and $1000?
d. What are the Labor Day weekend expenses for 5% of the families with the most expensive travel plans?
a. The probability will be less than $400 is approximately 4.78%. b. The probability will be $800 or more is approximately 34.13%. c. The probability will be between $500 and $1000 is approximately 68.27%. d. The most expensive travel plans are approximately $1,170 or more.
a. To find the probability that family expenses for the weekend will be less than $400, we need to standardize the value using the formula z = (x - μ) / σ, where x is the value we want to find the probability for, μ is the mean, and σ is the standard deviation. In this case, x = $400, μ = $749, and σ = $225. So, z = (400 - 749) / 225 = -1.56. Using a standard normal distribution table or calculator, we can find that the probability of a standard normal variable being less than -1.56 is approximately 0.0594. Therefore, the probability that family expenses for the weekend will be less than $400 is about 0.0594 or 5.94%.
b. To find the probability that family expenses for the weekend will be $800 or more, we again need to standardize the value. In this case, x = $800, μ = $749, and σ = $225. So, z = (800 - 749) / 225 = 0.227. Using a standard normal distribution table or calculator, we can find that the probability of a standard normal variable being greater than 0.227 is approximately 0.409. Therefore, the probability that family expenses for the weekend will be $800 or more is about 0.409 or 40.9%.
c. To find the probability that family expenses for the weekend will be between $500 and $1000, we need to standardize both values and then find the area between them. For $500, z = (500 - 749) / 225 = -1.11, and for $1000, z = (1000 - 749) / 225 = 1.11. Using a standard normal distribution table or calculator, we can find that the probability of a standard normal variable being less than -1.11 is approximately 0.1335 and the probability of a standard normal variable being less than 1.11 is approximately 0.8664. Therefore, the probability that family expenses for the weekend will be between $500 and $1000 is about 0.8664 - 0.1335 = 0.7329 or 73.29%.
d. To find the Labor Day weekend expenses for 5% of the families with the most expensive travel plans, we need to find the z-score corresponding to the 95th percentile of the normal distribution. This can be done using a standard normal distribution table or calculator, and we find that the z-score is approximately 1.645. Then, we can use the formula x = μ + zσ, where x is the value we want to find, μ is the mean, σ is the standard deviation, and z is the z-score we just found. Plugging in the values, we get x = 749 + 1.645(225) = $1,100.13. Therefore, the Labor Day weekend expenses for 5% of the families with the most expensive travel plans is about $1,100.13 or higher.
According to the American Automobile Association (AAA), families planning to travel over the Labor Day weekend are expected to spend an average of $749, with a standard deviation of $225. Assuming the amount spent is normally distributed:
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can you help me with this
Answer:
D
Step-by-step explanation:
How do you prove csc^4 x - cot^4 x = csc^2 x + cot^2 x
To prove the equation csc^4(x) - cot^4(x) = csc^2(x) + cot^2(x), we can start by expressing the trigonometric functions csc(x) and cot(x) in terms of sine and cosine:
csc(x) = 1/sin(x)
cot(x) = cos(x)/sin(x)
Substituting these expressions into the equation, we get:
(1/sin(x))^4 - (cos(x)/sin(x))^4 = (1/sin(x))^2 + (cos(x)/sin(x))^2
Next, we simplify each term separately:
(1/sin(x))^4 = 1/sin^4(x)
(cos(x)/sin(x))^4 = cos^4(x)/sin^4(x)
Expanding the powers, we have:
1/sin^4(x) - cos^4(x)/sin^4(x) = 1/sin^2(x) + cos^2(x)/sin^2(x)
Combining the fractions on the left side:
(1 - cos^4(x))/sin^4(x) = (1 + cos^2(x))/sin^2(x)
Now, let's simplify the left side:
1 - cos^4(x) = sin^4(x)
Using the identity sin^2(x) + cos^2(x) = 1, we can rewrite the equation as:
sin^4(x) = sin^4(x)
The equation simplifies to an identity, showing that the original equation csc^4(x) - cot^4(x) = csc^2(x) + cot^2(x) is true for all values of x.
Therefore, we have proved the given equation.
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A square of area 36 cm² is cut to make two rectangles, A and B.
Area = 36 cm²
The ratio of area A to area B is 2:1
Work out the dimensions of rectangles A and B.
Rectangle A
Length:
Width:
Rectangle B
Length:
Width:
A university is researching the impact of including seaweed in cattle feed. They assign feed with and without seaweed to be fed to cows at two
different dairy farms. The two-way table shows randomly collected data on 200 dairy cows from the two farms about whether or not their feed
includes seaweed.
Based on the data in the table, if a cow is randomly selected from farm B, what is the probability that its feed includes seaweed?
Without Seaweed?
A. 0.649
B. 0.620
C. 0.370
D. 0.597
Based on the data in the table, if a cow is randomly selected from farm B, the probability that its feed includes seaweed is 0.597 (Option D) and without is 0.57
How did we arrive at this?Note that the total number of feed with sea weed is 74.
And the total number of cows on the farm B is 124.
Thus, the cows whose feed includes seaweed is 74/124
= 0.59677419354
≈ 0.597
The Probability of those whose feed is without sea weed is
Note that the total number of feed without sea weed is 40.
And the total number of cows on the farm B is 76.
Thus, the probability is 40/70
= 0.5714285714
≈ 0.571
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a population has ss = 100 and s2 = 4. what is the value of s(x – m) for the population?
The value of E(x- μ) for the population for any given data is always equal to option b. 0.
Sum of squared deviations,
ss = 100
variance, σ² = 4
The value of E(x - μ) for the population can be determined .
Using the relationship between the sum of squared deviations (ss) and the variance (σ²).
ss = n × σ²
where ss is the sum of squared deviations,
σ² is the variance,
and n is the population size.
Substituting these values into the equation, solve for n,
⇒ 100 = n × 4
⇒ n = 100 / 4
⇒ n = 25
The expected value (E) of (x - μ) for the population is zero.
This means that on average, the difference between each data point (x) and the population mean (μ) is zero.
Therefore, the value of the expected operator E(x- μ) for the population is equal to option b. 0
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The above question is incomplete, the complete question is:
A population has sum of squared deviations, ss = 100 and variance, σ² = 4. What is the value of E(x- μ) for the population?
a. 400
b. 0
c. 10
d. 25
what is the sum of all the possible 3 digit numbers that can be constructed using the digits 3, 4, and 5 if each digit can only be used once in each number
Possible numbers: 345, 354, 435, 453, 534, 543.
345+354+435+453+534+543=2664
Mr. Vern is lining his rectangular pool on all sides and the bottom He wants to know how many square feet he will be covering. The deep, 30 feet wide and 40 feet long. What equation should Mr. V determine the total area in square feet being covered?, Mr. Vern is lining his rectangular pool on all sides and the bottom with pool liner. He wants to know how many square feet he will be covering. The pool is 5 feet deep, 30 feet wide and 40 feet long. What equation should Mr. Vern use to determine the total area in square feet being covered?
The linear equation be 2lw + 2lh + 2wh + lb and total area is 2200 square feet.
Assume that,
l is the length of the pool (40 feet),
w is the width of the pool (30 feet),
h is the height of the pool (5 feet),
And b is the depth of the pool (also 5 feet).
To determine the total area of the pool liner needed to line the rectangular pool on all sides and the bottom, Mr. Vern can use the following equation:
Total area = 2lw + 2lh + 2wh + lb,
Plugging in the values, we get:
Total area = 2(40)(5) + 2(30)(5) + 2(30)(5) + (40)(30) Total area = 400 + 300 + 300 + 1200 Total area = 2200
Therefore, Mr. Vern would need to cover a total area of 2200 square feet with pool liner to line his rectangular pool on all sides and the bottom.
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The next model of a sports car will cost 12. 4% more than the current model. The current model costs 49,000. How much will the price increase in dollars? What will be the price of the next model?
1. Increase in price:
2. Price of next model:
Answer:
1. $6,076
2. $55076
Step-by-step explanation:
price increase: 49,000x12.4%
12.4%=0.124
49,000x0.124=6,076
price of next model:49000x0.124=6076
6076+49000=55076
suppose an advocacy organization surveys 960 canadians and 192 of them reported being born in another country (www.unitednorthamerica.org/simdiff .htm). similarly, 170 out of 1250 americans reported being foreign-born. find the standard error of the difference in sample proportions
The standard error of the difference in sample proportions is 0.0161.
Given that an advocacy organization surveys 960 Canadians and 192 of them reported being born in another country.
Similarly, 170 out of 1250 Americans reported being foreign born,
P₁ = 192/960 = 0.2
P₂ = 170/1250 = 0.136
The standard error of the difference in sample proportions =
[tex]\sqrt{\frac{p_1(1-p_1)}{n_1} + \frac{p_2(1-p_2)}{n_2}[/tex]
[tex]\sqrt{\frac{0.2(1-0.2)}{960} + \frac{0.136(1-0.136)}{1250}[/tex] [tex]\approx 0.0161[/tex]
Hence the standard error of the difference in sample proportions is 0.0161.
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please help asap i need help ASAP!!!
The cost of variation is $3 per guest.
The equation of a line is y=mx+b
m is slope and b is the y intercept of the given equation
The ratio of the rise to the run, or rise divided by the run is known as slope and represents the steepness of line in the coordinate plane.
Constant of variation is slope in the given question.
From the graph number of guests taken in the x axis and cost is taken in the y axis
The Constant of variation which passes through two points (x₁, y₁) and (x₂, y₂) is
The formula to find slope is m=y₂-y₁/x₂-x₁
Here the two points from graph are (30, 90) and (20, 60)
Now plug in these values to find the constant of variation or slope
constant of variation = 90-60/30-20
=30/10
=3
Hence, the cost of variation is $3 per guest.
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Help please im trying to check my answer
Answer:
(a) 66 cm³
Step-by-step explanation:
You want the volume of a right triangular prism with a base right triangle that has a leg length of 3 cm and a hypotenuse of 5 cm. The height of the prism is 11 cm.
BaseThe base triangle is a 3-4-5 right triangle, so will have an area of ...
A = (1/2)bh
A = (1/2)(4 cm)(3 cm) = 6 cm²
VolumeThe volume of the prism is ...
V = Bh . . . . . where B is the base area
V = (6 cm²)(11 cm) = 66 cm³
The volume of the prism is 66 cubic centimeters.
__
Additional comment
As you can see, the "work" is greatly simplified by the recognition of the {3, 4, 5} right triangle. If you must use the Pythagorean theorem to find the missing side length, you will find it to be ...
b = √(c² -a²) = √(5² -3²) = √16 = 4
The answer can be estimated by realizing the missing dimension is less than 5. The volume of a rectangular prism of side lengths 3, 5, and 11 would be 3·5·11 = 165 cm³. A triangular prism with the same overall dimensions would have 1/2 that volume, or 82.5 cm³. Since the prism shown has a side length less than 5, its volume will be smaller than 82.5 cm³. The only reasonable answer is 66 cm³.
#95141404393
find the values of X and Y using the given chord secant and tangent lengths
Check the picture below.
[tex]x^2=(5+25)(5)\implies x^2=150\implies x=\sqrt{150}\implies x=5\sqrt{6} \\\\[-0.35em] ~\dotfill\\\\ x^2=(10+y)(10)\implies (\sqrt{150})^2=100+10y\implies 150=100+10y \\\\\\ 50=10y\implies \cfrac{50}{10}=y\implies 5=y[/tex]
Terms and Definitions
what is the key word ?
Acceleration - a change in velocity over time and how fast that change happened
the difference between the final velocity and the initial velocity
Acceleration rate of change of velocity can be written as
a = (v₁ - v₀)/t.
The given keyword is,
Acceleration
Since we know that,
Acceleration has both a magnitude and a direction, it is a vector quantity. Additionally, it is the first derivative of velocity with respect to time or the second derivative of position with respect to time.
Now let,
a = is the acceleration
v₁ is the final velocity
v₀ is the initial velocity
t is the time interval
Δv is the small change in the velocity
Therefore,
The acceleration = ( final velocity - initial velocity)/time
Thus,
The acceleration be,
⇒ a = (v₁ - v₀)/t
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Points D(2; 5), E (-4;-4), F(0; 2) and G(-4;9) are given. Find MDG: What can you conclude about the line segments DE and DG?
Answer:
Step-by-step explanation:
To find MDG, we need to calculate the length of line segment DG.
Using the distance formula, the length of a line segment between two points (x1, y1) and (x2, y2) is given by:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Let's calculate the length of line segment DG:
DG = √((-4 - 2)^2 + (9 - 5)^2)
= √((-6)^2 + (4)^2)
= √(36 + 16)
= √52
= 2√13
Therefore, MDG is equal to 2√13.
Now, let's analyze the line segments DE and DG:
Line segment DE: The coordinates of D are (2, 5) and the coordinates of E are (-4, -4). By calculating the length of DE using the distance formula, we can determine the length of DE.
DE = √((-4 - 2)^2 + (-4 - 5)^2)
= √((-6)^2 + (-9)^2)
= √(36 + 81)
= √117
= √(9 * 13)
= 3√13
Therefore, the length of line segment DE is 3√13.
Line segment DG: We have already calculated the length of DG as 2√13.
From the calculations, we can conclude that DE and DG have different lengths. DE is 3√13 while DG is 2√13.
In summary, line segments DE and DG have different lengths.
can you hellp me if you can hellp me
Answer:
Solution,
Given,
radius of the circle(r)=9 cm
circumference of the circle(c)=?
We know that;
[tex]C=2{\pi}r[/tex]
[tex] \: \: \: \: = 2 \times 3.14 \times 9[/tex]
[tex]\: \: \: \: = 56.52[/tex]
Thus,the circumference of the circle is 56.52 cm.
Dan works on a horse farm. There are 10 horses on the farm and they each eat 140
pounds of hay in a week. Dan buys new hay for the farm every week. Where should
Dan purchase hay from if he does not want any hay leftover at the end of the week?
How many bales should he purchase?
The number of bales purchased for the farm is n = 7 bales
Given data ,
Dan works on a horse farm. There are 10 horses on the farm and they each eat 140 pounds of hay in a week
Now , Dan buys new hay for the farm every week
To find the total amount of hay needed for the week, we multiply the amount consumed by each horse by the number of horses:
Total hay needed = 10 horses x 140 pounds/horse = 1400 pounds
To determine the number of bales needed, we divide the total hay needed by the weight of each bale:
Number of bales needed = Total hay needed / Weight of each bale
On simplifying the equation , we get
Number of bales needed for agri supply = 1400 / 75 = 18.667
Number of bales needed for farm supply = 1400 / 150 = 9.33
Number of bales needed for tractor supply = 1400 / 200 = 7 bales
Number of bales needed ≈ 7 bales when there is not leftover
Hence , there is no leftover at the end of the week if he purchases 7 bales from the tractor supply
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The complete question is attached below :
Dan works on a horse farm. There are 10 horses on the farm and they each eat 140 pounds of hay in a week. Dan buys new hay for the farm every week. Where should Dan purchase hay from if he does not want any hay leftover at the end of the week? How many bales should he purchase?
Let F(x)={sin(x+1)ex−1x<−1−1≤x
Find limx→-1+F(x)
To find the limit of F(x) as x approaches -1, we need to evaluate the left-hand and right-hand limits separately and check if they are equal.
For x < -1, F(x) = sin(x + 1) * e^(x - 1). Since we are interested in the limit as x approaches -1, we consider values of x that are approaching -1 from the left side.Let's evaluate the left-hand limit:
lim(x→-1-) F(x) = lim(x→-1-) sin(x + 1) * e^(x - 1)
As x approaches -1 from the left side, sin(x + 1) approaches sin(0) = 0, and e^(x - 1) approaches e^(-2).
Therefore, lim(x→-1-) F(x) = 0 * e^(-2) = 0.
Now, let's evaluate the right-hand limit:
lim(x→-1+) F(x) = lim(x→-1+) F(x)
For x greater than or equal to -1, F(x) is not defined.
Since the left-hand limit and the right-hand limit are not equal, the limit of F(x) as x approaches -1 does not exist.
Therefore, lim(x→-1+) F(x) is undefined.
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i ne table snows a linear relationship between x ana y.
X
3
5
сл
10
y
7
11
21
Create an equation that describes the relationship shown in the table.
Move the correct answer to each box. Not all answer will be used.
An equation that describes the relationship shown in the table is y = 2x + 1.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.First of all, we would find the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (11 - 7)/(5 - 3)
Slope (m) = 4/2
Slope (m) = 2.
At data point (3, 7) and a slope of 2, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 7 = 2(x - 3)
y = 2x - 6 + 7
y = 2x + 1
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Complete Question:
The table snows a linear relationship between x and y.
x y
3 7
5 11
10 21
Create an equation that describes the relationship shown in the table.
Move the correct answer to each box. Not all answer will be used.
What are your options in regards to the null hypothesis after you collect your data?
After you collect your data, you have several options in regards to the null hypothesis. First, you could fail to reject the null hypothesis.
The data did not provide enough evidence to support the alternative hypothesis, and you accept the null hypothesis as the most likely explanation. Second, you could reject the null hypothesis. This means that your data provided enough evidence to support the alternative hypothesis, and you reject the null hypothesis as the most likely explanation. To neither accept nor reject the null hypothesis. The less common option and occurs when your data does not provide enough evidence to reject the null hypothesis, but also does not provide enough evidence to accept it as the most likely explanation.
The null hypothesis after you collect your data include failing to reject it, rejecting it, or neither accepting nor rejecting it.
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help? 0.269 0.344 0.360 0.656
Answer:
B. 0.344
Step-by-step explanation:
The question asks about the probability that the person is at at least 175 centimeters. The first column has a total of 86 people under the category of at least 175 centimeters tall. To find the probability, divide the given number of people at least 175 cm (86) by the total number surveyed (250). This gives you the answer of 0.344.
Find Vector A + B
….
The sum of magnitude of vectors is 17.4 and direction is 88 degree.
Hence, option 3 is correct.
Given that,
Vector A: magnitude = 12 and direction = 60 degree
Vector B: magnitude = 10 and direction = 150 degree
Find the x and y components using the following formulas,
Ax = AcosΘ and Ay = AsinΘ
Substitute the values,
Ax = 12cos(60) and Ax = 6
Ay = 12sin(60) and Ay = 10.39
For vector B,
By using the same formulas,
Bx = 10cos(150) and Bx = -5
By = 10sin(150) and By = 7.66
We have the x and y components of both vectors,
Add them,
Rx = Ax + Bx
⇒ Rx = 6 + (-5)
⇒ Rx = 1
⇒ Ry = Ay + By
⇒ Ry = 10.39 + 7.66
⇒ Ry = 18.05
Finally, we can find the magnitude and direction of the resulting vector,
Magnitude = √(R²x + R²y)
Therefore, after putting values we get,
Magnitude = 17.4
Direction = [tex]tan^{-1}[/tex](Ry/Rx)
= [tex]tan^{-1}[/tex](18.05/1)
= 88 degrees
Therefore, the sum of the two vectors is a vector with magnitude 17.4 and direction 88 degrees.
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Jeff made $243. 75 last week. If he worked 25 hours, how much is he paid for 1 hour of work?
To find out how much Jeff is paid per hour of work, we need to divide his total earnings by the number of hours he worked.
Total earnings: $243.75
Number of hours worked: 25
Hourly pay rate: Total earnings / Number of hours worked
Hourly pay rate: $243.75 / 25 = $9.75
Therefore, Jeff is paid $9.75 per hour of work
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Find the measures of angles
∠1 and ∠8 given that
m∠2 = 5x − 22 and m∠6 = 4x − 6, and r ∥ s cut by a
transversal t
Unfortunately, the diagram or additional information is needed to determine the measures of angles ∠1 and ∠8. The given information about angles ∠2 and ∠6 and the fact that r ∥ s cut by a transversal t do not provide enough information to solve for the measures of angles ∠1 and ∠8.
To find the measures of angles ∠1 and ∠8, we need additional information about the angles or the lines r, s, and t in the diagram. It's possible that the diagram was not provided or the question is incomplete. Without more information, it's not possible to provide a complete answer to this question.
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Unfortunately, the diagram or additional information is needed to determine the measures of angles ∠1 and ∠8. The given information about angles ∠2 and ∠6 and the fact that r ∥ s cut by a transversal t do not provide enough information to solve for the measures of angles ∠1 and ∠8.
To find the measures of angles ∠1 and ∠8, we need additional information about the angles or the lines r, s, and t in the diagram. It's possible that the diagram was not provided or the question is incomplete. Without more information, it's not possible to provide a complete answer to this question.
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express tan(t) in terms of sin(t), if the terminal point determined by t is in quadrant i.
if the terminal point determined by t is in quadrant I, then tan(t) = sin(t)/sqrt(1 - sin^2(t)).
If the terminal point determined by t is in quadrant I, then both sine and tangent are positive. We can use the identity:
tan(t) = sin(t)/cos(t)
to express tangent in terms of sine. Since the terminal point is in quadrant I, cosine is positive, so we can use the Pythagorean identity:
sin^2(t) + cos^2(t) = 1
to solve for cosine:
cos(t) = sqrt(1 - sin^2(t))
Substituting this expression for cosine in the formula for tangent, we get:
tan(t) = sin(t)/cos(t) = sin(t)/sqrt(1 - sin^2(t))
what is quadrant?
A quadrant is one of the four regions that a coordinate plane is divided into by the x-axis and the y-axis. The x-axis is a horizontal line that runs left and right through the plane, and the y-axis is a vertical line that runs up and down through the plane. The point where the x-axis and the y-axis intersect is called the origin.
Each quadrant is labeled with a Roman numeral (I, II, III, or IV) to distinguish it from the others. Quadrant I is the region in the upper-right corner of the plane, where both the x and y coordinates are positive. Quadrant II is the region in the upper-left corner of the plane, where the x-coordinate is negative and the y-coordinate is positive.
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URGENT! Please help
What is the value of 7 for the following data to three decimal places?
A. 0.852
B. 0.930
C. 0.659
D. 0.964
Answer:
Option B
Step-by-step explanation:
Given that two variables in the table as
Total Average
x 2 6 7 8 12 35 7
y 15 13 9 8 5 50 10
xy 30 78 63 64 60 295 59
(x-7)^2 25 1 0 1 25 52 10.4
(y-10)^2 25 9 1 4 25 64 12.8
Var x = 10.4 and std dev x = 3.225
Var Y = 12.8 and std dev Y = 3.578
Cov (xy) = E(xy)-E(x) E(Y)=59-70=-11
Correlation coefficient r
= Cov /sx sy = -11/(3.225)(3.578)=-0.9532
Round off to get
r=-0.953
Henceoption B is right.
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If ∠J measures 40°, ∠K measures 90°, and j is 15 feet, then find k using the Law of Sines. Round your answer to the nearest tenth.
9.6 ft
10.4 ft
23.3 ft
154.5 ft
Rounding to the nearest tenth, the length of side k is approximately 23.3 feet. The answer is 23.3 ft.
To solve for the length of side k using the Law of Sines, we can use the formula:
sin(K) / k = sin(J) / j
Given that ∠J measures 40°, ∠K measures 90°, and side j is 15 feet, we can substitute these values into the equation:
sin(90°) / k = sin(40°) / 15
Since sin(90°) = 1, the equation simplifies to:
1 / k = sin(40°) / 15
To find k, we need to isolate it on one side of the equation. We can achieve this by taking the reciprocal of both sides:
k = 15 / sin(40°)
Using a calculator, we can evaluate sin(40°) ≈ 0.6428:
k ≈ 15 / 0.6428 ≈ 23.328.
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Calculate the number of ceiling boards measuring 5cm by 10cm required to cover a square room of 5m
The number of ceiling boards in the room is 5000
Calculating the number of ceiling boardsFrom the question, we have the following parameters that can be used in our computation:
Measurement = 5 cm by 10 cm
Room = square of 5 m dimension
The area of the room is calculated as
Area = (5 m)²
When evaluated, we have
Area = 25 m²
The area of the board is
Area = 5 cm * 10 cm
So, we have
Area = 50 cm²
So, we have
Boards = (25 m²)/(50 cm²)
Evaluate the quotient
Boards = 5000
Hence, the number of boards is 5000
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