in a group of 120 students,68 had riddena bus,78 had ridden the LRT,20 had riddenthe bus and the jeep ,19 had ridden the LRT and the jeep and 15 had ridden the bus,the LRT and the jeep.

a.how many had ridden the bus only?​

Answer:

Step-by-step explanation:

sum of angles in a triangle=180º

90+60x+30x=180

90+90x=180

90(1+x)=180

1+x=2

x=1

angle A=30º

Answer:

The height of the squirrel is 31 feet.

Step-by-step explanation:

You need to know your Right Triangle Trigonometry to do this problem.

Rt Triangle trig is all about ratios. Angles and ratios.

In your question, there is a rt triangle. The side measure given, 28 is next to the angle. The math word for "next to" is "adjacent" You know the adjacent side. The squirrel's height is the opposite side. The ratio that puts together adjacent and opposite is tangent.

tan Angle = opposite/adjacent

tan 48° = x/28

multiply both sides by 28

28•tan48° = x



You have to use a calculator that has trig functions. It will have buttons that say "sin", "cos", and "tan"



Enter 28 × tan48° =

It will return 31.0971504152

Your question asks you to round to the nearest whole.

x = 31

The squirrel's height in the tree is 31ft.

Answer: 41,000

Step-by-step explanation:

If the hundreds column 5 or more than it rounds up if it is lower it rounds down

Answer:

4x-2

Step-by-step explanation:

-2x + 3 - (5 - 6x)

-2x+3-5+6x

Collect Like Terms

4x+3-5

Calculate the difference, you should end up with 4x-2

In need of some Science help! If you can please go help me out! :)

Answer:

x = 12, z = 109

Step-by-step explanation:

12x - 73 = 71

12x = 71 + 73 = 144

x = 144/12 = 12

z = 180 - 71 = 109

The government agency as a monopolist will produce and sell internet connections up to the point where the marginal cost is 1/2. The price will be set at 1, given the perfectly elastic demand function.

In the scenario where a government agency has a monopoly in the provision of internet connections and the inverse demand function is given by p = 1, we can analyze the market equilibrium and the implications for pricing and quantity.

The inverse demand function, p = 1, implies that the market demand for internet connections is perfectly elastic, meaning consumers are willing to purchase any quantity of internet connections at a price of 1. As a monopolist, the government agency has control over the supply of internet connections and can set the price to maximize its profits.

To determine the optimal pricing and quantity, the monopolist needs to consider the marginal cost of providing internet connections. In this case, the marginal cost is given as 1/2. The monopolist will aim to maximize its profits by equating marginal cost with marginal revenue.

Since the inverse demand function is p = 1, the revenue received by the monopolist for each unit sold is also 1. Therefore, the marginal revenue is also 1. The monopolist will produce up to the point where marginal cost equals marginal revenue, which in this case is 1/2.

As a result, the monopolist will produce and sell internet connections up to the quantity where the marginal cost is 1/2. The monopolist will set the price at 1 since consumers are willing to pay that price.

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Answer I think it is a

Step-by-step explanation: A

The values of f(x) for the given x - values rounded to 4 decimal places are 0.0078, 0.0078, 0.0020, 0.0020, 0.0019 and 0.0013 respectively

Given the function :

Substitute the given value of x to obtain the corresponding f(x) values :

x = -0.6

f(x) = (tanπ(-0.6))/7(-0.6) = 0.0078358

x = -0.51

f(x) = (tanπ(-0.51))/7(-0.51) = 0.0078350

x = -0.501

f(x) = (tanπ(-0.501))/7(-0.501) = 0.001967

x = -0.5

f(x) = (tanπ(-0.5))/7(-0.5) = 0.001959

x = -0.4999

f(x) = (tanπ(-0.4999))/7(-0.4999) = 0.001958

x = 0.499

f(x) = (tanπ(-0.499))/7(-0.499) = 0.001951

x = -0.49

f(x) = (tanπ(-0.49))/7(-0.49) = 0.00188

x = -0.4

f(x) = (tanπ(-0.4))/7(-0.4) = 0.00125

Therefore, values which complete the table are 0.0078, 0.0078, 0.0020, 0.0020, 0.0019 and 0.0013

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Answer:

160

Step-by-step explanation:

The chance/probability of 10-year-old passenger cars passing an emission test is 80%.

200 10-year-old passenger cars will be tested next week.

How many of the 200 cars are expected to pass the emission test?

If there is an 80% chance of them passing the test then it means that 80% of the cars pass the test at any given time.

80% of 200 = 0.8 × 200 = 160

Hence, 160 (of the 200) cars are expected to pass the test.

Based on the general form of a wave function, the times the frequencies of the sound waves be the same in the interval [0°, 360°) is x = 180°, 210°, 270°, 330°.

Frequency is the number of vibrations of a wave per second.

The period of a wave is the time taken for one complete vibration.

Frequency and Period are inversely related.

Using the general form of a wave function:

where;

From the two wave functions:

y = 2sin2x

b = 2

period = 2π/2

period = π = 180°

Frequency =

y = −sin x

b = 1

Period = 2π/1

Period = 2π = 360°

Therefore, the times the frequencies of the sound waves be the same in the interval [0°, 360°) is x = 180°, 210°, 270°, 330°.

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Answer:

x = 0°, 180°, 210°, 330°

If you were to graph the two functions those would be the intersection points (after converting from radians to degrees)

In order to solve this exercise it is important to know that a Parallelogram is.

A Parallelogram is a Quadrilateral. It is a closed flat shape that has four sides.

By definition, some of the properties of a Parallelogram are:

1. The lengths of its opposite sides are equal.

2. Its opposite sides are parallel.

3. The opposite angles are congruent (which means that they have equal measure).

In this case you have the Parallelogram WXYZ. You can identify that the angle X and the angle Z are opposite. Therefore:

Knowing the measure of the angle X, you can determine that:

The answer is: Option B.

Answer:

The solution is any point in the common part of red and blue

The two lines intersect each other at (4 , 7)

Step-by-step explanation:

∵ y > 1/4 x + 6 ⇒ y = 1/4 x + 6

∵ y > 2x - 1 ⇒ y = 2x - 1

∴ 2x - 1 = 1/4 x + 6

∴ 2x - 1/4 x = 6 + 1

∴ 7/4 x = 7 ⇒ x = 7 ÷ 7/4

∴ x = 4

∴ y = 2(4) - 1 = 7

∴ The two lines intersect each other at (4 , 7)

∴ The solution is any point in the common part of red and blue

False, that is if the number of data observations is even, the median is generally considered to be the average of middle values not the first and last values.

The median is a simple measure of central tendency. To find the median, we arrange the observations in order from smallest to largest value. If there is an odd number of observations, the median is the middle value. If there is an even number of observations, the median is the average of the two middle values.

At least half of the observations are equal to or smaller than the median, and at least half of the measurements are equal to or greater than the median. The median divides the bottom half of observations from the upper half.

Even Number of Observations :

Suppose we have the monthly wages of 4 employees of a company. How would you find the median wage?

wages are 120,240,500,400

we have arranged their wages above from lowest to highest. This ranking will help us to determine the median. Using the method introduced earlier, the median is computed by taking the simple average of the (n/2)ᵗʰ = (4/2)ᵗʰ = 2ⁿᵈ and

(n/2 + 1)ᵗʰ = (2+1)ᵗʰ = 3ʳᵈ observations.

Therefore, the median is 240+500/2

= 370.

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Complete question

True/false

if the number of data observations is even, the median is generally considered to be the average of the first and last values

The percentage of young adults who exercised four or five days a week is 36%

Out of the 25 young adults surveyed, a total of 4 people exercised four days a week and 5 people exercised five days a week. To calculate the percentage of young adults who exercised four or five days a week, we add the number of people who exercised four days a week to the number of people who exercised five days a week, which gives us a total of 9.

We then divide this by the total number of people surveyed (25) and multiply by 100 to get the percentage.

So the percentage of young adults who exercised four or five days a week is

(9/25) x 100 = 36%

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The maximum area is 12.25 square feet

From the question, we have the following parameters that can be used in our computation:

Perimeter = 14 feet

This means that

P = 2(l + w)

So, we have

2(l + w) = 14

Divide by 2

l + w = 7

Make l the subject

l = 7 - w

The area is calculated as

A = lw

So, we have

A = (7 - w)w

Expand

A = 7w - w²

Differentiate and set to 0

7 - 2w = 0

So, we have

w = 3.5

Substitute w = 3.5 in A = (7 - w)w

A = (7 - 3.5) * 3.5

Evaluate

A = 12.25

Hence, the area is 12.25 square feet

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Complete question

There is 14 feet of fencing available to enclose a rectangular region. For what value of area is the area maximum

The probability of the four events are: Event 1: 1/84Event 2: 3/14Event 3: 15/28 Event 4: 5/21

The total number of drinks = 9The number of sweet teas = 3The number of unsweetened teas = 6If you select 3 drinks at random, the following events can take place:

Event 1: All three drinks are sweet teas. The probability of event 1 = (Number of ways in which all three drinks can be sweet teas) / (Number of ways to select 3 drinks)The number of ways in which all three drinks can be sweet teas = 3C3 = 1 (because all three sweet teas are already fixed)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84Therefore, the probability of event 1 = 1/84 = 1/84

Event 2: Exactly two drinks are sweet teas. The probability of event 2 = (Number of ways in which two drinks are sweet teas and one is an unsweetened tea) / (Number of ways to select 3 drinks)The number of ways in which two drinks are sweet teas and one is an unsweetened tea = (3C2 × 6C1) = 18 (because you can choose 2 sweet teas from 3 and 1 unsweetened tea from 6)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84Therefore, the probability of event 2 = 18/84 = 3/14

Event 3: Exactly one drink is a sweet tea. The probability of event 3 = (Number of ways in which one drink is a sweet tea and the other two are unsweetened teas) / (Number of ways to select 3 drinks)The number of ways in which one drink is a sweet tea and the other two are unsweetened teas = (3C1 × 6C2) = 45 (because you can choose 1 sweet tea from 3 and 2 unsweetened teas from 6)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84Therefore, the probability of event 3 = 45/84 = 15/28

Event 4: All three drinks are unsweetened teas. The probability of event 4 = (Number of ways in which all three drinks can be unsweetened teas) / (Number of ways to select 3 drinks)The number of ways in which all three drinks can be unsweetened teas = 6C3 = 20 (because you can choose 3 unsweetened teas from 6)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84 Therefore, the probability of event 4 = 20/84 = 5/21

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\(\begin{cases} v=5i-7j\\\\ w=3i+2j \end{cases}\qquad \begin{cases} < \stackrel{a}{5}~~,~~\stackrel{b}{-7} > \\\\ < \stackrel{a}{3}~~,~~\stackrel{b}{2} > \end{cases}\qquad \qquad \stackrel{magnitude}{\sqrt{a^2 + b^2}} \\\\[-0.35em] ~\dotfill\\\\ ||v||~~ - ~~||w||\implies \sqrt{5^2+(-7)^2}~~ - ~~\sqrt{3^2 + 2^2}\implies \sqrt{74}-\sqrt{13} ~~ \approx ~~ 5\)

Answer:

500

Step-by-step explanation:

Answer:

\(\Huge \boxed{\boxed{ x = 1}}\)

Step-by-step explanation:

Isolate the variable on one side of the equation before trying to solve it. It means that you should only have constants (numbers) on the other side of the equal sign and the variable alone on the one side.

To do this, you can add, subtract, multiply, divide, or use any other operation to both sides of the equation as long as you do the same thing on both sides.

Your final step depends on the equation and how you've simplified it. In general, you want to figure out how you arrived at the final equation by working backwards from it. You'll isolate the variable in the last action you took.

-------------------------------------------------------------------------------------------------------------

Step1: Subtract \(\bold{2x}\) from both sides

Step 2: Subtract 3 from both sides

Step 3: Divide both sides of the equation by 6

So the solution to the equation \(\bold{8x + 3 = 2x + 9}\) is \(\bold{x = 1}\).

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i) The statement P(A Ո B) = P(A) Ո P(B) is false.

ii) The statement P(A Ս B) = P(A) U P(B) is false.

iii) The statement P(A) U P(B) ⊆ P(A U B) is true.

Sets are groups of well-defined objects or components in mathematics. A set is denoted by a capital letter, and the cardinal number of a set is enclosed in a curly bracket to indicate how many members there are in a finite set. For example, set A is a collection of all the natural numbers, such as A = {1,2,3,4,5,6,7,8,…..∞}.

i) Let A ={0,1} and  B ={1,2}

Thus, A Ո B = {1}

P(A Ո B) = {∅, {0}, {1}, {2}, {0,1} , {1,2}, {0,2}}

P(A) = {∅, {0}, {1}, {0,1}}

P(B) =  {∅, {1}, {2},{1,2}}

P(A) Ո P(B) =  {∅, {1}}

∴ P(A Ո B) ≠ P(A) Ո P(B)

So, the given statement is false.

ii) Let A ={0,1} and  B ={1,2}

Thus, A Ս B = {0,1,2}

P(A Ս B) = {∅, {0}, {1}, {2}, {0,1} , {1,2}, {0,2}, {0,1,2}}

P(A) = {∅, {0}, {1}, {0,1}}

P(B) =  {∅, {1}, {2},{1,2}}

P(A) U P(B) =  {∅, {0}, {1}, {2}, {0,1} , {1,2}}

∴ P(A Ս B) ≠ P(A) U P(B)

So, the given statement is false.

iii)

If X⊆Y then P(X)⊆P(Y)                          (1)

If X⊆Z and Y⊆Z then X∪Y⊆Z.            (2)

Necessarily A⊆A∪B,

P(A)⊆P(A∪B);                           (a)

similarly, B⊆A∪B,

P(B)⊆P(A∪B).                           (b)

From (a) and (b), using (2), we conclude:

P(A) ∪ P(B) ⊆ P(A ∪ B).

So, the given statement is true.

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Let the number of hours worked by full timers be x

The difference between hours worked by the full timers and part timers is 4 hours

The hours worked by full timers can be expressed as

Hence, full timers work 4 hours more than the part timers.

The number of full time hours is

Hence, the number of full time hours, x, is 10 hours

Answer:

1.

\( \frac{n^{2} - 1 }{2} \)

2.

\( \sqrt{29} \)

Step-by-step explanation:

Area of triangle=1/2×b×h

=

\( \frac{1}{2} \times (n - 1)(n + 1)\)

\( \frac{( {n}^{2} + n - n - 1) }{2 } \)

\( \frac{ {n}^{2} - 1 }{2} \)

2. Area of triangle=14

\( \frac{ {n}^{2} - 1 }{2} = 14\)

\( {n}^{2} - 1 = 28\)

\( {n}^{2} = 29\)

\(n = \sqrt{29} \)

please rate well and mark BRAINLIEST.

thanks

Answer:

9

Step-by-step explanation:

3x^2 + 3x - 9

Substitute x = 2 into the equation.

3(2)^2 + 3(2) - 9

3(4) + 6 - 9

12 + 6 - 9

18 - 9 =

9

Answer:

• from first principles rule:

\({ \boxed{ \bf{ \frac{ \delta y}{ \delta x} = {}^{lim _{x} } _{h \dashrightarrow0} \: \frac{f(x + h) - f(x)}{h} }}}\)

• f(x) → (csc x)^½

• f(x + h) → {csc (x + h)}^½

\({ \rm{ \frac{ \delta y}{ \delta x} = {}^{lim _{x} } _{h \dashrightarrow0} \: \frac{ \{\csc(x + h) \} {}^{ \frac{1}{2} } - (\csc x ) {}^{ \frac{1}{2} } }{h} }} \\ \\ \hookrightarrow \: { \tt{rationalise : }} \\ \\ = { \rm{{}^{lim _{x} } _{h \dashrightarrow0} \: \frac{ \csc(x + h) - \csc x }{h \{ \{\csc(x + h) \} {}^{ \frac{1}{2} } + ( \csc x) {}^{ \frac{1}{2} } \} } }} \\ \\ = { \rm{{}^{lim _{x} } _{h \dashrightarrow0} \: \frac{1 - (\sin (x + h))( \csc x)}{h \{ \sin(x + h) \} \{ \csc(x + h) \} {}^{ \frac{1}{2} } \{ \csc x \} {}^{ \frac{1}{2} } }}} \\ \\ = { \rm{ = { \rm{{}^{lim _{x} } _{h \dashrightarrow0} \: \frac{1 - ( \sin(x) \cos(h) + \cos(x) \sin(h)) \csc x }{h \{ \sin(x + h) \} \{ \csc(x + h) \} {}^{ \frac{1}{2} } \{ \csc x \} {}^{ \frac{1}{2} } }}} }} \\ \\ = { \rm{ = { \rm{{}^{lim _{x} } _{h \dashrightarrow0} \: \frac{1 - \cos(h) + \cot(x) \sin(h) }{h \{ \sin(x + h) \} \{ \csc(x + h) \} {}^{ \frac{1}{2} } \{ \csc x \} {}^{ \frac{1}{2} } }}} }} \\ \\ { \tt{but : \sin(h) \approx h}} \\ { \tt{ : \cos(h) \approx 1 }} \\ \\ = { \rm{{{}^{lim _{x} } _{h \dashrightarrow0 \: } \: \frac{h \cot(x) }{h \{ \sin(x + h) \} \{ \csc(x + h) \} {}^{ \frac{1}{2} } \{ \csc x \} {}^{ \frac{1}{2} } } }}} \\ \\ { \tt{h \: tends \: to \: 0}} \\ \\ { \boxed{ \rm{ \frac{dy}{dx} = - \frac{1}{2 \sqrt{ \cot(x) \csc(x) } } }}}\)

The dairy farmer should use 1330 pounds of the 70% protein supplement and 570 pounds of the 20% protein ratio to make a 1900-pound high-grade 55% protein ration.

To determine the amounts of the 70% protein supplement and the 20% protein ratio needed to make a 1900-pound high-grade 55% protein ration, we can set up a system of equations.

Let's assume x represents the pounds of the 70% protein supplement and y represents the pounds of the 20% protein ratio.

The total weight equation is given by:

x + y = 1900

The protein content equation is given by:

(0.70x + 0.20y) / 1900 = 0.55

Simplifying the second equation, we get:

0.70x + 0.20y = 0.55 × 1900

0.70x + 0.20y = 1045

Now, we can solve this system of equations to find the values of x and y.

Rearrange the first equation to solve for x:

x = 1900 - y

Substitute this expression for x in the second equation:

0.70(1900 - y) + 0.20y = 1045

1330 - 0.70y + 0.20y = 1045

1330 - 0.50y = 1045

-0.50y = 1045 - 1330

-0.50y = -285

y = -285 / -0.50

y = 570

Now substitute this value of y back into the first equation to find x:

x + 570 = 1900

x = 1900 - 570

x = 1330

Therefore, the dairy farmer should use 1330 pounds of the 70% protein supplement and 570 pounds of the 20% protein ratio to make a 1900-pound high-grade 55% protein ratio.

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The equation shows that the number of toys that must be bought for them to have equal profit will be 212 toys.

From the information, it should be noted that the equation that can be used to represent the information about Jaclyn company will be:

= 2125 + (49.99 × x)

= 2125 + 49.99x

The equation that can be used to represent the information about Richie company will be:

= (39.95 × x)

= 39.95x

Therefore, we will equate both equations:

2125 + 49.99x = 39.95x

49.99x - 39.95x =2125

10.04x = 2125

x = 212

Therefore, the number of toys that must be bought for them to have equal profit will be 212 toys.

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