In triangle ABC, a = 10.7 cm, b = 9.0cm and ∠B=55°
a) Does the ambiguous case need to be considered? Give mathematical proof and draw both possible scenarios.
b) Determine the measure(s) of ∠A to 1 decimal place.

Answer: The exponent of a linear function is always 1.

Step-by-step explanation:

In mathematics, a linear function is defined as a function that can be represented by a straight line on a graph. The general form of a linear function is y = mx + b, where "m" represents the slope of the line and "b" represents the y-intercept. The exponent of a variable in a linear function is always 1, as there is no exponent applied to the variable.

Hi!

NOTE: When solving absolute value inequalities, > or ≥ means OR, and < and ≤ means AND.

|2x - 3| > 7

Since the absolute value is isolated, we can now solve.

First, remove absolute value signs, then solve for x.

2x - 3 > 7

2x > 10

x > 5

Now, we have to solve again, but this time we flip the inequality sign and switch positive 7 to a negative 7, like so:

2x - 3 < -7

2x < -4

x < -2

Now, as stated above, since it's a greater than symbol it means OR.

x > 5 OR x < -2

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The truth set of the predicate "6d is an integer" in the domain of integers (Z) is the set of all multiples of 1/6.

To find the truth set of the predicate "6d is an integer" in the domain of integers (Z), we need to determine all possible values of d that satisfy the condition.

An integer is defined as any whole number without a fractional or decimal part. In this case, we are looking for values of d that make the expression 6d an integer.

Since 6 multiplied by any integer will yield an integer, we can express the truth set as the set of all multiples of 1/6. This means that any value of d that can be represented as d = (1/6)n, where n is an integer, will satisfy the predicate.

In set-roster notation, the truth set can be written as {..., -2/6, -1/6, 0, 1/6, 2/6, ...}. This represents an infinite set of values that are multiples of 1/6.

To clarify, for example, if we substitute n = -1, we have d = (1/6)(-1) = -1/6, which is an element of the truth set. Similarly, if we substitute n = 2, we have d = (1/6)(2) = 2/6 = 1/3, which is also an element of the truth set. Thus, the truth set of the given predicate in the domain of integers (Z) consists of all multiples of 1/6.

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Answer:

Tony says that he does not have enough information to find the area of this parallelogram. Is he correct? Tony is correct, the base of the parallelogram is not given.

To solve a word problem using a one-step linear inequality, follow these steps: identify the given information, translate it into an inequality, isolate the variable, and write the solution. For example, if a store sells T-shirts for $15 each and you have at most $100 to spend, the number of T-shirts you can buy is represented by the inequality x ≤ 6, which means you can buy at most 6 T-shirts.

To solve a word problem using a one-step linear inequality, follow these steps:

For example, let's say you have the word problem: 'A store sells T-shirts for $15 each. You have at most $100 to spend. Write an inequality to represent the number of T-shirts you can buy.'

Step 1: Identify the given information. The store sells T-shirts for $15 each and you have at most $100 to spend.
Step 2: Translate the given information into an inequality. Let x represent the number of T-shirts. The inequality is 15x ≤ 100, since the total cost of the T-shirts should be at most $100.
Step 3: Isolate the variable. Divide both sides of the inequality by 15 to get x ≤ 6.67. Since you can't buy a fraction of a T-shirt, round down to the nearest whole number. The solution is x ≤ 6.
Step 4: Write the solution. The number of T-shirts you can buy is represented by the inequality x ≤ 6, which means you can buy at most 6 T-shirts.

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Answer:

Step-by-step explanation:

5, 5, 5, 16, 16, 28, 29, 32, 35, 48

Mode: 5, 16

Median: 44/2 = 22

range: 48 - 5 = 43

mean: (5 + 5 + 5 + 16 + 16 + 28 + 29 +32 + 35 + 48)/10 = 219/10 = 21.9

what? there are no images, i have no idea what you are saying

In physics lab, when you measure three quantities of x, y, and z, you can use these mathematical combinations to find meaningful relationships between these quantities:  

In this case, x=2.5 kg, y=0.8 m, and z=4.9 kg/m.

Based on the given quantities' scale, we know that x, y, and z have a relationship where:

z = x/y

Then, the mathematical combinations that might be meaningful are:

- (x/y) - z: This combination gives you the difference between the ratio of x and y, and z. This could be meaningful if you are trying to find the difference between two quantities that have different units.

- (x/z) - y: This combination gives you the difference between the ratio of x and z, and y. This could be meaningful if you are trying to find the difference between two quantities that have different units.

- x - (yz): This combination gives you the difference between the ratio of x and z, and y. This could be meaningful if you are trying to find the difference between two quantities that have different units.

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Answer:the surface area of the pyramid is

16 square feet

Step-by-step explanation:

I found this on a website called quizlet and it showed the answer to this problem

Answer:

A. 20ft

Step-by-step explanation:

Answer:

d. 98.5

Step-by-step explanation:

Triangles:

5 x 4 = 20/2 = 10

Circle:

5² x 3.14 = 78.5

Add both of them 98.5

The depth of the water is changing at a rate of approximately 0.39 m/s when the radius of the top of the water is 10 meters.

To find the rate at which the depth of the water is changing, we can use related rates.

Given:
Height of the cone (h) = 8 meters
Base radius (r) = 26 meters
Rate of filling (dV/dt) = 12 m³/s
Radius of the top of the water (x) = 10 meters

First, we establish the relationship between the height and radius of the cone using similar triangles. The ratio of the height to the radius is constant, so we have h/r = 8/26.

Next, we differentiate both sides of the equation with respect to time (t) to find dh/dt in terms of dx/dt. This gives us (dh/dt)/(dr/dt) = 0.3077.

We can then substitute the given values into the equation: (dh/dt)/(dx/dt) = 0.3077. Rearranging the equation, we find that dx/dt = (dh/dt) / 0.3077.

To find the value of dh/dt, we can substitute the given rate of filling, dV/dt = 12 m³/s, into the equation. Solving for dh/dt, we get dh/dt = 3.693 m/s.

Finally, we substitute the values of dh/dt and 0.3077 into the equation to find dx/dt. This gives us dx/dt ≈ 0.39 m/s.

Therefore, the depth of the water is changing at a rate of approximately 0.39 m/s when the radius of the top of the water is 10 meters.

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Answer:

\(\text {The \ area \ of \ the \ shaded \ segment, A} = 3 \cdot \pi - \dfrac{9}{4} \cdot \sqrt{3}\)

Step-by-step explanation:

The details of the circle that has the shaded segment, and the segment are;

The radius of the circle, r = 3

The angle of the arc of the segment, θ = 120°

The area of a segment, A, is given as follows;

\(A = \dfrac{\theta}{360^{\circ}} \times \pi \times r^2 - \dfrac{1}{2} \times r^2 \times sin(\theta)\)

The area of the given segment is therefore;

\(A = \dfrac{120^{\circ}}{360^{\circ}} \times \pi \times 3^2 - \dfrac{1}{2} \times 3^2 \times sin(120^{\circ}) = \dfrac{12\cdot \pi-9\cdot \sqrt{3} }{4} = 3\cdot \pi - (9/4)\cdot \sqrt{3}\)

The average velocity from t = 2s to t = 4s would be - 48 ft/s.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that an object is thrown upward with initial velocity of 48 feet per second from a high of 120 feet. The height of the object t seconds after it is thrown is given by h(t) = - 16t² + 48t + 120.

Average rate of change of velocity with time is called average velocity. Mathematically -

v{avg.} = Δx/Δt                                                         .... Eq { 1 }

Δx = x(4) - x(2)

Δx = - 16(4)² + 48(4) + 120 - {- 16(2)² + 48(2) + 120}

Δx = - 96

Δt = 4 - 2 = 2

So -

v{avg.} = Δx/Δt = -96/2 = - 48 ft/s

Therefore, the average velocity from t = 2s to t = 4s would be - 48 ft/s.

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The farmer will purchase five bags of kind A and six bags of type B.

Per bag, Type A includes 9 pounds of oats and 3 pounds of maize.

Per bag, Type B includes 2 pounds of oats and 10 pounds of maize.

The farmer is looking for a blend that comprises at least 57 pounds of oats and 75 pounds of maize.

Allow the farmer to mix type A feed = x pounds.

and feed type B = y pounds

(9x + 2y) pounds of oats when blended

Corn amount when combined: (3x + 10y) pounds

Oats equation: 9x + 2y = 57 ———— (1)

Corn equation: 3x + 10y = 75 ————- (2)

Subtract equation (2) from equation (2) by multiplying it by three (1)

3(3x + 10y) - (9x + 2y) = 75×3 - 57

9x + 30y - 9x - 2y = 225 - 57

28y = 168

y = 6 bags

derived from the equation (1)

9x + 2×6 = 57

9x + 12 = 57

9x = 57 - 12

9x = 45

x = 5 bags

Because the business has 15 bags of each sort, each bag costs $4.

As a result, the cost of 5 bags of type A and 6 bags of type B is = (54) + (64)

= 20 + 24

= $44

The farmer intends to buy five bags of kind A and six bags of type B.

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Answer:

h ≈ 29.98

Step-by-step explanation:

diameter = 12m

volume = \(1130m^{3}\)

radius = 6m

The equation to find the height given radius and volume:

\(h = \frac{3(V)}{\pi r^2}\)

Plug in values

Answer:

Given:-

Diameter=12m

Volume=1130m³

Takeπ=3.14

To find:-

Height of cone=?

Step-by-step explanation:

Solution:-

Radius=d/2

= 12/2

=6m

Volume of cone=1/3πr²h

h= 3v/πr²

= 3×1130/3.14× 6²

= 3390/113.04

= 29.98m

hence, the height of cone is 30m.

Answer:

a = -4

Step-by-step explanation:

(a + 2)/2 = - 1

a+2 = -1 * 2

a = - 2 - 2

a = -4

Answer:

-2.5

Step-by-step explanation:

soo your objective is to make a alone

first remove the denominator

a+2 / 2 = -1

a + 2 = -1/2

now minus 2 to  both sides

a = -1/2 - 2

a = -2 1/2

The total cost of each utility eliminating 450 tons of pollution is $180,000.

To calculate the total cost for each utility to eliminate 450 tons of pollution, we need to multiply the cost per ton of pollution elimination by the number of tons each utility needs to eliminate.

For People's Electric, the cost of eliminating one ton of pollution is $400. So, to eliminate 450 tons, the total cost would be 450 tons * $400/ton = $180,000.

For Municipal Energy, the cost of eliminating one ton of pollution is $350. Again, to eliminate 450 tons, the total cost would be 450 tons * $350/ton = $157,500.

Therefore, the total cost for each utility to eliminate 450 tons of pollution is $180,000 for People's Electric and $157,500 for Municipal Energy.

The cost calculation is based on the given information that each utility is provided with 450 pollution permits by the government. These permits allow them to legally produce a ton of pollution. By setting a limit on the number of permits, the government aims to reduce pollution by half. The utilities have the option to trade permits with each other.

In this scenario, People's Electric has a higher cost of eliminating pollution per ton compared to Municipal Energy ($400 vs. $350). It means that People's Electric would find it more expensive to reduce pollution through internal measures like investing in cleaner technology or implementing environmental initiatives. On the other hand, Municipal Energy has a lower cost, indicating that they have relatively more cost-effective methods for pollution reduction.

Given these costs, it is more beneficial for People's Electric to purchase permits from Municipal Energy rather than eliminating the pollution themselves. By purchasing permits, People's Electric can meet the pollution reduction target at a lower cost. Conversely, Municipal Energy can generate additional revenue by selling their permits.

This permit trading mechanism allows for cost efficiency in achieving the government's pollution reduction goal. The total cost for each utility is determined by multiplying the cost per ton of pollution elimination with the number of tons they need to eliminate.

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Answer:

Step-by-step explanation:20

Answer:

is A

Step-by-step explanation:

The statement, in hyperbolic geometry, if three points are not collinear, there is always a circle that passes through them is false.

What is circle?

A circle is a basic geometric shape in mathematics that is defined as a set of points in a plane that are equidistant from a fixed point called the center. The distance between any point on the circle and the center is known as the radius of the circle.

False.

In hyperbolic geometry, if three points are not collinear, there is not always a circle that passes through them. This is in contrast to Euclidean geometry, where three non-collinear points always determine a unique circle.

In hyperbolic geometry, the concept of a circle is different, and the properties of circles are different as well. In fact, in hyperbolic geometry, circles can have infinitely many distinct properties, and not every set of three non-collinear points can be part of a circle.

Therefore, the statement, in hyperbolic geometry, if three points are not collinear, there is always a circle that passes through them is false.

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Answer:

A.To convert counts into relative frequencies, divide the count by the total number of items. In the above table, the first count is for men / Rom-com (count=6), so 6/60 = 0.1. Like the two-way frequency table, the totals in the right column and bottom row are called marginal distributions.

B.The sum of the relative frequency column is 2020, or 1.

The last entry of the cumulative relative frequency column is one, indicating that one hundred percent of the data has been accumulated.

C.(i cant find it)

D.also cant find

E. sorry cant find

F.same with this one

Step-by-step explanation:

Sorry i got the first 2 tho

Answer:

Part A

Find the relative frequencies by rows.

                       Male   Female    Total

      American|| 11     ||    6        ||  17

Non-American|| 9    ||   14        ||  23

________________________________

Part B

Find the relative frequencies by columns.

                        Male    Female

American       || 11      || 6

Not American||   9    || 14

Total               ||  20  || 20

________________________

Part C

Of the male golfers, do the top golfers tend to be American? Why or why not?

Answer: Yes, the top golfers tend to be American because in the charts there are more American men than non-American men.

Part D

Of the female golfers, do the top golfers tend to be American? Why or why not?

Answer: The top golfers of the females don't tend to be American because in the charts there are more non-American women than American women.

Part E

Of the Americans, are the male golfers or the female golfers more likely to be highly ranked?

Answer: The American male golfers are more likely to be highly ranked.

Part F

Of the non-Americans, are the male golfers or the female golfers more likely to be highly ranked?

Answer: Of the non-Americans, the female golfers are more likely to be highly ranked.

Step-by-step explanation:

Hope this helps anyone who needs it. Goodluck on anything else!

Answer: a=-2 is better

Step-by-step explanation:

If two variables are correlated, a change in one must directly produce a change in the other. (False)

Correlation is a statistical measure that indicates the extent to which two or more variables fluctuate together. It is a value between -1 and 1 that represents the strength of the relationship between two variables.

False. If two variables are correlated, a change in one may or may not directly produce a change in the other. Correlation means that there is a relationship between two variables, but it does not necessarily mean that one causes the other. It's possible for two variables to be correlated without any causal relationship between them.

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Answer:

B

Step-by-step explanation:

A compound sentence is a sentence that has at least two independent clauses joined by a comma, semicolon or conjunction. ... An example of a compound sentence is, 'This house is too expensive, and that house is too small.

Hope this helps!!!

hello rhere, the answer to this is B

Answer:

C. Graph C

General Formulas and Concepts:

Algebra II

Step-by-step explanation:

A cubic function would be f(x) = x³. When we graph this, it should look like Graph C.

Answer:

c

Step-by-step explanation:

The expression is evaluated to 1/9. Option D

We need to know that index forms are described as mathematical forms used in the representation of number or variables that are too large or too small in more convenient forms.

Also, other names for these index forms are scientific notation and standard forms.

From the information given, we have that;

\(3^-^\sqrt[3]{8}\)

Now, find the cube root of the exponent with value of 8, we have;

∛8 = 2

Substitute the value, we have;

3⁻²

Express as a fraction, we get;

1/3²

Find the square of the denominator

1/9

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Thus,  the 95% confidence interval for the population variance is (54.95, 1274.12) ounces^2. This means that we are 95% confident that the true variance of the population lies within this interval.

To construct the confidence interval for the population variance of the given sample, we can use the Chi-square distribution.

Since we are given a 95% level of confidence, the critical values for the Chi-square distribution with degrees of freedom (df) equal to n-1 (n=17) and a significance level of 0.05/2 (two-tailed test) are 7.261 and 28.412, respectively.

Using the formula (n-1)s^2/χ^2(df,α/2) and (n-1)s^2/χ^2(df,1-α/2), where s^2 is the sample variance and α is the significance level, we can calculate the lower and upper bounds of the confidence interval. Substituting the given values, we get:

Lower bound: (17-1)×(98.5294)/28.412 = 54.9471
Upper bound: (17-1)×(98.5294)/7.261 = 1274.1194

Therefore, the 95% confidence interval for the population variance is (54.95, 1274.12) ounces^2. This means that we are 95% confident that the true variance of the population lies within this interval.

It is important to note that this interval does not contain any negative values, which is expected for a variance measure. Also, since the sample is assumed to be from a normally distributed population, this assumption should be checked using appropriate tests or techniques.

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The given differential equation is `(27xy + 45y²) + (9x² + 45xy)y' = 0`.We have to solve this differential equation by using integrating factor `u(x, y) = (xy(2x+5y))-1`.The integrating factor `u(x,y)` is given by `u(x,y) = e^∫p(x)dx`, where `p(x)` is the coefficient of y' term.

Let us find `p(x)` for the given differential equation.`p(x) = (9x² + 45xy)/ (27xy + 45y²)`We can simplify this expression by dividing both numerator and denominator by `9xy`.We get `p(x) = (x + 5y)/(3y)`The integrating factor `u(x,y)` is given by `u(x,y) = (xy(2x+5y))-1`.Substitute `p(x)` and `u(x,y)` in the following formula:`y = (1/u(x,y))* ∫[u(x,y)* q(x)] dx + C/u(x,y)`Where `q(x)` is the coefficient of y term, and `C` is the arbitrary constant.To solve the differential equation, we will use the above formula, as follows:`y = [(3y)/(x+5y)]* ∫ [(xy(2x+5y))/y]*dx + C/[(xy(2x+5y))]`We will simplify and solve the above expression, as follows:`y = (3x^2 + 5xy)/ (2xy + 5y^2) + C/(xy(2x+5y))`Simplify the above expression by multiplying `2xy + 5y^2` both numerator and denominator, we get:`y(2xy + 5y^2) = 3x^2 + 5xy + C`This is the general solution of the differential equation.

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