There are three quarters, five dimes, and twelve pennies in a bag.
Once a coin is drawn from the bag, it is not replaced. If two coins
are drawn at random, determine each probability.

1. P(a quarter and then a penny)

2. P(a nickel and then a dime)

3. P(two pennies)

4. P(a dime and then a quarter)

Answer:

The time taken for $200 invested at 7% annual interest compounded yearly:

[tex]\boxed{\mathrm{10.245 \; {years}}}[/tex]

which roughly works out to
[tex]\boxed{\mathrm{10\;years\;and\;3\;months}}[/tex]

Step-by-step explanation:

The formula for the accrued value of an amount P deposited at i% interest for a time period of t years compounded annually is given by the formula

[tex]\boxed{A = P(1 + r)^t\;\cdots[1]}[/tex]

Here A is the accrued value, P the principal and r = i/100

If you are given A, P and r we can compute t by taking the logarithms on both sides

In Equation [1] we get
[tex]\dfrac{A}{P} = (1 + r)^t \;\cdots[2][/tex]

Taking logs on both sides,
[tex]\log A - \log P = \log((1+r)^t)\\\\\log x^a = a \log x\\\\\\[/tex]

Therefore the right side becomes
[tex]t \log (1+r)[/tex]

Replacing right side of equation [2] with this expression yields

[tex]\log A - \log P = t \log (1+r)\\\\\textrm{Or, }\\\\t =\dfrac{ \log A - \log P}{\log (1 + r)}\\\\[/tex]

This is the general equation for determining how long it will take for the principal P to reach the value A if compounded annually at rate r(in decimal)

Since we are interested in seeing our principal P=200 double to A = 400 at r = 7% = 7/100 = 0.07
and
1 + r = 1 + 0.07 = 1.07

[tex]t = \dfrac{\log 400 - \log 200}{\log 1.07}\\\\[/tex]

[tex]t = \boxed{10.245 \; \textrm{years}}[/tex]

or approximately

[tex]\boxed{\mathrm{10\;years\;and\;3\;months}}[/tex]

Answer:

10.24 years (approx. 10 years 3 months)

Step-by-step explanation:

Most fixed annuities pay annual compound interest.

[tex]\boxed{\begin{minipage}{7 cm}\underline{Annual Compound Interest Formula}\\\\$ A=P\left(1+r\right)^{t}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

Given:

To calculate after how many years the value of the annuity will double, substitute the given values into the formula and solve for t:

[tex]\implies 400=200(1+0.07)^t[/tex]

[tex]\implies 2=(1.07)^t[/tex]

[tex]\implies \ln 2=\ln (1.07)^t[/tex]

[tex]\implies \ln 2=t \ln 1.07[/tex]

[tex]\implies t=\dfrac{\ln 2}{\ln 1.07}[/tex]

[tex]\implies t=10.2447683...\rm years[/tex]

Therefore, the value of the annuity will double after 10.24 years (approximately 10 years 3 months).

Answer: The total bill including tax and gratitude is $35.20

And each one of the 5 friends paid $10 for the bill.

So the total amount paid is $10*5 = $50

If each person paid $10 and the total bill was $35.20

then the change will be $50-$35.20 = $14.80

And since they split the bill equally then each one of them will get back $14.80/5 = $2.96

So each person will get back $2.96

Step-by-step explanation:

The fraction that voted for the gym is calculated as: 5/28.

To find out what fraction voted for the gym, you have to subtract the fractions that voted for the restaurant and the library from 1, which represents the total number of people surveyed.

You can do this by adding the fractions that voted for the restaurant and the library and then subtracting the sum from 1.

(1/4) + (4/7) = (7/28) + (16/28) = (23/28)

so 1 - (23/28) = (5/28)

Therefore, 5/28 of the people surveyed voted for the gym.

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The result is that h(x) = 0 for all x except for x = -2 and x = 2, where h(x) = 6.

f(x)   | -2 | -1 | 0 | 1 | 2

-------|----|----|----|----|----

f(x)   | 5  | -3 | 0 | -3 | 5

g(x)   | -2 | -1 | 0 | 1 | 2

-------|----|----|----|----|----

g(x)   | 6  | 0  | 0 | 0  | 6

h(x)   | -2 | -1 | 0 | 1 | 2

-------|----|----|----|----|----

h(x)   | 6  | 0  | 0 | 0  | 6

h(x) = g(f(x))

For x = -2, h(x) = g(f(-2)) = g(5) = 6

For x = -1, h(x) = g(f(-1)) = g(-3) = 0

For x = 0, h(x) = g(f(0)) = g(0) = 0

For x = 1, h(x) = g(f(1)) = g(-3) = 0

For x = 2, h(x) = g(f(2)) = g(5) = 6

Since f is an odd function and g is an even function, then h(x) = g(f(x)) will be an even function. This means that for any given x, h(x) will always equal 0 or a positive value. For the set of values provided above, the result is that h(x) = 0 for all x except for x = -2 and x = 2, where h(x) = 6.

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Answer:

[tex](0,-2)[/tex]

Step-by-step explanation:

Let the coordinates of the desired point be [tex](a, -a^2-2)[/tex]. Let the distance of this point from [tex](0,1)[/tex] be [tex]f(a)[/tex].

By the distance formula, [tex]f(a)=\sqrt{a^2+(a^2+3)^2}[/tex].

Clearly, [tex]f(a)[/tex] is minimized when the radicand is minimized.

Clearly, the radicand is always increasing, so the minimum is achieved at the left endpoint of the maximal domain of [tex]f(a)[/tex], which is [tex]a=0[/tex].

So, the coordinates are [tex](0,-2)[/tex].

The point on the curve y = -x^2 - 2 that is closest to the point (0, 1) will be (0, -2)

From the information, we want to know the point on the curve y = -x^2 - 2 that is closest to the point (0, 1).

Let the coordinates of the desired point be illustrated as (a - a² - 2).

The distance of the point from (0, 1) is depicted as f(a).

When the radicand is minimized, f(a) is minimized.

In this case, the minimum will be achieved at the left endpoint of the maximal domain of f(a) which is a = 0.

Therefore, the coordinates will be (0, -2).

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Hector has to put the fixed point of the compass on points A and C.

Option (C) is correct.

What is the angle bisector of an angle?

The angle bisector of an angle is a line, ray, or segment that divides an angle into two congruent angles. It is a line that bisects (divides into two equal parts) the angle.

For example, if you have a right angle of 90 degrees, the angle bisector would be a line that divides the angle into two 45-degree angles.

In the given figure, Hector is using a compass and straightedge to construct the bisector of angle CEB.

So he has to put the fixed point of the compass on points A and C.

Hence, Hector has to put the fixed point of the compass on points A and C.

Option (C) is correct.

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The proportion of students that had a grade at least 5 points greater than the 25th percentile is given as follows:

0.7054 = 70.54%.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for this problem are given as follows:

[tex]\mu = 78, \sigma = 36[/tex]

The 25th percentile is X when Z = -0.675, hence:

-0.675 = (X - 78)/36

X - 78 = -0.675 x 36

X = 53.7

The proportion of students with a grade of at least 58.7 is one subtracted by the p-value of Z when X = 58.7, hence:

Z = (58.7 - 78)/36

Z = -0.54

Z = -0.54 has a p-value of 0.2946.

1 - 0.2946 = 0.7054 = 70.54%.

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While the new helmets decrease the probability of injury resulting from a scooter accident, but they also incentivize individuals to ride more recklessly, which could increase the number of scooter collisions and therefore injuries to renters.

The reason for the above statement is based on the concept of risk compensation. When the perceived risk of an activity is reduced, individuals may engage in more risky behavior. For example, if individuals believe that wearing a helmet makes them safer while riding a scooter, they may feel less concerned about the potential consequences of riding recklessly, leading to an increase in the number of accidents. On the other hand, the helmet does decrease the probability of injury in the event of a crash, but an increase in the number of crashes could lead to an overall increase in the number of injuries, offsetting the protective effect of the helmets. Therefore, the net impact of the new helmets on the number of scooter injuries is unclear, and further study is needed to determine their overall effect.

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Answer:

-1

Step-by-step explanation:

Add 2 to both sides of the equation: -7 + 2 = 5x - 2 + 2. This gives you -5 = 5x.

Divide both sides of the equation by 5: -5/5 = 5x/5. This gives you -1 = x.

So the solution to the equation is x = -1.

Alternatively, you can also use inverse operations to solve the equation by isolating x to one side.

Add 2 to both sides of the equation: -7 + 2 = 5x - 2 + 2. This gives you -5 = 5x

Divide both sides of the equation by 5: -5/5 = 5x/5. This gives you -1 = x

So the solution to the equation is x = -1.

Using the empirical rule, 95% of vehicles travel between 60 miles per hour and 80 miles per hour.

Generally, Given that

To find the percent of vehicles whose speeds are between 60 miles per hour and 80 miles per hour

60 = 70-(2*5) ,

this shows that the 58 value is 2 standard deviations below the mean

and

80 = 70 +( 2*5)

This shows that the 74 value is 2 standard deviations above the mean

Using the empirical rule, we know that 95% of data fall within 2 standard deviations from the mean.

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Answer:

110

Step-by-step explanation:

180-70 =110

Answer:

3% = 56

100% = ?

Rule of three:

56 x 100

—————

3

Answer = 1,866.667 ≈ 1.867

Step-by-step explanation:

dont mind the answer below have a great day ______

                                                                                            \|/            

To solve the system of equations using elimination, we can follow these steps:

Multiply the first equation by 4, and the second equation by 2:

20x + 8y = 12

8x - 16y = 24

Add the two equations together:

20x + 8y = 12

8x - 16y = 24

28x - 8y = 36

Solve for x by dividing both sides of the equation by 28:

x = 36/28 = 9/7

Substitute the value of x back into one of the original equations:

5x + 2y = 3

5(9/7) + 2y = 3

45/7 + 2y = 3

2y = -42/7

Solve for y by dividing both sides by 2:

y = -21/7

So the solution of the system of equations is (x,y) = (9/7, -21/7)

It is also worth noting that we could have also multiplied the first equation by -2 and the second equation by 5 and added them together, this will also lead us to the same solution.

It represents the output values, hence the claim that "The notation "f(x)" (f of x) is another means of encoding y-values in a function" is accurate.

An expression that can be used to define and depict the relationship between two or more variables in a data collection is referred to as a function in mathematics.

In conclusion, this means that a function typically illustrates the link between a data set's input values (x-values or domain) and output values (y-values or range), as well as demonstrating how the components in a table are uniquely paired (mapped).

Generally speaking, the output values (y-values or range) of a data set (function) are displayed on the y-coordinate of a graph, and they are typically denoted by either the notation f(x) or y.

The complete question is:

The notation "f(x)" (f of x) is another way of representing y-values in a function. True or False?

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Step-by-step explanation:

(6n+5)°(4n-5)°

use the method of expand

6n(4n-5)+5(4n-5)

24n²-30n+20n-25

24n²- 10n -25

use middle term/ quadratic formula

n=5/4 (1.25) or n= -5/6 (-0.833333)

The velocity after 3 second is -118 ft/sec and the velocity after falling 108 feet is -87.6 ft/sec.

(a)

For the given position function

[tex]s(t)=-16t^2+v_0.t+s_0[/tex]

The ball is dropped from top of the building of height 220 ft, therefore

[tex]s_0=220ft[/tex]

Also, the initial velocity of the ball is −22 feet per second, thus.

[tex]v_0=22\frac{ft}{s}[/tex]

We will differentiate the position function to find the velocity function and then calculate velocity at (a) t=3sec and (b) after failing 108 ft.

Differentiate Position function to acquire the velocity function v(t).

[tex]s(t)=-16t^2+v_0.t+s_0\\\\s'(t)=-32t+v_0[/tex]

Now substitute t=3s,

v(3) = -32(3) + (-22)

v(3)= -118 ft/sec

b)

To find the velocity of ball after falling 108 ft, first we need to find the time at which ball is dropped 108 ft. and then find velocity at that time using velocity function.

let s(t)=108 ft, then using position function, we can write

[tex]s(t)=-16.t^2+v_0t+s_0\\\\108=-16t^2+(-22)t+220\\\\-16t^2-22t+112=0[/tex]

After solving the quadratic equation, we get

t= -3.42 and 2.05

Since time always positive,

therefore t=2.05 sec.

v (2.05) = -32(2.05)-22

v (2.05) = -87.6 ft/sec

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Answer:

8 days

Step-by-step explanation:

I assume you meant $0.15/day late fee (15 cents per day)?  If so, the answer is:

x = # of days late

$2.00 + ($0.15/day)x = $3.20

($0.15/day)x = $3.20 - $2.00 = $1.20

x = $1.20/ ($0.15/day) = 8 days

If the mean time between unscheduled maintenance of LCD displays in a hospital's CT scan facility is 4,000. The probability of unscheduled maintenance in exactly 5,000 hours is:.7135.

Using this formula to the probability of unscheduled maintenance in exactly 5,000 hours

P ( X < 5000) = 1 - e^(-λx)

Where:

e = exponent

-λ = Operating hour

x = Number of hours

Let plug in the formula

P ( X < 5000) = 1 - e^(-(1/4000) × 5000)

P ( X < 5000) = 1- e^-1.25

P ( X < 5000)  = 1 - .2865

P ( X < 5000)  = .7135

Therefore the probability is .7135.

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It would take 17 days to build a similar house with 25 workers.

Inverse proportion is a type of proportionality relationship. If two quantities are inversely proportional then as one quantity increases, the other decreases.  In inverse proportion, the product of the given two quantities is equal to a constant value

One house was built in 85 days by 5 workers;

The relationship will be;

d ∝ 1/n

where

n = number of workers

d = number of days

d = k/n

when d = 5

k = 85

k = 5 x 85

k = 425

when n = 25

d = 425/25

d = 17

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The standard form of a related quadratic function is,

⇒ (x² - 5x - 36)

An algebraic equation with the second degree of the variable is called an Quadratic equation.

We have to given that;

The solutions of a quadratic equation are -4 and 9.

Let the factors of the quadratic equation are,

⇒ (x - (-4)) (x - 9)

⇒ (x + 4) (x - 9)

⇒ (x² - 9x + 4x - 36)

⇒ (x² - 5x - 36)

Thus, The quadratic function is,

⇒ (x² - 5x - 36)

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A coordinate plane is a two-dimensional graph that is used to locate points in a plane using an x-axis and a y-axis.

The slope of the line is (4-(-4))/(7-1) = 8/6 = 4/3.

The y-intercept is -4.

So the equation of the line is y = (4/3)x - 4.

We know that the area of triangle BCD is 15 square units. To find the possible coordinates of point D, we can use the formula for the area of a triangle (A = (1/2)bh). Since we know the area and the base, we can find the height of the triangle and use that to find the possible coordinates of point D.

The equation of the line is y = (4/3)x - 4. We can use this equation to find the y-coordinate of point D.

y = (4/3)x - 4

15 = (1/2)(x)((4/3)x - 4)

By solving the equation above, we can find the possible x coordinate of point D, which are (-2, -4/3) and (12, 4). Therefore, the possible coordinates of point D are (-2, -4/3) and (12, 4).

Note: you can use the same formula to find the y coordinate if you were given the x coordinate of D, but it gives the same solution.

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The quadrilaterals in a and b have the missing values of x as 85° and 57° respectively and can be best described as a scalene quadrilateral.

A scalene quadrilateral is a four-sided polygon in which all four sides have different lengths and all four angles have different measures. This is also known as an asymmetric quadrilateral.

we shall evaluate for the missing values of x as follows:

x + 109° + 96° + 70° = 360° {sum of interior angles of a quadrilateral}

x + 275° = 360°

x = 360° - 275° {subtract 275° from both sides}

x = 85°

x + 85° + 94° + (180° - 58°) = 360° {sum of interior angles of a quadrilateral}

x + 301 = 360°

x = 360° - 303° {subtract 303° from both sides}

x = 57°

Therefore, the missing values of x for quadrilaterals in a and b are 85° and 57° respectively, and can be best described as a scalene quadrilateral.

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Simplify all:

Answer:

Step-by-step explanation:

50% of 200 is =100

Using the Time-Distance Formula, it will take Adbi 2 hours.

We can use the time-distance formula to find how long it will take for Abdi to catch up with Bashir. The time-distance formula is distance = speed x time.

Let t be the time in hours that it takes for Abdi to catch up with Bashir.

We know that the distance Abdi has covered is 4 miles more than Bashir, and the relative speed between the two runners is 8mph - 6mph = 2mph.

So we can write the equation:

4 = (8 - 6) * t

Solving for t, we get t = 4/2 = 2 hours.

So it will take Abdi 2 hours to catch up with Bashir.

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The value of g(2) = -1/4 and the value of g(-2) is π/2 - 3/2

Consider function g(x)

[tex]g(x) = \int\limits^x_1 {f(t)} dt[/tex]

Here, function f be the continuous function defined on interval [-4, 3]

The graph of function f is shown below.

It consists of three line segments and a semicircle centered at the origin, is given above.

For x = 2,

g(2)

[tex]=\int\limits^2_1 {f(t)} dt[/tex]

= -(1/2) × 1 × (1/2)                .........(From the graph of function f)

= -1/4

For x = -2,

g(-2)

[tex]=\int\limits^{-2}_1 {f(t)} dt\\\\=-\int\limits^{1}_{-2} {f(t)} dt[/tex]

= -(3/2 - π/2)                .........(From the graph of function f)

= π/2 - 3/2

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The complete question is:

Let f be the continuous function defined on [-4, 3] whose graph, consisting of three line segments and a semicircle centered at the origin, is given above. Let g be the function given by [tex]g(x) = \int\limits^x_1 {f(t)} dt[/tex]

Frin dthe values of g(2) and g(-2)

The value of the variable , x is 10. 33

It is important to note that in mathematics, complementary angles are defined as angles that sum up to 90 degrees.

Some properties of complementary angles are;

From the information given, we have the angles as;

Equate the angles to 90 degrees

8x - 9 + x + 6 = 90

collect like terms

8x + x = 90 +3

add the like terms, we get;

9x = 93

Make 'x' the subject of formula by dividing both sides by 9

x = 93/9

x = 10. 33

Hence, the value is 10.33

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Elizabeth will practice piano for 252 minutes in one week by solving function f(x)=504x where x = time in multiple of 2years.

What is a function?

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain or range. A function is generally denoted by f(x) where x is the input. The general representation of a function is y = f(x).

There are several types of functions in math. Some important types are:

Injective function or One to one function: When there is mapping for a range for each domain between two sets.

Surjective functions or Onto function: When there is more than one element mapped from domain to range.

Polynomial function: The function which consists of polynomials.

Inverse Functions: The function which can invert another function.

Now,

As given

f(x)=504x where x = time in multiple of 2 years

For 1 year x=1/2

Hence,

y=504*1/2

y=252 minutes

Elizabeth will practice piano for 252 minutes in one week.

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