Type the correct answer in each box. If necessary, use / for the fraction bars,
Write the function for the parabola shown with its directrix in the graph.
f(x) =
4
3
2
→
&
تنا
2 3
(x-
y = -2.25

Digoxin has a half-life of 35 hours, so it takes 70 hours for the toxic plasma concentration to decline to a therapeutic plasma concentration of 2ng/ML.

Digoxin has a half-life of 35 hours, which means it takes 35 hours for the quantity of digoxin in the body to be decreased by half. The dangerous plasma concentration of 8ng/ML must be decreased to a therapeutic plasma concentration of 2ng/ML in this circumstance.

To calculate how long this will take, we need to use the formula:

Time = (Toxic Concentration - Therapeutic Concentration) / (0.5 x Half-Life)

Time = (8ng/ML - 2ng/ML) / (0.5 x 35hrs)

Time = 6ng/ML / (17.5hrs)

Time = 0.342hrs

Time = 70hrs

As a result, the dangerous plasma concentration of 8ng/ML will take 70 hours to decrease to a therapeutic plasma concentration of 2ng/ML.

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On the basis of x-value at x = 0 function is left continuous  and at x = 2 function is continuous from left and right both.

Function 'f' is continuous from the right, or from the left, or neither:

x = 0 (smaller value )

[tex]\lim_{x \to 0-} f(x)[/tex]

= [tex]\lim_{x \to 0-}[/tex] ( 1 + x² )

= 1+ 0

= 1

[tex]\lim_{x \to 0+} f(x)[/tex]

= [tex]\lim_{x \to 0+}[/tex] ( 2 - x)

= 2 - 0

= 2

[tex]\lim_{x \to 0} f(x)[/tex]

= f(0)

= 1 + 0²

= 1

[tex]\lim_{x \to 0-} f(x)[/tex] = f(0)

It is left continuous.

x = 2 (larger value )

[tex]\lim_{x \to 2-} f(x)[/tex]

= [tex]\lim_{x \to 2-}[/tex] ( 2 - x )

= 2 - 2

= 0

[tex]\lim_{x \to 2+} f(x)[/tex]

= [tex]\lim_{x \to 2+}[/tex] ( x - 2)²

= ( 2- 2)²

= 0

[tex]\lim_{x \to 2} f(x)[/tex]

= f(2)

= 2 - 2

= 0

[tex]\lim_{x \to 2-} f(x) = \lim_{x \to 2+} f(x)[/tex] = f(2)

It is continuous from both right and left.

Therefore, the function is continuous from left at x= 1 and x = 2 it is continuous from both left and right side.            

The above question is incomplete ,the complete question is:

Find the x-value at which f is discontinuous and determine whether f is continuous from the right, or from the left, or neither.

f(x) = 1 + x² if x ≤ 0

        2 − x if 0 < x ≤ 2

        (x − 2)² if x > 2

x = (smaller value)

continuous from the right, or continuous from the left, or neither

x = (larger value)

continuous from the right, or continuous from the left, or neither.

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On using the formula for compound interest the amount of time it will take until the account of Gracie has a balance of $0 is 4 years.

What is Compound Interest?

The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest. Compound interest is commonly abbreviated C.I. in mathematics.

The initial deposit made by Gracie is P = $30,000

The rate at which the interest is earned r = 3.1% = 3.1/100 = 0.031

The withdrawal amount is W = $150

The number of times interest is compounded n = 52 weeks

The formula for compound interest becomes -

P = W[1 - {1 + (r/n)}^(-nt)] / (r/n)

Substitute the values into the equation -

30000 = 150[1 - {1 + (0.031/52)}^(-52)t] / (0.031/52)

Divide both sides with 150 and simplify -

200 = [1 - ({1 + 0.00059}^(-52)t)]/0.00059

200 = [1 - (1.00059)^(-52)t)]/0.00059

Multiply both sides with 0.00059 -

0.118 = 1 - (1.00059)^(-52)t

(1.00059)^(-52)t = 1 - 0.118

(1.00059)^(-52)t = 0.882

Using one to one property, and power property -

-52t log 1.00059 = log 0.882

t = (log 0.882/log 1.00059) / -52

t = (-0.0545/0.000256) / -52

t = -212.890625/ -52

t = 4.09 ≈ 4

Therefore, the time value is obtained as 4 years.

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Answer:

Step-by-step explanation:

21.7 IS ALSO EQUAL TO 50% . SO IT WOULD BE =20

Answer:

10.16 lb

Step-by-step explanation:

This is a classic example of a problem that can be solved using dimensional analysis. To find the weight of a single shock absorber or brake pad set, you need to divide the total weight by the number of items in the box.

Weight of a single shock absorber = Total weight of shock absorbers / Number of shock absorbers in the box

= 101.6 lb / 8

= 12.7 lb

Weight of a single brake pad set = Total weight of brake pad sets / Number of brake pad sets in the box

= 101.6 lb / 10

= 10.16 lb

Therefore, a single shock absorber weighs 12.7 lb and a single brake pad set weighs 10.16 lb.

An equation representing the number of points received by the winning team on one day of the competition is P = winning team's points on one day.

Here is an equation to represent the number of points received by the winning team on one day of the competition:

Let's call the number of points received by the winning team on one day of the competition "P".

Then, the equation to represent this would be:

P = winning team's points on one day of the competition

Note: This equation is only a representation, and the actual calculation of the winning team's points would depend on various factors such as the rules of the competition, the performance of the players, etc.

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Answer: 55+ (8* M)

Step-by-step explanation: I think that's the answer

Answer: Expanding the expression:

(2x * 2^+3) * (4x + 5) - 8x * (x^2^-2)

Start with the first set of parentheses:

2x * 2^+3 = 2x * 8 = 16x

Next, the second set of parentheses:

16x * (4x + 5) = 16x * 4x + 16x * 5 = 64x^2 + 80x

Finally, the third set:

-8x * (x^2^-2) = -8x * x^2^-2 = -8x * (1/x^2) = -8/x

So the final expanded form is:

64x^2 + 72x - 8/x

Step-by-step explanation:

The interquartile range of the following data set 4, 6, 10, 13, 18, 28, 34, 46, 50, 58 is 36.

What is interquartile range?

The difference between the third and the first quartile is defined by the interquartile range. The partitioned values known as quartiles divide the entire series into four equally sized segments. There are so three quartiles. The first quartile, also known as the lower quartile, is marked by Q1, the second quartile by Q2, and the third quartile, sometimes known as the upper quartile, is denoted by Q3. The lower quartile less the upper quartile equals the interquartile range.

The data set given is - 4, 6, 10, 13, 18, 28, 34, 46, 50, 58

Divide the data set into two parts -

D1 = 4, 6, 10, 13, 18

D2 = 28, 34, 46, 50, 58

The two middle value for data set is 18 and 28.

The median of D1 and D2 is -

Median = (18 + 28) / 2

Median = 46 / 2

Median = 23

The middle value for D1 is Q1 = 10 and for D2 is Q3 = 46.

The interquartile range is given as -

Q3 - Q1

46 - 10

36

Therefore, the interquartile range is 36.

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Let the random variables x and y have joint pdf as follows: f(x,y) = 1/5(11x^2 + 4y^2) so Cov(x,y) (round off to third decimal place) is 0.241.

The covariance formula in statistics is used to evaluate the relationship between two variables. In essence, it serves as a gauge for the variation between two variables. Covariance is calculated by multiplying the units of the two variables, and it is expressed in units. Any positive or negative value might be the variance.

E[(X−EX)(Y−EY)]

=E[XY−X(EY)−(EX)Y+(EX)(EY)]

=E[XY]−(EX)(EY)−(EX)(EY)+(EX)(EY)

=E[XY]−(EX)(EY).

E(Y) = ∫ 1/x dx = ∫ 11/5 = ln 11/5 = 0.788

E(XY) = E[X 1/X]= 1

It is feasible to get the correlation coefficient formula from the covariance using the aforementioned formula, and vice versa. Units of covariance are calculated by multiplying the units of the two provided variables.

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The linear speed of the bicycle is 20891.59 inches / min

The bike moving in 19.78 mph

As per the given data:

A bicycle with 20-in.-diameter wheels

Determine the speed that needs to be determined either angular or linear. Determine the given speed and radius.

Determining the linear speed is the task at hand. The indicated angular speed is 190 rpm.

To find the linear speed when the angular speed and the radius of the circular object are given, k revolutions per minute [tex]$ =\frac{k \text { revolutions }}{1 \text { minute }} \times \frac{2 \pi}{1 \text { revolution }} \\[/tex]

[tex]$=\frac{2 \pi k}{\text { minute }}[/tex]

For every cycle of the 7-inch sprocket, the 4-inch goes around

[tex]$\frac{7}{4}$[/tex] = 1.75 times.

Therefore 190 × 1.75+ π × 20 = 20891.59 inches / min

Therefore the linear speed of the bicycle is 20891.59 inches / min

Now, determine how fast the bike is moving in mph.

[tex]$\frac{20891.59}{12} \times \frac{60}{5280}$[/tex]

= 19.78 mph

Bike moving in 19.78 mph.

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A bicycle with 20-in.-diameter wheels has its gears set so that the chain has a 7-in. radius on the front sprocket and 4-in. radius on the rear sprocket. the cyclist pedals at 190 rpm.

Find the linear speed of the bicycle (correct to at least two decimal places) in/min

How fast is the bike moving in mph (to two decimal places)?

The corresponding sample space is S = {x|150 ≤ x ≤ 150}.

An experiment that records the number of bushels (and fractions of bushels) of corn produced in an acre.

The yield is assumed to be between 150 and 250 bushels.

A sample space is a collection of probable outcomes from a random event. The letter "S" is used to denote the sample space. Events are the subset of possible experiment results.

Depending on the experiment, a sample area could contain a variety of results. Discrete or finite sample spaces are those that have a finite number of outcomes.

Then the sample space should be

S = {x|150 ≤ x ≤ 150}

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The complete question is:

Consider an experiment that records the number of bushels (and fractions of bushels) of corn produced in an acre. The yield is assumed to be between 150 and 250 bushels.

Determine the corresponding sample space.

Tomando cocientes veremos que:

a) La probabilidad es 0.84

b) En este caso es 0.16

Primero queremos encontrar la probabilidad de que una bolsa tenga el peso correcto, la probabilidad esta dada por el cociente entre el numero de bolsas con el peso correcto y el numero total de bolsas analizadas, entonces tendremos:

P  = 2100/2500 = 0.84

b) Ahora lo mismo, pero con una bolsa de peso menor o mayor, tenemos:

125 que pesan mas

275 que pesan menos

Por un total de 125 + 275 = 400

Entonces la probabilidad es:

P = 400/2500 = 0.16

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La pregunta completa es:

En una empresa de papas fritas una máquina automática debe llenar las bolsas manteniendo una determinada cantidad de gramos, sin embargo, en algunas ocasiones los paquetes de papas pueden pesar más o menos del peso establecido. Se revisaron 2500 bolsas de los últimos días, en las cuales 2100 bolsas tuvieron el peso correcto, 275 tuvieron un peso menor y 125 tuvieron un peso mayor

a) ¿Cuál es la probabilidad de que tenga el peso correcto?

b) ¿Cuál es la probabilidad de que tenga un peso menor o mayor?​

to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below.

[tex](\stackrel{x_1}{-8}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-4}-\stackrel{y1}{4}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{(-8)}}} \implies \cfrac{-8}{0 +8} \implies \cfrac{ -8 }{ 8 } \implies - 1[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{- 1}(x-\stackrel{x_1}{(-8)}) \implies y -4 = - 1 ( x +8) \\\\\\ y-4=-x-8\implies {\Large \begin{array}{llll} y=-x-4 \end{array}}[/tex]

The probability that a person surveyed gets the news by reading the paper, given that he or she is under 40 is 10%. The Option A is correct.

We are given that number of people who read paper and under 40 is 4 and number of people who are under 40 is 40.

We need to find the probability that a person surveyed gets the news by reading the paper given that he or she is under 40.

We will use the "Conditional probability": P (Person that read the paper given that he or she is under 40) is given by:

= P(read the paper and under age 40) / P(person who are under age 40)

= 4 / 40

= 0.1

= 10%

Full questions"A survey asked people of different ages whether they get their news by reading the paper. What is the probability that a person surveyed gets the news by reading the paper, given that he or she is under 40? If necessary, round your answer to the nearest percent. A.10% B.14% C.5% D.90%

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Pablo's error was that he added the equations.

A possible first step is to subtract the equations.

The solution of the system is x = -2 and y = 8.

One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

Given:

We have s system of equations,

3x + 4y = 26   {equation 1}

2x + 4y = 28   {equation 2}

Pablo is solving the system of equations shown and says that the first step is to add the equations together to eliminate the y variables.

To eliminate the y-variable:

Subtract equation 2 to equation 1.

3x - 2x = 26 - 28

x = -2

Then y = 8.

Therefore, the solution of the system is x = -2 and y = 8.

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Answer:

The statement Cov(aX + b, cW) = ac Cov(X,W) is true.

Step-by-step explanation:

Starting with the definition of covariance:

Cov(aX + b, cW) = E((aX + b) - E(aX + b))(cW - E(cW))

Using linearity of expectation:

Cov(aX + b, cW) = E(a(X - E(X)) + (b - E(b)))(c(W - E(W)))

Expanding and rearranging the product:

Cov(aX + b, cW) = acE(X - E(X))(W - E(W)) + E(b - E(b))E(c(W - E(W)))

Since the expectation of a constant is the constant itself and E(b - E(b)) = 0, the above expression simplifies to:

Cov(aX + b, cW) = ac Cov(X,W)

To calculate the proportion of the optimal risky portfolio that should be invested in stock A, we need to use the formula for a two-stock portfolio.

Let x be the proportion of the portfolio invested in stock A, then [tex](1 - x)[/tex]is the proportion invested in stock B.

The expected return of the portfolio,[tex]E(Rp)[/tex], can be calculated as:

[tex]E(Rp) = x * E(Ra) + (1 - x) * E(Rb)[/tex]

The standard deviation of the portfolio, σp, can be calculated as:

[tex]σp = sqrt(x^2 * σa^2 + (1 - x)^2 * σb^2 + 2x * (1 - x) * σa * σb * ρab)[/tex]

where σa is the standard deviation of stock A, [tex]σb[/tex] is the standard deviation of stock B, and [tex]ρab[/tex] is the correlation coefficient between the returns of A and B.

Substituting the given values, we get:

[tex]E(Rp) = x * 0.12 + (1 - x) * 0.08 = 0.1σp = sqrt(x^2 * 0.18^2 + (1 - x)^2 * 0.03^2 + 2x * (1-x) * 0.18 * 0.03 * 0.50)[/tex]

The optimal risky portfolio is the one that has the maximum Sharpe ratio, which is defined as:

Sharpe ratio =[tex](E(Rp) - Rf) / σp[/tex]

where Rf is the risk-free rate of return.

By equating the derivative of the Sharpe ratio to zero and solving for [tex]x[/tex], we can find the optimal proportion of the portfolio to be invested in stock A. So, the proportion of the optimal risky portfolio that should be invested in stock A is 56%.

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The expression that represents the area of the rectangle is 18x² + 63x + 55.

What is the multiplication of polynomials?

Multiplying polynomials is a basic concept in algebra. Multiplication of two polynomials will include the product of coefficients to coefficients and variables to variables.

The area is just length times width:

(3x + 5)(6x + 11) = 18x² + 63x + 55

The degree of the expression is the highest power which is in 18x²

Above we multiplied 2 polynomials (3x + 5) and (6x + 11) and obtained another polynomial. This demonstrated the closure property of polynomials

Hence, the expression that represents the area of the rectangle is 18x² + 63x + 55.

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Original loan amount was 270,384 and if paid a total of 360,000 then the interest rate of loan is, 6.6%

Simple interest is an amount which is calculated for a certain period of time and for a certain rate, in simple interest calculation there are three factors which we consider: principal amount(P), rate(R) and time(T).

Every time we calculate simple interest the principal values will be the same unlike compound interest.

Formula;    Simple Interest(I) =  P × R × T/100

Given that,

Original loan amount = 270,384

Total amount paid = 360,000

Interest  = 89616

Suppose, time duration = 5 years

Interest rate = ?

I =  P × R × T/100

89616 = (270,384 x R x 5)/100

R = 6.62

Hence, the interest rate is 6.6 %

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The required interest paid against the loan of the Original loan amount was 270,384.

Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan.

Amount = Principal [1 + rate×time]

Here,
The original loan amount was 270,384 you paid a total of 360,000.
Interest paid can be evaluated by subtraction of the original amount from the paid amount,
interest paid =  paid amount - the original amount
interest paid = 360,000 - 270,384
interest paid = 89,616

Thus, the required interest paid against the loan of the Original loan amount was 270,384.

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Answer:

below

Step-by-step explanation:

Need the diagram......

(b) The number of people to be selected from those who responded "yes" in the stratified random sample is 14.

(c) A statistical advantage of using the stratified random sample instead of the simple random sample is that it ensures a proportional representation of each stratum (in this case, "yes" and "no" responses) in the sample, reducing the risk of bias and increasing the accuracy of the results.

The calculation is determined by dividing the total number of samples (20) by the number of strata (2) plus 1, then multiplying by the number of samples for each stratum. The result of 20 / (2 + 1) * 2 is

20 / 3 * 2

= 40 / 3

= approximately 13.33, which is rounded up to 14 people.

In a simple random sample, the individuals selected may not accurately reflect the proportions of the two responses in the population. This can result in incorrect conclusions and decision-making. With the stratified random sample, the proportions of "yes" and "no" responses in the sample are maintained, providing a more accurate representation of the population.

Additionally, stratified random sampling allows for separate analysis of each stratum, which can provide additional insights into the population. Overall, stratified random sampling is a more robust method for obtaining accurate and representative results in a survey setting.

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Each person get 4/5 of the e leftover bag of beads.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other.

From the question,

The total number of leftover beads is 1/5

4 people are to share the leftover beads

so,

the ratio will be 1/5 ÷ 1/4

1/5 x 4

=4/5

Hence, each person will get 4/5 of the beads

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Based on the definition of congruent triangles, the measures are:

4. m<R = 75°

5. XY = 6

6. m<X = 55°

7. m<S = 50°

Congruent triangles are two triangles that have the same size and shape. This means that all corresponding sides and angles of the two triangles are equal in measure.

Since triangles QRS are congruent to each other, therefore, their corresponding parts will be equal. Thus:

4. m<R = 180 - 55 - 50

m<R = 75°

5. XY = QR = 6

6. m<X = m<Q

m<X = 55°

7. m<S = m<Z

m<S = 50°

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If S = {a, b}, then S will be C. not an integral domain.

A nonzero commutative ring known as an integral domain is one in which the product of any two nonzero components is nonzero.

A nonzero commutative ring that belongs to an integral domain has nonzero elements that are all cancellable when multiplied. A ring that has a nonzero element set that is a commutative monoid under multiplication is known as an integral domain.

If S = {a, b}, then S is not an integral domain, as the product of a and b is undefined, and it is not a field because it does not have a multiplicative identity element. It is also not a commutative ring without unity, as it does not have an additive identity element.

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Youth unemployment rate change from April to July is 25%.

Youth labor force participation rate in July is 7.27%.

Rate of change is the speed at which the variables changes with respect to time.

From April to July​ 2015, the number of employed youth​ 16- to​ 24-years old rose by 2.1 million to 20.3 million

Youth unemployment increased from 2.1 million to 2.8 million.

In​ July, the youth labor force grew by 2.8 million to a total of 23.1 million.

Youth population was 38.5 million.

[tex]labor force rate =\frac{labor force}{adult population} *100[/tex]

                       = [tex]\frac{2.8}{38.5} *100[/tex] = 7.27%

[tex]unemployment rate = \frac{number of unemployment}{labor force} *100[/tex]

                              = [tex]\frac{2.8-2.1}{2.8} *100[/tex]=25%

Hence, youth unemployment rate change from April to July is 25%.

Youth labor force participation rate in July is 7.27%.

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The simplified expression (2x/7 - 1/4)² is given as follows:

(2x/7 - 1/4)² = 4x²/49 - x/7 + 1/16.

The expression for this problem is defined as follows:

(2x/7 - 1/4)².

The square of a subtracted binomial notable product is given as follows:

(a - b)² = a² - 2ab + b².

The parameters for this problem are given as follows:

Hence the terms of the expression are given as follows:

Hence the simplified expression is defined as follows:

(2x/7 - 1/4)² = 4x²/49 - x/7 + 1/16.

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Answer: x= 90

Step-by-step explanation: