Only 1/9 enrolled students in a school were absent. There were 4512 students present. How many students are enrolled in the school?

Answer:

33 % is the answer.

Step-by-step explanation:

The value provided is 10 and possible out comes of getting a result is 3 as there are 3 grades namely (A,B and C) are mentioned. When converted to 100s, 100/33 gives 33.33% as the answer, when rounding off gives 33.

Answer: D) 59°

Step-by-step explanation:

As we are already given that the population of gas mileage follows a normal distribution with a mean of 24 miles per gallon and a standard deviation of 6 miles per gallon, i.e., μ = 24 and σ = 6. We need to find the probability that a car will get exactly 22 miles-per-gallon.

We know that the probability density function for the normal distribution is given by: f(x) = (1/σ√(2π))e^(-(x-μ)²/2σ²)Putting the given values in the above formula: f(x) = (1/6√(2π))e^(-(x-24)²/2(6)²).

We need to find f(22), so putting x = 22 in the above formula, we get: f(22) = (1/6√(2π))e^(-(22-24)²/2(6)²)f(22) = (1/6√(2π))e^(-4/36)f(22) = (1/6√(2π))e^(-1/9)f(22) = (1/6√(2π)) × 0.8767 (rounded off to four decimal places) f(22) = 0.0451 (rounded off to four decimal places).

Therefore, the probability that a car will get exactly 22 miles-per-gallon is 0.0451 or 4.51% (rounded off to two decimal places).

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Answer:

The point that lies in the solution set to the following system of inequalities is (1,10).

To check, substitute the values of x and y into each inequality:

ys > x-5

y < x+4

For the point (1,10):

10 > 1-5 is true (10 > -4)

10 < 1+4 is true (10 < 5)

Therefore, (1,10) satisfies both inequalities and lies in the solution set. The other three points do not satisfy at least one of the inequalities, and thus do not lie in the solution set.

Step-by-step explanation:

The impulse response of a system represents its output when the input is an impulse function, typically denoted as \( \delta(t) \) in continuous-time systems or \( \delta[n] \) in discrete-time systems.

Mathematically, it is the response of the system to an idealized instantaneous input signal.

In the given continuous-time system, the input signal is \( x(t) = 12 \sin(5\pi t - \pi/2) \). To determine the impulse response, we need to find the output when the input is an impulse function.

Since an impulse function is defined as \( \delta(t) \), we can rewrite the input as \( x(t) = 12 \sin(5\pi t - \pi/2) \cdot \delta(t) \).

Now, we need to find the output of the system when the input is \( x(t) = 12 \sin(5\pi t - \pi/2) \cdot \delta(t) \). This will give us the impulse response.

However, for the second part of your question, you have provided a difference equation for a discrete-time system. The impulse response for a discrete-time system is obtained in a similar manner, but with the input as an impulse sequence \( \delta[n] \). By substituting the input as \( x[n] = \delta[n] \) into the difference equation, you can solve for the output sequence, which represents the impulse response.

If you have any further specific questions or need more assistance, please let me know.

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Answer:

Part of the solution region includes a negative number of tomato plants in a row; therefore, not all solutions are viable for the given situation.

Step-by-step explanation:

got right on edmentum/plato

Answer:

r = \(\frac{29x}{2\pi }\)

x = \(\frac{2\pi r}{29}\)

Step-by-step explanation:

C = 2\(\pi\)r

29x = 2\(\pi\)r  --------- (i)

divide both sides of (i) by 2\(\pi\)

r =  \(\frac{29x}{2\pi }\)

but when you divide both sides of (i) by 29, you get

x = \(\frac{2\pi r}{29}\)

Answer:

The radius is 6.25 inches

Explanation:

The radius of a circle is half the diameter of the said circle.

If the diameter of a circle is D, then the radius is D/2.

Given a diameter of 12.5 inches

The radius is 12.5/2 = 6.25

The radius is 6.25 inches.

The distance of a = 1 / 2 pi, b = 1 pi, and c = 3 / 2 pi.

The complete movement of an object, regardless of direction, is referred to as distance. The amount of ground a thing travels from its starting point to its destination is also referred to as distance.

Given:

The time, t = π / 2 sec,

Calculate the distance by using the formula given below,

\(Distance = r\times time\)

So, for distance, a = 1 × π / 2 =  π / 2

for distance, b = 1 × π =  π

for distance, c = 1 × 3 π / 2 =  3 π / 2

Therefore, the distance of a = 1 / 2 pi, b = 1 pi, and c = 3 / 2 pi.

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Answer:

I'm not sure and as I guess it may be 5a³.

Answer:

2.1 divided by 12.8=0.172413

Step-by-step explanation:

0 0 0. 1 7 2 4 1 3

1 2 1 8 2 1 0. 0 0 0 0 0 0

     − 0                

       2 1              

     −   0              

       2 1 0            

     −     0            

       2 1 0 0          

     − 1 2 1 8          

         8 8 2 0        

       − 8 5 2 6        

           2 9 4 0      

         − 2 4 3 6      

             5 0 4 0    

           − 4 8 7 2    

               1 6 8 0  

             − 1 2 1 8  

                 4 6 2 0

               − 3 6 5 4

                   9 6 6

Answer:

28 c

bc it is an isosoles triangle

Step-by-step explanation:

Answer:

31°

Step-by-step explanation:

So we can tell one of the triangles is an isosceles because the two dashes on the sides mean the sides are of equal length. We can calculate the top angle of this triangle by:

90 - 28 = 62

Now we can calculate the other two angles, which are the same:

180 - 62 = 118

118 ÷ 2 = 59

So now we know two angles of the big triangle we can calculate angle x:

180 - 59 - 90 =  31

So x = 31°

Hope this helps!

It has been proven that the opposite sides of the parallelogram ABCD are equal

We are told that ABCD is the parallelogram and AC is a diagonal. We observe that the diagonal AC divides parallelogram ABCD into two triangles, namely, ∆ABC and ∆CDA.

Thus, we have o first prove that these triangles are congruent.

In ∆ABC and ∆CDA, w note that BC || AD and AC is a transversal.

Thus, BCA = DAC (Pair of alternate angles)

And AC = CA (reflexive property of congruency)

So, ∆ABC and ∆CDA are congruent (ASA rule).

Therefore, the corresponding parts AB = CD and AD = BC

Hence proved.

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Answer:

Answer option 2

Step-by-step explanation:

When a shape is rotated counterclockwise by 90°, each point of the shape is moved in a circular motion in the counterclockwise direction by 90° around the fixed point of rotation.

As the triangle is rotated about point O, the position of point O does not change (i.e. it is "fixed").

Line segment OA is horizontal in the original figure. When it is rotated 90° counterclockwise, it becomes vertical, where A is above O.

Line segment BA is vertical in the original figure. When it is rotated 90° counterclockwise, it becomes horizontal, where B is to the left of A.

Therefore, the figure that represents the image after the given rotation is the second answer option.

Answer:

Answer option number two.

Answer:

well if a is 12 it means that would become 144/12. simplified to a whole number is 12. so 12-2.4 would = 9.6

Step-by-step explanation:

Answer:

9.6

\(12^{2}\)/12 cancels out

12-2.4=9.6

Answer:

b/w 19 & 55

Step-by-step explanation:

average of four equally weighted 100-point tests,

mark has scored 90, 86, and 85 on the first three.

C average = 70 and 79

90+86+85+x = 4*70 = 280, so x=19

90+86+85+x = 4*79 = 316, so x=55

It will take approximately 14.9 years for a $5,000 deposit in a savings account with a 3.3% interest rate to grow to $10,000.

To calculate the time it takes for the balance to reach $10,000, we need to use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount (initial deposit), r is the interest rate (in decimal form), n is the number of times interest is compounded per year, and t is the number of years.

In this case, we have a $5,000 deposit (P), an interest rate of 3.3% (r = 0.033), and we want to find out how many years (t) it will take for the balance to reach $10,000 (A = $10,000).

Substituting the values into the formula, we get 10,000 = 5,000(1 + 0.033/n)^(n*t).

To solve for t, we can use trial and error or an iterative approach. By trying different values of t, we find that after approximately 14.9 years, the balance will grow to $10,000.

Therefore, it will take approximately 14.9 years for the balance to grow from $5,000 to $10,000 in a savings account with a 3.3% interest rate.

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Answer:

(4,8)

Step-by-step explanation:

The solution is where the two lines intersect.

The graphs intersect at x=4 and y = 8

(4,8)

Answer:    B: (4,8)

Step-by-step explanation:

y = 3x +2           you will go to positive to on the graph and go up 3 and to the right two because it is positive until you can't no more.

y = -6x + 32

you will go to +32 on the graph and then go down six and since there is no number under -6 you will replace it with one so it will look like this -6x/1

Sam travels on the highway for approximately 1.4 hours.

We know that Sam's total travel time is 1.5 hours plus the time he spends on the highway, which we'll call "x" hours. So his total travel time can be represented as:

Total travel time = 1.5 + x

We also know that the total distance he travels is 140 miles. We can use the formula:

distance = rate x time

to set up two equations, one for his travel on city roads and one for his travel on the highway. Let's start with the city roads:

distance = rate x time

distance = 35 mph x 1.5 hours

distance = 52.5 miles

So Sam travels 52.5 miles on city roads, which means he still has to travel:

140 miles - 52.5 miles = 87.5 miles

on the highway. Now we can set up an equation for his travel on the highway:

distance = rate x time

87.5 miles = 65 mph x x hours

Solving for x, we get:

x = 87.5 miles / (65 mph)

x ≈ 1.35 hours

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I have solved the question in general, as the given question is incomplete:

The complete question is:

Sam is driving a distance of 140 miles from his house to visit Melissa. Sam takes city roads , on which can he travel an average of 35 mph for a total of 1.5 hours . Sam also takes the highway , on which he travels an average of 65 mph for a total of x hours . approximately how long does Sam travels on the highway , to the nearest tenth of an hour ?

Answer:

20 bulbs

Step-by-step explanation:e

Answer:

Step-by-step explanation:

\(Area \ of \ triangle = \dfrac{1}{2}bh\\\)

                            \(=\dfrac{1}{2}*8*3\\\\\\= 4*3\\\\\\= 12 \ ft^{2}\)

Area of rectangle = length *width

                             = 8 * 5

                              = 40 ft²

Area of the figure = Area of rectangle + 2* area of the triangle

                         = 40 + 2*12 = 40 + 24

                         = 64 ft²

20 milliliters is equal to 1.352037 tablespoons. To convert any amount of milliliters to tablespoons, simply divide the volume in milliliters by 14.7867648.

A milliliter (mL) is a unit of volume in the metric system. It is equal to one cubic centimeter (cc). One tablespoon (tbsp) is equal to 14.7867648 milliliters (mL). To convert 20mL to tablespoons, we can use the formula:

Tablespoons = milliliters ÷ 14.7867648

To calculate the number of tablespoons, we divide 20 by 14.7867648.

Tablespoons = 20 ÷ 14.7867648

Tablespoons = 1.352037

Therefore, 20 milliliters is equal to 1.352037 tablespoons. To convert any amount of milliliters to tablespoons, simply divide the volume in milliliters by 14.7867648.

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Answer: $2.50

Step-by-step explanation:

     To find the answer, we will divide each previous amount by 2 (finding half) until we reach day four.

Starting with $20 on day one.

$20 / 2 = $10 on day two

$10 / 2 = $5 on day three

$5 / 2 = $2.50 on day four

Answer:

yes

Step-by-step explanation:

Answer:

0.45

Explanation:

Probability of bad motherboard(MB) = 0.30

Probability of bad hard-drive(H) = 0.40

Probability of bad motherboard and hard-drive (MB and H) = 0.15

P(MB U H)= P(MB) + P(H) -P(MB and H)

=0.30+0.40-0.15=0.55

Probability that a 5 year old computer would have no problems of motherboard and hard-drive =

1-P(MB U H) = 1-0.55= 0.45

In this model of sovereign default, equation (9) states that consumption under repayment (CR) is equal to the product of consumption under default (CD) and the ratio of the sum of one plus the interest rate (1+r) and the loan (L). The equation suggests that when the government chooses to repay its debt, consumption is reduced compared to defaulting.

This can be explained by the fact that when the government repays the loan, it needs to allocate a portion of its resources to debt servicing, resulting in a decrease in available funds for consumption. On the other hand, defaulting allows the government to avoid the burden of debt repayment and allocate more resources towards consumption.

In this model, sovereign default is costly. Equation (10) shows that consumption under default (CD) is equal to output (Y) minus a fraction (ƒ) of output (fY). When the government defaults, it incurs a cost equal to the fraction ƒ of its output. This cost arises because defaulting leads to a loss of confidence in the government's ability to honor its obligations, which can result in higher borrowing costs and reduced access to credit in the future.

Additionally, defaulting may lead to economic disruptions, such as capital flight and reduced investment, which can further harm the country's economy and future output. Therefore, while defaulting may provide temporary relief from debt servicing, it comes with significant costs that can have long-term negative consequences for the nation.

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The sides indicated in the triangles are 1) c²=25   2) BC = 45  3) BC = 33

The cosine rule, also known as the law of cosines, is a trigonometric formula that relates the lengths of the sides of a triangle to the cosine of one of its angles.  It can be used to calculate the missing sides of a triangle or to find a missing angle.

The formula is given as a² = b² + c² – 2bc cos x, where a, b, and c are the lengths of the sides of a triangle ABC, and x, y, and z are the angles between the sides of the triangle

1) c² = 29²+13²-2*29*13cos41

c² = 841 + 169 -2*13*19*0.7547

c²= 1010-372.8218

c²= 637.1782

c √637.1782

c =25

2)  bc² =21²+30²-2*21*30cos123

BC = 441+900 +686

BC = √2027

BC = 45

3)

c² = 17²+28²-2*17*28cos91

BC²= 289+784 -+16.6

BC² = 1089.6

BC  = √1089.6

BC = 33

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The law of cosines and the law of sines are used in finding the indicated measurements, which values are presented as follows;

The law of cosines states that, where the lengths of two sides of a triangle and the included angle are b, c, and A, then, the square of the third side can be found using the formula;

1) The law of cosines indicates that we get;

AB = √(29² + 13² - 2×29×13×cos(41°)) ≈ 21

2) The law of cosines indicates that we get;

BC = √(30² + 21² - 2×30×21×cos(123°)) ≈ 45

3) The law of cosines indicates that we get;

BC = √(28² + 17² - 2×28×17×cos(91°)) ≈ 33

4) The law of cosines indicates that we get;

BC = √(14² + 9² - 2×14×9×cos(17°)) ≈ 6

5) The law of cosines indicates that we get;

AB = √(13² + 12² - 2×13×12×cos(134°)) ≈ 23

6) The law of cosines indicates that we get;

AB = √(20² + 22² - 2×20×22×cos(95°)) ≈ 31

7) The law of cosines indicates that we get;

14² = 9² + 6² - 2×9×6×cos(A)

2×9×6×cos(A) = 9² + 6² - 14²

cos(A) = (9² + 6² - 14²)/(2×9×6)

m∠A = arccos((9² + 6² - 14²)/(2×9×6)) ≈ 137°

8) The law of cosines indicates that we get;

BC = √(17² + 22² - 2×17×22×cos(143°)) = √(773 - 748·cos(143°))

The law of sines indicates that we get;

sin(B)/17 = sin(143°)/(√(773 - 748·cos(143°)))

sin(B) = 17 × sin(143°)/(√(773 - 748·cos(143°)))

m∠B = arcsin(17 × sin(143°)/(√(773 - 748·cos(143°)))) ≈ 16°

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Answer:

The expected value is 0

Game is fair

Step-by-step explanation:

Probability = required outcome / Total possible outcomes

Number of red cards = 26

Numbw rof black cards = 26

Total number of cards = 52

If a red card is chosen, amount paid is doubled

If a black card is chosen, no winning or amount is collected.

Net money won or lost on choosing a red card = ($2 - $1) = $1

Net amount won on choosing a black card = $0 - $1 = - $1

P(red) = 26 /52 = 1/2

P(blue) = 26 /52 = 1/2

Expected value (E):

E = x*p(x)

E(X) = (1/2 * 1) + (1/2 * - 1)

E(X) = 1/2 - 1/2 = 0

Hence, since the expected value is 0 ; then the game is fair

The derivative of the function is 27e^9x/√(6+6e^9x).

The derivative of the function y=√(6+6e^9x) can be found using the chain rule. The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function.

First, let's find the derivative of the outer function, which is the square root function. The derivative of √x is 1/(2√x).

Next, let's find the derivative of the inner function, which is 6+6e^9x. The derivative of 6 is 0 and the derivative of 6e^9x is 54e^9x.

Now, we can apply the chain rule and multiply the derivative of the outer function by the derivative of the inner function to get the derivative of the entire function.

The derivative of y=√(6+6e^9x) is (1/(2√(6+6e^9x)))(54e^9x) = 27e^9x/√(6+6e^9x).

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