Solve each right triangle. Round answers to the nearest tenth

The probability that a randomly selected adult does not meet the "US-military"  standards is 16%.

The "IQ-scores" follow a normal distribution having mean = 100 and  standard deviation = 15.

In order to find the probability that a randomly selected adult does not meet US-military enlistment standards (which is an IQ score of less than 85),

We need to find the area under the normal-distribution curve to the left of 85,

Using the z-score formula, we can convert the IQ score of 85 to a standard score (z-score):

⇒ z = (x - μ)/σ,

Where x = IQ score, μ = mean, and σ = standard deviation.

Substituting the values,

We get,

⇒ z = (85 - 100)/15 = -1,

The area to left of -1 in a standard normal distribution table, we get approximately 0.1587 = 15.87% ≈ 16%.

Therefore, the required probability is 16%.

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The statement " a shadow price indicates how much the optimal value of the objective function will increase per unit increase in the right-hand side of a constraint" is true because  shadow prices provide valuable information about the marginal value of resources and constraints in linear programming problems

A shadow price represents the marginal value of a resource or constraint in a linear programming problem. It indicates how much the optimal value of the objective function will increase if the right-hand side of a constraint is increased by one unit, while keeping all other constraints and variables fixed. The shadow price of a constraint is calculated by adding one unit to the right-hand side of the constraint and re-solving the linear programming problem.

The resulting increase in the objective function value is the shadow price of that constraint. Shadow prices are useful in making decisions about resource allocation, pricing, and capacity planning in a variety of industries such as manufacturing, transportation, and energy.

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The only significant variation between the red and black graphs is the scales used for the x and y axes. The two graphs both display the same quadratic function.

x ax2 + bx + c = 0 is a quadratic equation, which is a second-degree polynomial problem in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.

Given :

The quadratic function f(x) = -16x2 + 120x + 10 is depicted in both the red and black graphs, however, they are plotted at various scales. In comparison to the black graph, the red graph has a narrower range on both the x and y axes.

On both graphs, the parabola's vertex, or lowest point on the curve, is situated at x = 3.75 and y = 412.5.

This indicates that the cannonball's maximum height is 412.5 feet, and it does so at a horizontal distance of 3.75 feet from the cannon.

The only significant variation between the red and black graphs is the scales used for the x and y axes. The two graphs both display the same quadratic function.

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Accοrding tο the given infοrmatiοn, a linear relatiοnship between time and pοpulatiοn οccurs when the change in pοpulatiοn οver a given periοd is cοnstant οr prοpοrtiοnal tο the pοpulatiοn size at the beginning οf the periοd.

In a graph, a linear relatiοnship is a pattern in which the pοints οn a scatter plοt tend tο fall alοng a straight line. A linear relatiοnship means that there is a cοnstant rate οf change between twο variables, such that when οne variable increases by a certain amοunt, the οther variable increases οr decreases by a cοnstant amοunt as well.

A situatiοn in which a city's pοpulatiοn grοws at a cοnstant rate οver time wοuld exhibit a linear relatiοnship between time and pοpulatiοn. As time passes, the pοpulatiοn wοuld increase by a fixed amοunt. This is an example οf linear grοwth, and it cοuld be mοdeled by a linear equatiοn such as P = mt + b, where P is the pοpulatiοn, m is the slοpe (the rate οf grοwth), t is time, and b is the initial pοpulatiοn at time t=0.

Similarly, if a pοpulatiοn is decreasing by a fixed percentage each year, then the relatiοnship between time and pοpulatiοn will alsο be linear. As time passes, the pοpulatiοn will decline by a cοnstant percentage οf the previοus year's pοpulatiοn.

In general, a linear relatiοnship between time and pοpulatiοn οccurs when the change in pοpulatiοn οver a given periοd is cοnstant οr prοpοrtiοnal tο the pοpulatiοn size at the beginning οf the periοd.

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Ordering the probabilities from most likely to occur to least likely to occur:

P(football, then volleyball) = 1/49

P(volleyball, then volleyball) = 1/25

P(baseball, then football, then volleyball) = 3/1000

P(baseball, then football, then football) = 5/2944

P(event) = (number of ways the event can occur) / (total number of possible outcomes)

P(volleyball, then volleyball) if the ball is replaced after the first selection:

The probability of selecting a volleyball on the first draw is:

P(volleyball on first draw) = 10/50 = 1/5

Since the ball is replaced after the first selection, the probability of selecting a volleyball on the second draw is also 1/5. Therefore:

P(volleyball, then volleyball) = P(volleyball on first draw) * P(volleyball on second draw) = 1/5 * 1/5 = 1/25

P(baseball, then football, then volleyball) if the balls are replaced after each selection:

The probability of selecting a baseball on the first draw is:

P(baseball on first draw) = 15/50 = 3/10

Since the ball is replaced after each selection, the probability of selecting a football and a volleyball on the second and third draw respectively is also 1/10. Therefore:

P(baseball, then football, then volleyball) = P(baseball on first draw) * P(football on second draw) * P(volleyball on third draw) = 3/10 * 1/10 * 1/10 = 3/1000

P(baseball, then football, then football) if the balls are not replaced after each selection:

The probability of selecting a baseball on the first draw is:

P(baseball on first draw) = 15/50 = 3/10

Since the ball is not replaced after the first selection, the probability of selecting a football on the second draw is:

P(football on second draw) = 5/49

Since the ball is not replaced after the second selection, the probability of selecting a football on the third draw is:

P(football on third draw) = 4/48

Therefore: P(baseball, then football, then football) = P(baseball on first draw) * P(football on second draw) * P(football on third draw) = 3/10 * 5/49 * 4/48 = 5/2944

P(football, then volleyball) if the ball is not replaced after the first selection:

The probability of selecting a football on the first draw is:

P(football on first draw) = 5/50 = 1/10

Since the ball is not replaced after the first selection, the probability of selecting a volleyball on the second draw is:

P(volleyball on second draw) = 10/49

Therefore: P(football, then volleyball) = P(football on first draw) * P(volleyball on second draw) = 1/10 * 10/49 = 1/49

Ordering the probabilities from most likely to occur to least likely to occur:

P(football, then volleyball) = 1/49

P(volleyball, then volleyball) = 1/25

P(baseball, then football, then volleyball) = 3/1000

P(baseball, then football, then football) = 5/2944

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Answer:

tan(sin^-1(-1)) is undefined.

The inverse sine function returns a value between -pi/2 and pi/2, and since sin(-pi/2) = -1, sin^-1(-1) = -pi/2. However, at -pi/2, the tangent function is undefined since it results in a vertical asymptote.

Answer:

Column 1:

[tex]\pi/3[/tex] (given)

[tex]5\pi/4[/tex]

[tex]11\pi/6[/tex]

Column 2:

[tex]\sqrt{3}/2[/tex]

[tex]-\sqrt{2}/2[/tex] (given)

[tex]-1/2[/tex]

Column 3:

all given

Column 4:

[tex]\sqrt{3}[/tex]

[tex]1[/tex]

[tex]-\sqrt{3}/3[/tex] (given)

Step-by-step explanation:

Solved by using unit circle and inverse trig functions

Answer:

area=192.6yards^2

Step-by-step explanation:

9×2.2=19.8÷2= 9.9 for area of one of the triangles

19.2×9=172.8 for area of the rectangle

21.4-19.2=2.2

2.2×9=19.8÷2=9.9

19.8+172.8=192.6

Answer: its a

Step-by-step explanation:

Answer: 210

Step-by-step explanation:

The value of 14x15 is 210.

If an art teacher ordered 26 sets for class and there are 100 markers in each set, then the total number of markers is:

26 x 100 = 2600

Therefore, there would be 2600 markers in 26 sets.

Assuming that the clock is circular, the length of the minute hand is the radius.

The distance that the tip of the minute hand moves in a given time is the length of an arc along the circle.  

If s is the length of arc, then s = rθ, where r is the radius and θ is the measure (in radians) of the central angle formed by the initial position and the final position of the minute hand (measured clockwise).  

(a)

r = 2.5"

20 minutes is 1/3 of an hour.

Since there are 2π radians in 1 rotation of the minute hand (1 hour),

θ = (1/3)(2π) = 2π/3.

So, s = rθ = (2.5")(2π/3) = 10π/3 inches ≈ 5.24"

(b)

A = π x ^ 2 x 2

3.14 x 15 x 15 = 706.5

The area of the watch face is covered by the minute hand in 30 minutes is 706.5

hope you understood this question

Answer:

8 students are in the Environmental Club

Step-by-step explanation:

Answer: 5% of 160 is 8, so there are 8 students in the environmental club.

Step-by-step explanation:

Answer:

To draw a line graph, you need to plot your data on the graph. For example, if you have the data for the number of cars produced in a year, you would plot the number of cars on the Y-axis and the year on the X-axis. Then, you would trace both lines to the point where they intersect and place a dot on the intersection. You would repeat this process for each year and then connect the dots with a line.

Banks and financial institutions offer card loans to people who do not apply for them for a variety of reasons, including to extend credit to those with a high risk of default, to attract potential customers, and to build customer loyalty.

A loan is an agreement between a borrower and a lender in which the borrower receives an amount of money (principal) from the lender, and agrees to repay the lender with interest. The terms of the loan usually specify the repayment period, interest rates, and fees associated with the loan. Examples of loans include mortgages, student loans, car loans, and personal loans.

Card loans are a type of revolving credit that allow people to borrow money from a bank or financial institution and then pay it back, with interest, over time. Banks and financial institutions offer card loans to people who do not apply for them for a variety of reasons.

First, card loans are offered to those who are considered high credit risks, such as those with no prior credit history or a low credit score. By offering card loans, banks and financial institutions can extend credit to these individuals and help them establish a credit history. The loan may come with a higher interest rate than those offered to individuals with good credit, but it can still be beneficial for those who need access to credit.

Second, card loans are often offered as a way to entice potential customers to open accounts with the bank or financial institution. Banks may offer a low introductory interest rate and other incentives, such as rewards or cash back, to encourage new customers to open an account with them.

Finally, banks and financial institutions may offer card loans to help build customer loyalty. When customers use a bank's card for their purchases and pay off their balance each month, they may become more likely to use the bank's other services in the future.

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Complete questions as follows-
Why, do you think, do banks and financial institutions offer card loans to people that do not apply for it?

Answer:

Step-by-step explanation:

Given : O is the centre of the circle with radius r. AB, CD and EF are the diameters of the circle. ∠OAF = ∠OCB = 60°.

To Find : What is the area of the shaded region?​

Solution:

∠OAF =   60°

OA = OF  = Radius

=> ΔOAF is Equilateral Triangle

∠OCB = 60°

OC = OB Radius

Hence ΔOCB  is Equilateral Triangle

∠AOF = 60° , ∠BOC = 60°

=> ∠COF = 180° - 60° - 60° = 60°   as  AC is straight Line

∠DOE  = ∠COF ( vertically opposite angle )

∠DOE  =   60°

ΔODE is also an equilateral Triangle

Each sector has 60 ° angle

Area of shaded region  =  (60/360)πr² - (√3/4) r²

= r² (π/6 - √3/4)

= (r²/6) (π  - 3√3/2)

Area of 3 shaded regions

= 3  (r²/6) (π  - 3√3/2)

= (r²/2) (π  - 3√3/2)

(r²/2) (π  - 3√3/2)  is the correct answer

Answer:

the gradient of the line is 7.

Step-by-step explanation:

To find the gradient of the straight line that passes through the points (3,1) and (8,36), we use the formula:

Gradient = (change in y) / (change in x)

The change in y is the difference between the y-coordinates of the two points, which is:

36 - 1 = 35

The change in x is the difference between the x-coordinates of the two points, which is:

8 - 3 = 5

Therefore, the gradient of the straight line is:

Gradient = (change in y) / (change in x) = 35 / 5 = 7

So the gradient of the line is 7.

We need to find the measure of angle m∠2.

Given that AB∥DE, C is the point of intersection of line AE and line DB, m∠1 = 80°, and m∠2 : m∠3 = 2 : 3.

Step 1: Identify the alternate interior angles. Since AB∥DE, we know that ∠1 and ∠2 are alternate interior angles.

Step 2: Use the property of alternate interior angles. The property of alternate interior angles states that if two parallel lines are cut by a transversal, the alternate interior angles are congruent. Therefore, m∠1 = m∠2.

Step 3: Substitute the given values. We know that m∠1 = 80°, so m∠2 = 80°. Hence, the measure of angle 2 (m∠2) is 80°.

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Answer:

25?

Step-by-step explanation:

sorry if this is wrong

Here are the factored expressions for the given expressions:

Factored expression: 3(2r^2 - rs - s^2)

Factored expression: x(2x + 3)(3x - 4)

Factored expression: 8mn^2(m - n)(m - 3n)

To factor these expressions, we need to find the common factors among the terms in each expression and factor them out.

6r^2 - 3rs - 3s^2

First, we notice that all three terms have a common factor of 3. We can factor it out:

3(2r^2 - rs - s^2)

The quadratic expression inside the parentheses cannot be factored further using integers, so the factored expression is:

3(2r^2 - rs - s^2)

6x^3 - x^2 - 12x

In this expression, we can factor out x:

x(6x^2 - x - 12)

Now, we can factor the quadratic expression inside the parentheses:

x(2x + 3)(3x - 4)

So, the factored expression is:

x(2x + 3)(3x - 4)

8m^3n^2 - 32m^2n^3 + 24mn^4

In this expression, we can factor out 8mn^2:

8mn^2(m^2 - 4mn + 3n^2)

Now, we can factor the quadratic expression inside the parentheses:

8mn^2(m - n)(m - 3n)

So, the factored expression is:

8mn^2(m - n)(m - 3n)

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Answer:

america

Step-by-step explanation:america!!

Answer:

4

Step-by-step explanation:

k(2/9)=4

not 8

:)

Answer: To compute the volume of a prism, we need to know the area of the base and the height of the prism. Assuming that the prism has a rectangular base, the formula for the volume of the prism is:

Volume = Area of Base × Height

Let's assume that the length and width of the rectangular base are both equal to 2d (since we don't have specific dimensions). The height of the prism is also equal to d, as given.

When d = 1:

The area of the base is 2d × 2d = 4 square units

The height is d = 1 unit

Therefore, the volume is:

Volume = Area of Base × Height = 4 × 1 = 4 cubic units

When d = 2:

The area of the base is 2d × 2d = 8 square units

The height is d = 2 units

Therefore, the volume is:

Volume = Area of Base × Height = 8 × 2 = 16 cubic units

When d = 1/2:

The area of the base is 2d × 2d = 1 square unit

The height is d = 1/2 unit

Therefore, the volume is:

Volume = Area of Base × Height = 1 × (1/2) = 1/2 cubic units

So, the volume of the prism is 4 cubic units when d=1, 16 cubic units when d=2, and 1/2 cubic units when d=1/2.

Step-by-step explanation:

The equation y = a√x² is equal to y = 0.1√x² given that y = 0.4 when

x = 4. We also found that when x = 100, y = 10 and when y = 1.4, x = 14.

Given y = a√x² and y = 0.4 when x = 4.

a. To find y in terms of x, we substitute the given values into the equation y = a√x² as follows:

0.4 = a√4²

0.4 = 4a

Dividing both sides by 4, we get:

a = 0.1

Therefore, the equation becomes:

y = 0.1√x²

b. To find y when x = 100, we substitute x = 100 in the equation y = 0.1√x² as follows:

y = 0.1√10000

y = 10

Therefore, when x = 100, y = 10.

c. To find x when y = 1.4, we substitute y = 1.4 in the equation y = 0.1√x² as follows:

1.4 = 0.1√x²

Squaring both sides, we get:

1.96 = 0.01x²

Dividing both sides by 0.01, we get:

x² = 196

Taking the square root of both sides, we get:

x = ±14

Since x represents a distance, it cannot be negative. Therefore, x = 14.

Therefore, when y = 1.4, x = 14.

In conclusion, we found that the equation y = a√x² is equal to y = 0.1√x² given that y = 0.4 when x = 4. We also found that when x = 100, y = 10 and when y = 1.4, x = 14.

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Answer: 1. 3(17-y)

Step-by-step explanation: multiply 3 to 17 and y, which you get (51) and (3). Subtract it to get 48, which is equivalent to 60 - 3y - 9 = 48

if it's wrong, i'm sorry

hope this helps!!

The angle measure directly affects the length of the side opposite that angle in a triangle.

The larger the angle, the longer the side opposite it, and the smaller the angle, the shorter the side opposite it.

It appears that the student question is asking about the relationship between angle measures and the side opposite that angle.

This is a concept from triangle properties, specifically the Angle-Side relationship.
To answer this question, let's follow these steps:
1. Identify the angle in question.
2. Observe the side opposite the angle.
3. Determine the relationship between the angle measure and the side length.
Step 1: Identify the angle in question
The student question mentions an angle measure, but it is not clearly specified.

However, we can still discuss the general relationship between angle measures and the side opposite that angle in a triangle.
Step 2: Observe the side opposite the angle
In a triangle, each angle has a side that is directly opposite to it.

For example, in a triangle ABC, angle A is opposite to side BC, angle B is opposite to side AC, and angle C is opposite to side AB.
Step 3: Determine the relationship between the angle measure and the side length

This relationship is essential in understanding the properties of triangles and can be helpful in solving various geometry problems.
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Answer: { (-1/2)x - 1, -2 ≤ x ≤ 4

Step-by-step explanation:

Let's start with the first line:

The line passes through two points: (-5, 8) and (-2, 2). The hollow circle at (-5, 8) indicates that this point is not included in the graph, while the closed circle at (-2, 2) indicates that this point is included.

We can find the slope of the line using the two points:

slope = (change in y) / (change in x) = (2 - 8) / (-2 - (-5)) = -6 / 3 = -2

Using point-slope form, we can write the equation of the line as:

y - 2 = -2(x - (-2))

Simplifying:

y - 2 = -2x - 4

y = -2x - 2

Next, let's consider the second line:

The line passes through two points: (-2, -2) and (4, -5). The hollow circle at (-2, -2) indicates that this point is not included in the graph, while the closed circle at (4, -5) indicates that this point is included.

We can find the slope of the line using the two points:

slope = (change in y) / (change in x) = (-5 - (-2)) / (4 - (-2)) = -3 / 6 = -1/2

Using point-slope form, we can write the equation of the line as:

y - (-2) = (-1/2)(x - (-2))

Simplifying:

y + 2 = (-1/2)x + 1

y = (-1/2)x - 1

Now we can write the piecewise function:

f(x) = { -2x - 2, -5 ≤ x < -2

{ (-1/2)x - 1, -2 ≤ x ≤ 4

This piecewise function represents the two lines graphed on the given axes, where the first line is defined for x values between -5 and -2 (inclusive on -2 but not on -5), and the second line is defined for x values between -2 and 4 (inclusive on both).

Answer:

1,45

Step-by-step explanation:

[tex] \frac{29 \times 5\%}{100\%} = 1.45[/tex]

Answer:

  y = -1/500x² +2/5x

Step-by-step explanation:

You want the equation for the path of a football that is thrown 200 m downfield and reaches a maximum height of 20 m.

The initial height is not given. The equation is much more easily written if we assume it is zero, or we assume the launch height is the same height at which the ball is caught.

We know the maximum height is reached halfway between the launch point and the final point of interest. Then we're required to write the equation of a parabola that passes through the points (0, 0), (100, 20), and (200, 0).

Since we know the x-intercepts, we can write the equation as ...

  y = ax(x -200)

Then all we have to do is find the value of 'a' so the equation has (100,20) as a solution.

  20 = a(100)(100 -200) = -10000a

  a = -1/500 . . . . . divide by -10000

The equation of the path of the football is ...

  y = (-1/500)(x)(x -200)

  y = -1/500x² +2/5x

__

Additional comment

When x=185, y = -1/500(185)(185 -200) = 15/500(185) = 5.55 . . . meters

The domain is [0, 200]; the range is [0, 20].

To achieve that distance and height, the football would need to be thrown at a speed in excess of 119 miles per hour. For comparison, the fastest baseball pitch ever thrown was 108.1 miles per hour.

The level of the liquid is dropping at a rate of 9/(4π) inches per second when the liquid is 1 inch deep.

We are given that the filter is in the shape of a vertex-down cone, with a height of 6 inches and a diameter of 4 inches at its open (upper) end. We are also given that the liquid drips out the bottom of the filter at a constant rate of 3 cubic inches per second.

Let's let h be the height of the liquid in the cone, and let V be the volume of the liquid in the cone.

The volume of a cone is given by the formula:

V = (1/3)πr²h,

where r is the radius of the cone. Since the diameter of the cone at its open end is 4 inches, the radius is 2 inches. Thus, we have:

V = (1/3)π(2²)h = (4/3)πh.

Now, we need to find dh/dt, the rate at which the height of the liquid is dropping, when the liquid is 1 inch deep. Since the liquid is dripping out of the filter at a constant rate of change 3 cubic inches per second, we have:

dV/dt = -3.

Taking the derivative of the equation for V with respect to t, we get:

dV/dt = (4/3)π dh/dt.

Substituting -3 for dV/dt, and substituting 1 for h, we get:

-3 = (4/3)π dh/dt.

Solving for dh/dt, we get:

dh/dt = (-3)/(4/3)π = -9/(4π) inches per second.

Therefore, the level of the liquid is dropping at a rate of 9/(4π) inches per second when the liquid is 1 inch deep.

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