Angle EFG is 80
Find side of angle x

The only possible value of angle S 5.5°

We can use the law of cosines to find the measure of angle S in triangle STU. The law of cosines states that:

\(c^2 = a^2 + b^2 - 2ab cos(C)\)

where c is the side opposite angle C, and a and b are the other two sides.

In this case, we know the lengths of sides s and u, and the measure of angle U. We can use the law of cosines to solve for the length of side t:

\(t^2 = s^2 + u^2 - 2su cos(U)\\t^2 = 97^2 + 32^2 - 2(97)(32) cos(10^\circ)\\t \approx 95.05 cm\)

Now we can use the law of cosines again to solve for the measure of angle S:

\(cos(S) = (u^2 + t^2 - s^2) / (2ut)\\\\cos(S) =\frac {(32^2 + 95.05^2 - 97^2)} {(2(32)(95.05))}\\\)

cos(S) ≈ 0.9965

S ≈ 5.5° or S ≈ 354.5°

Since we want to find all possible values of angle S, we need to consider the two possible angles: S ≈ 5.5° or S ≈ 354.5°.

However, in a triangle, the sum of the measures of the angles must be 180°, so the only possible value of angle S is:

S ≈ 5.5°

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Answer:

75/96 or in its simplest form, 25/32

Step-by-step explanation:

1. Convert both fractions into improper fractions

2. Use KFC

15/8 ÷ 12/5 = 15/8 × 5/12

Hope this help!

Cutting 6-inch squares from each corner of a 20x12-inch tin sheet creates an open box with dimensions 8x0x6 inches.

By cutting 6-inch squares from each corner of a 20x12-inch tin sheet, you can create an open box.

The box's dimensions will be 8x0x6 inches. The width of 0 inches indicates that the tray has no width, resembling a line segment.

The explanation involves finding the maximum volume by taking the derivative of the volume function and setting it to zero.

The critical points are obtained by solving the resulting cubic equation, which yields two possible values: x = 10 and x = 6.

However, since x cannot exceed half the width or length of the sheet, the smaller value, x = 6 inches, is chosen.

Thus, the tray dimensions are determined, and it can be visualized as an open box with a length of 8 inches, no width, and a height of 6 inches.

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To set up an integral for the area of the surface obtained by rotating the curve x = y - y², we need to use the formula for the surface area of a revolution:

S = ∫2πy√(1 + (dy/dx)²)dx

First, we need to find dy/dx:

dy/dx = 1 - 2y

Next, we need to substitute x = y - y² into the formula:

S = ∫2π(y - y²)√(1 + (1 - 2y)²)dx

Finally, we need to rearrange the equation to get y in terms of x:

y - y² = x

y² - y + x = 0

Using the quadratic formula, we can solve for y:

y = (-1 ± √(1 - 4x))/2

Now we can substitute this back into the formula for S:

S = ∫2π((-1 ± √(1 - 4x))/2)√(1 + (1 - 2((-1 ± √(1 - 4x))/2))²)dx

This is the integral that we need to set up for the area of the surface obtained by rotating the curve x = y - y². We do not need to evaluate the integral, as the question only asks us to set it up.

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Answer:    x= 48  y= 89

Step-by-step explanation:

to find x add all of the angles in the shape then subtract that from 360...

(360- 312)

to find y a line -------- is 180 degrees so just do 180- 91       = 89

hope this helped

make me the brainilest plzzzz

Answer:

The y intercept of Function A is less than the y intercept of Function B.

Step-by-step explanation:

To find the y-intercept of the equation for A set x=0 and solve for y

Y=4(0)+1 therefore the y intercept for equation A is y=1

To find the y intercept for graph B you find the point where the graph intercepts the y axis which in this case it looks like it intercepts(crosses) the y axis at y=2

Therefore equation A y- intercept(y=1) < equation B y-intercept (y=2)

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The given statement "In one scene in 8 1/2, Guido steps onto an elevator that takes on the characteristics of a confession booth" is True.

What is 8 1/2?8 1/2 is an Italian drama movie which was released in the year 1963. It was directed by Federico Fellini. The movie is widely recognized as a highly influential classic of world cinema. The story is about a renowned filmmaker named Guido Anselmi. He is in the middle of making a film but is struggling to come up with a plot for it. In one scene of the movie, Guido steps onto an elevator that takes on the characteristics of a confession booth.MAIN ANS:True, In one scene in 8 1/2, Guido steps onto an elevator that takes on the characteristics of a confession booth.The elevator in 8 1/2 takes on the characteristics of a confession booth as a result of its setting and characters. The elevator setting in the film emphasizes that Guido is in a confessional box and is confessing his sins. It was a unique way of depicting Guido's guilt. The way the elevator shook and rattled, making him feel like he was in a confessional box, was symbolic of how he felt. It was as if he was being taken to a higher power who was listening to him.

The scene emphasizes the religious imagery in the movie. It allows us to gain insight into Guido's psyche and the struggles he was having. The religious imagery in the movie suggests that Guido is trying to connect with a higher power to overcome his guilt. The scene also shows the extent to which he is willing to go to gain clarity.

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Answer:

nCr = 14!/3!11! =364

Step-by-step explanation

The calculated probability of spending $240 or more on a party at the first given venture is 0.62% while for the given second venture it is 1.5%.

Probability refers to chances that are linked to the suitable number of outcomes available concerning the initiation or occurrence of a given event taking place in a certain time at a dignified place.

To find the probability we are using the formula

z = (μ-x)/σ

for the first case the possible probability calculated is

z = (250-240)/16

z = 0.62%

for the second case the possible probability calculated is

z = (260 - 230)/16

z = 1.5%

The calculated probability of spending $240 or more on a party at the first given venture is 0.62% while for the given second venture it is 1.5%.

Therefore, the answer to the given question is simple we should go with the second venture cause it has higher probability in comparison with the first venture.

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Answer:

Step-by-step explanation:

The answer is mentioned above.

Hope it helps.

Answer:

The original price of an item less a discount of 20% is 0.8p where p is the original price

Step-by-step explanation:

Here, we want to write an algebraic expression that represents the original price of an item less a discount of 20%

Let the original price of the item be p

The meaning of the ‘less’ is that we are subtracting 20% of the price from the original price ;

So 20% of the price will be 20/100 * p = 20p/100 = p/5 = 0.2p

So let’s take this away from the original price p

That will be;

p - 0.2p = p(1-0.2) = 0.8p

Answer:

Step-by-step explanation:

Answer:

B, X = 2

Step-by-step explanation:

Since 55 divided by 5 parts is each x + 9, that means 5(x + 9) = 55. Distributing, we get 5x + 45 = 55, and subtracting 45 from each side gets us 5x = 10. Dividing each side by 5 gets us x = 2.

Step-by-step explanation:

(x+9) * 5 = 55

9 * 5 = 45

55-45 = 5

x = 1

Both a frequency table and a frequency distribution are tools used to organize and summarize data, particularly in statistical analysis. They both display the frequency or count of occurrences of each unique value or category in a dataset.

The main difference between a frequency table and a frequency distribution is the type of data they are used to summarize. A frequency table is typically used to display the frequency of occurrence of qualitative or categorical data. It lists the categories or classes of data and the number of observations that fall into each category. For example, a frequency table could display the number of students in a class that received an A, B, C, D, or F grade in a course.

On the other hand, a frequency distribution is typically used to display the frequency of occurrence of quantitative or numerical data. It groups the data into classes or intervals and lists the number of observations that fall into each class or interval. For example, a frequency distribution could display the number of times a coin toss resulted in 0, 1, or 2 heads in a series of 10 tosses.

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A common at-home workout that features high-intensity cardio, and strength-building exercises, and focuses on total body fitness might be a 21-day or 60-day "challenge". Thus, the correct option is C.

Body fitness may be defined as an ability of a person to perform daily physical activities with normal performance, endurance, and strength. This fitness assists the individual in the regulation of disease, fatigue, and stress and reduced inactive behavior.

People who performed high-intensity cardio, and strength-building exercises, in their home and focus on total body fitness must be actively involved in the 21-day or 60-day "challenge".

A 21-day or 60-day "challenge" would be self-selected by an individual in order to maintain their overall physical fitness.

Therefore, the correct option for this question is C.

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In 5 years the demand will be about $19.33 million.

Given:

The formula for compound growth is \(E = B \times (1 + R)^T\), where E is ending value, B is beginning value, R is rate of growth, and T is the amount of time.

Demand for electrical services (B) = $12 million per year

Growth rate (R) = 10%

T= 5 years

Computation:

Substitute all values in the formula , we get

\(E = 12 \times (1 + 0.1)^5\\\\=12(1.1)^5\\\\=12\times1.61051=19.32612\approx19.33\)

In 5 years the demand will be about $19.33 million.

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Answer: it D

Step-by-step explanation: just took the test

You answer would be mate it would be x=66

the slope of the line is 4

Answer:

It equals 0

Step-by-step explanation:

Hope it helps!

The probability of randomly selecting a male is dependent upon the gender distribution of the population from which the selection is made.

For example, if the population is evenly split between males and females, then the probability of randomly selecting a male would be 50%. Alternatively, if the population had more females than males, then the probability of selecting a male would be lower than 50%.

In general, the probability of randomly selecting a male is determined by the ratio of males to females in the population. For example, if there were twice as many females as males, then the probability of randomly selecting a male would be 33.3%. Similarly, if there were four times as many females as males, then the probability of randomly selecting a male would be 25%.

These probabilities can also be applied to specific populations. For example, the United States Census Bureau estimates that there are 101.8 males for every 100 females in the US population. Therefore, the probability of randomly selecting a male from the US population is approximately 50.9%.

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"The mean will be higher than the median in any distribution that" ;

has a positively skewed distribution

A positively skewed distribution is one in which the majority of data values are clustered towards the lower end of the range, while the rest of the values are spread out towards the higher end of the range. As a result, the mean (the average of all the data values) will be higher than the median (the middle value of the data set).

This is because the mean is affected by the higher values in the distribution, while the median is not.

Positively skewed distributions are common in real-world data sets and are often seen in income distributions, stock market returns, and other economic data.

For example, a distribution of incomes may have a few very high earners pushing up the mean, while the majority of people make much lower amounts, resulting in a median that is lower than the mean.

Similarly, stock market returns may have a few very large returns that pull the mean up, while the majority of returns are much lower, resulting in a median that is lower than the mean.

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The lengths of the piece she should cut is = 3  2/3

acc to our question-

hence,The lengths of the piece she should cut is = 3  2/3

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For number 22:

7y=8x-14 ; y=6

Plugging in y, we get:

7*6 = 8x - 14

42 = 8x-14

56 = 8x

x = 7

Comparing answers, x is, indeed 7.

Michael's opportunity cost of a sculpture is 2 paintings per sculpture.

According to the table, Michael can produce either 3 sculptures or 6 paintings in a day. Therefore, the opportunity cost of producing one sculpture for Michael is 2 paintings, as he could have produced 2 additional paintings instead of the sculpture.

Opportunity cost represents the trade-off between two options and helps decision makers understand the benefits and drawbacks of different choices. In this case, by choosing to produce a sculpture, Michael is forgoing the opportunity to produce 2 paintings.

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In order to display the distribution of grades (a, b, c, d, f) in a course, it would be correct to use a bar chart.

To create a bar chart to display the distribution of grades in a course, you would first need to gather the data on the number of students who received each grade. Once you have gathered this data, you can use a computer software tool or graph paper and a pencil to create the bar chart.

When creating the chart, you would label the x-axis with the different grades (a, b, c, d, f) and the y-axis with the number of students. Then, you would draw a bar for each grade, with the height of the bar representing the number of students who received that grade. You can also add a legend to the chart to provide more information about the data, such as the percentage of students who received each grade.

Thus, a bar chart would be the best to use for dispaying the distribution of grades.

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Answer:

c

Step-by-step explanation:

I believe its c I've done this last semester

The distance is the same that was covered.

Distance is speed multiplied by time.

Mr O takes 30 minutes and Mr Gordon takes 1 hour.

So the speed of Mr O is given by:

Convert the speed in meter per second.

The speed of mr G is:

So the difference between the speeds is:

So Mr O is 2.9167 m/s faster than Mr Gordon.

Answer:

you have to answer the question and then solve the question