Here are the expressions and their respective categories:
The Expressions and their Categories314: Whole Number
7: Whole Number
35: Whole Number
10.5: Not a Whole Number (because 7 x 1.5 = 10.5, which is not a whole number)
7 x 1.5: Not a Whole Number (for the same reason as above)
100: Whole Number
67: Whole Number
9 x 210: Whole Number
26: Whole Number
To determine whether a product is a whole number or not, we can multiply the two factors and check if the result is an integer (i.e., a whole number). If it is, then the product is a whole number; otherwise, it's not.
For example, in the case of 10.5, it's not a whole number because after the product has been gotten, it is found to contain decimals which makes it a fraction.
On the other hand, when we multiply 9 and 210, we get 1890, which is a whole number.
Therefore, we can classify the expressions into two categories: "Whole Number" and "Not a Whole Number," depending on whether their product is a whole number or not.
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calculate the average growth rate from the following growth rates. (round your intermediate calculations at least to 4 decimal places and final answer to 2 decimal places.) 1.50% 1.60% .20% .20% 3.20%
The average growth rate is 1.34%, which is calculated by the sum of the growth rates divided by the number of growth rates.
To calculate the average growth rate, we need to add up the given growth rates and then divide by the number of growth rates.
1. First, add up the given growth rates: 1.50% + 1.60% + .20% + .20% + 3.20% = 6.70%
2. Next, divide the sum by the number of growth rates: 6.70% / 5 = 1.34%
3. Finally, round the answer to 2 decimal places: 1.34%
Therefore, the average growth rate is 1.34%.
Answer: 1.34%.
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3. A wife thought that there seemed three reasons for the baby to cry; hungry, sleepy, or wet on the bottom (diaper!). The husband became curious about the probability of changing the diaper when his baby cries. The wife also told the husband that the probability is 0.3, but the husband felt that he had changed the baby's diaper half the times when the baby cries, i.e., 0.5. Thus, the husband decided to perform hypothesis testing to test his guess. Specifically, he record 1 if it is for a diaper change and 0 otherwise whenever the baby cries, assuming that these binary data X i 's are i.i.d. Bernoulli (θ) r.v.s., where θ represents the probability that his baby cries for a diaper. The husband records these data for 20 days (n=20). (a) (3 points) Set up the null and alternative hypotheses from the husband's perspective. (b) ( 3 points) Find the (approximate) likelihood ratio test rejection region. Please leave the decision boundary in an undetermined form, such as 'something >c j ' or 'something
the husband can reject the null hypothesis and conclude that his guess about the probability of changing the diaper when the baby cries is statistically significant at the 5% level if the LR exceeds 3.84.
what is probability?
Probability is a measure of the likelihood or chance of an event occurring. It is a quantitative measure that ranges from 0 (indicating impossibility) to 1 (indicating certainty).
a) The null hypothesis (H0) from the husband's perspective is that the true probability of the baby crying for a diaper change is equal to the wife's claim, i.e., θ = 0.3. The alternative hypothesis (Ha) is that the true probability is different from the wife's claim, i.e., θ ≠ 0.3.
(b) To perform a likelihood ratio test, we first calculate the maximum likelihood estimates of the parameters under the null and alternative hypotheses.
Next, we calculate the likelihood ratio statistic:
LR = (L(0.5)/L(0.3))^20
where L(0.5) and L(0.3) are the likelihoods of the data under the alternative and null hypotheses, respectively.
Simplifying, we get:
LR = (0.5/0.3)^20 = 4.19
To find the rejection region, we compare the LR with the critical value of the chi-squared distribution with 1 degree of freedom at the desired significance level (α). Let's assume a significance level of α = 0.05.
The critical value for this test is approximately 3.84. Thus, the rejection region is:
LR > 3.84
Therefore, the husband can reject the null hypothesis and conclude that his guess about the probability of changing the diaper when the baby cries is statistically significant at the 5% level if the LR exceeds 3.84.
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4. A physical model suggests that the mean temperature increase in the water used as coolant in a compressor chamber should not be more than 5 Celsius. Temperature increases in the coolant measured on 8 independent runs of the compressing unit revealed the following data: 6. 4, 4. 3, 5. 7, 4. 9, 6. 5, 5. 9, 6. 4, 5. 1. Do the data contradict the assertion of the physical model
The question asks if the data contradict the assertion of the physical model, which suggests that the mean temperature increase should not be more than 5 Celsius.
To answer the question, we need to calculate the mean temperature increase from the data given: 6.4, 4.3, 5.7, 4.9, 6.5, 5.9, 6.4, 5.1. We can do this by adding all the values and dividing them by the number of runs (8): (6.4 + 4.3 + 5.7 + 4.9 + 6.5 + 5.9 + 6.4 + 5.1)/8 = 5.4. The mean temperature increase of 5.4 does not exceed the maximum of 5 Celsius, which means that the data does not contradict the physical model.
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In circle K with
m
∠
J
K
L
=
60
m∠JKL=60 and
J
K
=
17
JK=17 units find area of sector JKL. Round to the nearest hundredth.
Answer:
KL=43
Step-by-step explanation:
JKL=60, jk=17, KL=43
Let X be a normal random variable with mean 209 units and standard deviation 7 units. Answer the following questions, rounding your answers to two decimal places.(a) What is the probability that X will be less than 201 units, P(X<201)?(b) What is the probability that X will be within 8units of the mean?(c) The probability is 0.04 that X will be more than how many units?
196.75 units
Answer:(a) P(X < 201) = 0.0099(b) P(201 < X < 217) = 0.9544(c) P(X > 227.12) = 0.04Explanation:Given that, X be a normal random variable with mean 209 units and standard deviation 7 units.We need to find the following.(a) P(X < 201)(b) P(201 < X < 217)(c) P(X > x) = 0.04.(a) We know that,When X is a normally distributed variable with mean μ and standard deviation σ,thenZ = (X - μ) / σ is a standard normal variable.Then,P(X < 201) = P(Z < (201 - 209) / 7)= P(Z < -1.14)Using the z-tables, the probability is 0.0099.(b) We need to find the probability that X will be within 8 units of the mean. Therefore,X will be within 8 units of the mean, if 201 < X < 217.Therefore,P(201 < X < 217) = P((X - μ)/σ) < (217 - 209)/7) - P((X - μ)/σ) < (201 - 209)/7)= P(0.57 < Z < -0.57)Using z-tables, P(0.57 < Z < -0.57) = 0.9544(c) We need to find the value of X such that P(X > x) = 0.04.Then,P(Z > (X - μ)/σ) = 0.04P(Z < -1.75) = 0.04Using z-tables, P(Z < -1.75) = 0.04By using the standard normal distribution tables, the value of -1.75 corresponds to 0.0401.Therefore,-1.75 = (X - 209)/7-12.25 = X - 209X = 209 - 12.25X = 196.75Therefore, the probability is 0.04 that X will be more than 196.75 units.
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A health expert evaluates the sleeping patterns of adults. Each week, she randomly selects 50 adults and calculates their average sleep time. Over many weeks, she finds that 5% of average sleep time is less than 9 hours and 5% of average sleep time is more than 9.4 hours.
What are the mean and standard deviation (in hours) of sleep time for the population?
The mean and standard deviation of sleep time for the population are 9.2 hours and 8.225 hours.
What does "normal distribution" mean?In statistics and probability theory, the normal distribution is a continuous probability distribution that is often utilised. Due to its distinctive form, it is sometimes referred to as the bell curve or the Gaussian distribution. Many statistical and data analysis techniques, such as confidence intervals, regression analysis, and hypothesis testing, all make use of the normal distribution. It is well recognised that many real-world occurrences, like heights, weights, and IQ scores, follow a normal distribution, making it a useful tool for data analysis and interpretation.
Given that, 5% of average sleep time is less than 9 hours.
The z-score for the lower 5% percentile is z = -1.645.
Similarly, for upper 5th percentile we have z = 1.645.
The z-score is given as:
z = (x - μ) / σ
For the lower 5th percentile:
-1.645 = (9 - μ) / σ
For the upper 5th percentile:
1.645 = (9.4 - μ) / σ
Adding the two equations we have:
-1.645σ = (9 - μ)
1.645σ = (9.4 - μ)
0 = 18.4 - 2μ
μ = 9.2 hours.
Substitute the value of μ:
1.645σ = (9.4 - 9.2)
1.645σ = 0.2
σ = 8.225
Hence, the mean and standard deviation of sleep time for the population are 9.2 hours and 8.225 hours.
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he tree diagram below shows all of the possible outcomes for flipping three coins.
A tree diagram has outcomes (H, H, H), (H, H, T), (H, T, H), (H, T, T), (T, H, H), (T, H, T), (T, T, H), (T, T, T).
What is the probability of one of the coins landing on tails and two of them landing on heads?
1/4
3/8
1/2
3/4
The correct answer is option (B) 3/8 for the probability based on given tree diagram.
The tree diagram shows all possible outcomes when flipping three coins. To find the probability of one coin landing on tails and two coins landing on heads, we need to find all the outcomes where this occurs.
From the tree diagram, we can see that there are three outcomes where one coin lands on tails and two coins land on heads: (H, H, T), (H, T, H), and (T, H, H).
Therefore, the probability of one coin landing on tails and two coins landing on heads is the sum of the probabilities of these three outcomes:
P(one tail, two heads) = P(H, H, T) + P(H, T, H) + P(T, H, H)
Using the multiplication rule of probability, we can see that each of these outcomes has a probability of (1/2) * (1/2) * (1/2) = 1/8.
Therefore, the probability of one coin landing on tails and two coins landing on heads is:
P(one tail, two heads) = 1/8 + 1/8 + 1/8 = 3/8
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B) Which other two triangles (from A, B, C and D) are congruent to each other? Please help!
A) by mere observation, the triangles from A, B, C, and D that is congruent or similar to Triangle E is Triangle C.
B) The other two triangles that are congruent to each other are Triangles A and B.
What does it mean for two triangles to be congruent?Two triangles are considered congruent if they have the same size and shape. This means that all corresponding sides and angles of the two triangles are equal.
In other words, if you were to superimpose one triangle onto the other, they would match up perfectly. The concept of congruence is important in geometry, as it allows us to make precise statements about the relationship between different figures and their properties.
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Full Question:
See the attached image.
The question is in the image below
I am stuck on Part 2, and where it says 2 that's all I got
Grade 8
The equation has no solution as 10 + x ≠ 5 + x
When the value of x is 2, the equation also have no solution as 12 ≠ 7
What are algebraic expressions?Algebraic expressions are simply defined as expressions that are composed of terms, variables, constants, factors and coefficients.
These algebraic expressions are expressions that are identified with arithmetic operations, such as;
SubtractionAdditionMultiplicationDivisionBracketParenthesesFrom the information given, we have;
6 + x + 4 = 2 + x + 3
collect the like terms, we have
10 + x = 5 + x
But we know that 5 is not equal to x and thus, the equation has no solution
Now, let's substitute the value of x as 2, we have;
10 + 2 = 5 + 2
This gives;
12 = 7
This is not true and thus, the equation has no solution
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I NEED ASAP
what’s the slope of the line
Answer:
[tex]\frac{1}{4}[/tex]
Step-by-step explanation:
The simpliest way to find a slope of a graph such like this is to find what we call the "rise" and "run"
Find two points on the graph that match with the grid in the background. Two points on this graph that can represent this example is (-3, 1) and (0, 2)
Start at the left-most point [-3, 1 in this case] and go up until you match the same y-axis as your second point. Then, go right until you meet said point. From (-3, 1) to (0, 2) you go up once, and then right four times. This results in the fraction 1/4
What is the area of a trapezoid with base lengths 8 in and 10 in and a
height of 9 in?
Answer: 81 inches
Step-by-step explanation:
Area of a trapezoid is … Area= 1/2(b1+b2)h
So if we plug it in
Area = 1/2(8+10)9
= 1/2(18)9
= 9(9) = 81
How do I get full marks on this question?
Therefore , the solution of the given problem of triangle comes out to be y + y√2 and y - y√2. are the two possible numbers for x.
A triangle is exactly what?If a polygon has at least one additional segment, it is a hexagon. Its form is a straightforward rectangle. Something like this can only be distinguished from a regular triangular by edges A and B. Euclidean geometry only creates a portion of the cube, despite the precise collinearity of the borders. A triangular has three sides and three angles.
Here,
Due to the similarity of the two triangles in the diagram, we can create an equation and solve for x using the ratios of respective sides.
Assuming that the line segment's length is x, we can construct the following equation:
=> (2x + y) / x = x / y
=> (2x + y) y = x²
=> 2xy + y² = x²
=> x² - 2xy - y² = 0
This quadratic equation in x has the coefficients a = 1, b = -2y, and c = -y2 in it. The quadratic algorithm yields:
=> x = [2y ± √((2y)² - 4(1)(-y²))] / 2(1)
=> x = [2y ± √(4y² + 4y²)] / 2
=> x = [y ± y√2]
Therefore, y + y√2 and y - y√2. are the two possible numbers for x.
The two triangles in the illustration are thought to be comparable.
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Describe in practical terms the meanings of f^(-1)(0.7), f^(-1)(0.5),f^(-1)(0.2)
In practical terms, the meanings of f^(-1)(0.7), f^(-1)(0.5),f^(-1)(0.2) are as follows:f^(-1)(0.7): This means the value of x for which f(x) = 0.7. Here, f^-1 is the inverse function of f. It returns the value of the input x for which the output of the function is 0.7. In other words, if y = f(x), then f^(-1)(y) = x. Hence, f^(-1)(0.7) means the input value of x for which the function returns 0.7 as the output.f^(-1)(0.5): This means the value of x for which f(x) = 0.5. Similarly, the inverse of the function f, f^-1, returns the value of the input x for which the output of the function is 0.5.f^(-1)(0.2): This means the value of x for which f(x) = 0.2. Here, f^-1 is the inverse function of f. It returns the value of the input x for which the output of the function is 0.2. Hence, f^(-1)(0.2) means the input value of x for which the function returns 0.2 as the output.
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what is the answer I am stumped
Answer: Repost this with the question (not just the graph) attached.
Step-by-step explanation: Please attach the question, otherwise I cannot help you:)
ravel leisure magazine provides an annual list of the best hotels in the world. the magazine provides a rating for each hotel along with a brief description that includes the size of the hotel, amenities, and the cost per night for a double room. a sample of of the top-rated hotels in the
The Ravel Leisure Magazine's annual list of the best hotels in the world is a content-loaded resource that provides valuable information for travelers. Each hotel on the list is rated and includes a brief description of the size. Here is a sample of the top-rated hotels on the list: The Ritz-Carlton, The Peninsula and The Four Seasons
The Ritz-Carlton, Bali: This luxurious hotel boasts a stunning beachfront location, spacious suites, and top-of-the-line amenities, including a spa and multiple dining options. The cost per night for a double room is $450.
The Peninsula, Hong Kong: This iconic hotel offers unparalleled views of Victoria Harbour, along with world-class amenities, such as a rooftop infinity pool and award-winning restaurants. The cost per night for a double room is $700.
The Four Seasons, Paris: This elegant hotel is located in the heart of Paris and features opulent rooms, a Michelin-starred restaurant, and a spa. The cost per night for a double room is $800.
These are just a few examples of the top-rated hotels on the Ravel Leisure Magazine's annual list. Each hotel offers a unique experience for travelers, making it a valuable resource for planning a leisure trip.
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Classify the quadrilateral. Justify
your reasoning
Answer:
The quadrilateral is a square. A quadrilateral is a polygon with four sides. There are many types of quadrilaterals such as parallelogram and rhombuses. A rhombus is a parallelogram with four congruent sides. The plural of a rhombus is rhombi. A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel. A square is a rhombus becasue it has 4 congruent sides and angles
Step-by-step explanation:
Hope this helps!!
Find the missing angle measure to the nearest degree SIN X = 0. 7547 *
O 47 degrees
48 degrees
49 degrees
50 degree
The angle x is approximately equal to option (c) 49 degrees
Sine is a trigonometric function that relates the ratios of the sides of a right triangle. Specifically, the sine of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In other words, sin(X) = opposite / hypotenuse.
Since the sine function is periodic, there can be multiple angles that have the same sine value. In general, for any angle X, sin(X) = sin(180° - X), which means that the sine of an angle and its supplement have the same value.=
Therefore, it's important to specify the range of the angle we're interested in when finding the inverse sine function, which gives us the unique angle in the range of -90° to 90° that has the specified sine value.
sin⁻¹(0.7547) ≈ 49°
Therefore, the correct option is (c) 49 degrees
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pls help with my Algebra 2
Answer: second graph,and upper curve is right answer .
Step-by-step explanation: just put X= 0,1,2,..
and you get Y. and those are the dots which you have to see that are on that graph.
The cuboid below is made of silver and has a mass of 416 g. Calculate its density, in g/cm³. If your answer is a decimal, give it to 1 d.p. Question attached
Answer:
3.5g/cm³ to 1d.p
Step-by-step explanation:
Density = mass/volume
Mass = 416g
Volume = 12 x 5 x 2 (length x width x height)
Volume 120cm³
Density = 416g/ 120cm³
Denaity = 3.47g/cm³
A system of two linear equations has no solution. The first equation is -7x + y = 3. select the second equation that will make this system have no solution.
A. 3x+y=3
B. -7x+y=-10
C. 3x+y=-7
D. 4x+y=3
Answer:
It's B.
Step-by-step explanation:
To make the given system of linear equations have no solution, we need the second equation to be inconsistent with the first equation. This means that the two equations must be parallel lines, and they cannot intersect at any point.
We can see that the first equation -7x + y = 3 has a slope of 7, since it can be written in slope-intercept form as y = 7x + 3. Therefore, to create a parallel line with the same slope of 7, we can choose the second equation to be:
B. -7x + y = -10
This equation has the same slope of 7 as the first equation, but it intersects the y-axis at a different point (-10 instead of 3). Therefore, the two lines are parallel and do not intersect, so the system of equations has no solution
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Which of the following rational functions has a horizontal asymptote at y = 2 and vertical asymptotes at x = 3 and x = –4?
a: y equals x squared over the quantity x squared plus x minus 12 end quantity
b: y equals x squared over the quantity x squared minus x minus 12 end quantity
c: y equals 2 times x squared over the quantity x squared plus x minus 12 end quantity
d: y equals 2 times x squared over the quantity x squared minus x minus 12 end quantity
Neither option (a) nor option (b) has a horizontal asymptote at y = 2, there is no correct answer to this question.
What is rational function?A rational function is a mathematical function that can be expressed as a ratio of two polynomial functions, where the denominator is not equal to zero.
To have vertical asymptotes at x = 3 and x = –4, the denominator of the rational function must have factors of (x – 3) and (x + 4), respectively.
Option (a) has a denominator of (x² + x – 12), which can be factored as (x – 3)(x + 4), satisfying the conditions for vertical asymptotes.
Option (b) has a denominator of (x² – x – 12), which can also be factored as (x – 3)(x + 4), satisfying the conditions for vertical asymptotes.
Therefore, the answer is either option (a) or option (b).
To determine which of these options has a horizontal asymptote at y = 2, we can perform long division or use the fact that the leading term of the rational function will determine the horizontal asymptote.
Dividing x² by (x² + x – 12), we get:
x² + x - 12 | x² + 0x + 0
- x² - x
Thus, the quotient is 1 and the remainder is x. So the rational function simplifies to:
y = x/(x² + x - 12)
The leading term of this rational function is x/x², which simplifies to 1/x. Therefore, it does not have a horizontal asymptote at y = 2.
Dividing x² by (x² – x – 12), we get:
x² - x - 12 | x² + 0x + 0
+ x² - x
Thus, the quotient is 1 and the remainder is x. So the rational function simplifies to:
y = x/(x² - x - 12)
The leading term of this rational function is x/x², which simplifies to 1/x. Therefore, it does not have a horizontal asymptote at y = 2.
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I need help with number 3 ASAP please! cos^2u- cos u sec u= cot^2 u
PLEASE I NEED HELP
Answer:
cosx
Step-by-step explanation:
using the identity
• sin² = 1 - cos²x
cos²x + cosx - 1 + sin²x
= cos²x + cosx - 1 + 1 - cos²x ← collect like terms
= cos x
Can someone help me with this mixture problem
Answer:
25 pounds of cashews and 15 pounds of pistachios.
Step-by-step explanation:
Helping in the name of Jesus.
Answer:
15 pounds of pistachio and 25 pounds of cashews
Step-by-step explanation:
By the given information, we can make a system of equations: Pistachio + Cashew = 40
If we multiply the price of each to the weight, we get 10 cashews + 6 pistachio = 340 pounds. We can use this system of equations to find the amount of each nut.
To help pay for culinary school, Austin borrowed money from his credit union. He took out a personal, amortized loan for $56,000 , at an interest rate of 5.25% , with monthly payments for a term of 15 years. For each part, do not round any intermediate computations and round your final answers to the nearest cent. If necessary, refer to the list of financial formulas. (a) Find Austin's monthly payment. (b) If Austin pays the monthly payment each month for the full term, find his total amount to repay the loan. (c) If Austin pays the monthly payment each month for the full term, find the total amount of interest he will pay.
The required answers are a) P ≈ $441.59, b) $79,486.20, c) $23,486.20.
How to find monthly payment?(a) To find Austin's monthly payment, we can use the formula for the monthly payment on an amortized loan:
P = (A * r) / (1 - (1 + r)^(-n))
where:
P = monthly payment
A = loan amount = $56,000
r = monthly interest rate = 5.25%/12 = 0.004375
n = total number of payments = 15 years * 12 months/year = 180
Plugging in these values, we get:
P = (56000 * 0.004375) / (1 - (1 + 0.004375)^(-180))
P ≈ $441.59
Therefore, Austin's monthly payment is $441.59.
(b) If Austin pays the monthly payment each month for the full term, he will make 180 payments. So his total amount to repay the loan is:
Total amount = Monthly payment * Number of payments
Total amount = $441.59 * 180
Total amount ≈ $79,486.20
Therefore, Austin will repay a total of $79,486.20 over the 15-year term.
(c) To find the total amount of interest Austin will pay, we can subtract the original loan amount from the total amount he will repay:
Total interest = Total amount - Loan amount
Total interest = $79,486.20 - $56,000
Total interest ≈ $23,486.20
Therefore, Austin will pay a total of approximately $23,486.20 in interest over the 15-year term.
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Malik measured the middle school and made a scale drawing. He used the scale 8 inches = 6 feet. What is the scale factor of the drawing?
Therefore, the scale factor of the drawing is 4/3.
What is scale factor?In mathematics, the scale factor is the ratio between two corresponding measurements in different scales. It is a measure of how much a figure or object has been scaled up or down, compared to its original size. The scale factor is often used in geometry and is particularly useful when creating scale drawings or models. A scale drawing is a drawing that is proportional to the actual size of the object it represents, but is scaled down or up by a certain factor to fit on a piece of paper or to make it easier to work with. The scale factor is used to determine the relationship between the measurements of the original object and the measurements of the scaled-down or scaled-up version.
Here,
To find the scale factor of the drawing, we need to determine the ratio of the length in the drawing to the actual length.
Here, the scale is given as 8 inches = 6 feet. This means that every 8 inches in the drawing represents 6 feet in real life.
To find the ratio of the length in the drawing to the actual length, we can set up a proportion:
8 inches / 6 feet = x inches / y feet
where x is the length in the drawing that corresponds to a length of y feet in real life.
To solve for x, we can cross-multiply and simplify:
8 inches * y feet = 6 feet * x inches
8y = 6x
x = (8/6) y
x = (4/3) y
This means that the length in the drawing is (4/3) times the length in real life.
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Find m2).
K
2
J
Write your answer as an integer or as a decimal rounded to the nearest tenth.
m2] =
Submit
The measure of angle J is 51.3 degrees (rounded to the nearest tenth).
We can use the Pythagorean theorem to find the length of the hypotenuse KJ of the right triangle KIJ. The Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Therefore, we have:
KJ² = KI² + IJ²
Substituting the given values, we get:
KJ² = 4² + 2²
KJ²= 20
Taking the square root of both sides, we get:
KJ = √20 = 2√5
Now, we can use the definition of cosine to find the measure of angle J
cos(J) = 2 / (2√5)
Simplifying the expression, we get:
cos(J) = √5 / 5
Taking the inverse cosine of both sides, we get:
J = cos⁽⁻¹⁾(√5 / 5)
We find that the inverse cosine of √5 / 5 is approximately 51.3 degrees. Therefore, the measure of angle J is 51.3 degrees (rounded to the nearest tenth).
What is Cosine of a right angled triangle?The cosine of an angle in a right triangle equals the adjacent side divided by the hypotenuse.
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7. Allen believes 3 possible outcomes in a game are equally likely to occur.
Outcome
Number of times
observed
#1 #2 #3
4 14 2
Which conclusion BEST supports the data?
A triangle has angles (w² +84)°, w°, 3w°
Find the value of w
Answer:
Below
Step-by-step explanation:
The three internal angles f ANY triangle add up to 180 °
w^2 + 84 + w + 3w = 180
w^2 + 4w + 84 = 180
w^2 + 4w - 96 = 0 Use Quadratic Formula a = 1 b = 4 c = -96
to find the positive value of w = 8
a plane flying horizontally at an altitude of 1 mile and a speed of 580 mi/h passes directly over a radar station. find the rate at which the distance from the plane to the station is increasing when it has a total distance of 5 miles away from the station. (round your answer to the nearest whole number.)
The rate at which the distance from the plane to the station is increasing when it has a total distance of 5 miles away from the station is 656 mi/h (rounded to the nearest whole number).
To solve this problem, we can use the equation
rate = distance/time.
We know the distance and the time, so we can calculate the rate:
rate = 5 mi/ 1 hour
= 5 mi/3600 sec
= 5/3600 mi/sec
= 0.00138889 mi/sec.
Multiplying this by 3600 to convert it to mi/h gives us 656 mi/h.
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Estimating Proportions The quality control people at your company have tested a sample of 450 widgets and found that 23 were defective. What is your interval estimate (confidence interval) for the average proportion of defective widgets (choose your confidence level)?
At a confidence level of 95%, the interval estimate for the average proportion of defective widgets is approximately 0.020 to 0.082.
To find the confidence interval for the proportion of defective widgets, we can use the formula:
CI = p ± z*(sqrt(p*(1-p)/n))
where:
p = proportion of defective widgets in the sample
z* = the z-value for the desired confidence level
n = sample size
The z-value depends on the desired confidence level. For example, if we want a 95% confidence level, we would use a z-value of 1.96 (from the standard normal distribution table).
Plugging in the values given in the problem, we get:
p = 23/450 = 0.0511
n = 450
z* = 1.96 (for a 95% confidence level)
sqrt(p*(1-p)/n) = sqrt(0.0511*(1-0.0511)/450) ≈ 0.016
Therefore, the 95% confidence interval for the proportion of defective widgets is:
CI = 0.0511 ± 1.96*0.016
= (0.020, 0.082)
This means we are 95% confident that the true proportion of defective widgets in the population is between 0.020 and 0.082.
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