Select the correct answer.
Consider the graph and the equation of function f.
f(x)=2 sin (1/2x) + 1

Answer:...

-4+8x+2xy

Step-by-step explanation:

The probability that a randomly selected student will like pizza but not chicken nuggets is (28n - 8)/(28n + 7), where 28n is the students who like pizza and 8 is students who like both pizza and chicken nuggets.

To find the probability that a randomly selected student will like pizza but not chicken nuggets.

Let P = the number of students who like pizza but not chicken nuggets

Then, P = the number of students who like pizza - the number of students who like both pizza and chicken nuggets

P = 28n - 8

So, the probability that a randomly selected student will like pizza but not chicken nuggets is:

P(Pizza but not nuggets) = P/(Total number of students)

We can find the total number of students who like either pizza or chicken nuggets by adding the number of students who like pizza and the number of students who like chicken nuggets, and then subtracting the number of students who like both:

Total number of students = 28n + 15 - 8 = 28n + 7

So, the probability that a randomly selected student will like pizza but not chicken nuggets is:

P(Pizza but not nuggets) = P/(Total number of students) = (28n - 8)/(28n + 7)

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It will take approximately 25 hours and 1 minute for there to be 150mg of aspirin left in the bloodstream.

We have,

To determine how long it will take for there to be 150mg of aspirin left in the bloodstream, we can use the concept of half-life.

The half-life of aspirin is given as 6 hours, which means that after every 6 hours, the amount of aspirin in the bloodstream reduces by half.

Let's calculate the number of half-lives required to reach 150mg:

Initial amount of aspirin = 625mg

Final amount of aspirin = 150mg

625mg / 150mg = 4.17

This means it will take approximately 4.17 half-lives for the amount of aspirin in the bloodstream to reduce from 625mg to 150mg.

Since each half-life is 6 hours, we can calculate the total time it will take:

Total time = Number of half-lives * Half-life duration

Total time = 4.17 x 6 hours

Total time ≈ 25 hours and 1 minute

Therefore,

It will take approximately 25 hours and 1 minute for there to be 150mg of aspirin left in the bloodstream.

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The equation 2 (p+ 7) = 4 - 8p has only one solution that is; -9.

We know that solution of an equation refers usually to the values of the variables involved in that equation that if substituted in place of that variable would give a true mathematical statement.

We need to determine the solutions does the equation 2 (p+ 7) = 4 - 8p have;

Now solving for p,

2 (p+ 7) = 4 - 8

Open the bracket,

2p+ 14 = 4 - 8

Combine the like terms,

2p = -4 - 14

2p = -18

p = -18/2 = -9

Therefore, the equation has only one solution which is -9.

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The equation for the proportion, p, of consumers who shop with coupons is: p = C/N where C is the number of consumers who use coupons and N is the total number of consumers asked.

An equation is a mathematical statement that indicates the equality of two expressions. It consists of two expressions separated by an equal sign (=). The expression on the left side of the equal sign is equivalent to the expression on the right side. Equations can have one or more variables, which are usually represented by letters such as x, y, or z. The goal in solving an equation is to determine the value(s) of the variable(s) that make the equation true. This involves manipulating the expressions on both sides of the equal sign using algebraic operations such as addition, subtraction, multiplication, and division, to isolate the variable on one side of the equation. Equations are used in many areas of mathematics and science to represent relationships between variables and to solve problems. They are also used in various fields such as engineering, physics, and economics to model real-world situations and make predictions based on mathematical analysis.

Here,

This equation represents the ratio of the number of consumers who use coupons to the total number of consumers. It is commonly used in statistics and market research to measure the prevalence of a certain behavior or preference among a population. By calculating the proportion of consumers who use coupons, businesses can make informed decisions about their pricing strategies, promotions, and advertising campaigns.

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Answer:

45

Step-by-step explanation:

8 - 16 + 48 + 5

-8 + 48 + 5 =

40 + 5 =

45

Hope that helps!

The composition (f o g)(x) = 10/(x+10) and its domain is all real numbers except x = -10.

a) To find (f o g) (x), we need to substitute g(x) into f(x) wherever we see x. That is,

(f o g) (x) = f(g(x)) = f(10/x) = (10/x) / (10/x + 1)

b) To find the domain of (f o g) (x), we need to look for any values of x that make the denominator of the expression equal to zero, since division by zero is undefined. Thus, we solve the equation:

10/x + 1 = 0

10/x = -1

x = -10

Therefore, the domain of (f o g) (x) is all real numbers except x = -10, since that value makes the denominator equal to zero. In interval notation, the domain is:

(-∞, -10) U (-10, ∞)

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The given differential equation:

y''' − 2y'' + y' = 2 − 24ex + 40e5x,

y(0) = 1/2, y'(0) = 5/2, y''(0) = −11/2

Therefore, the next solution is 13/2

Differential Equation:

In mathematics, a differential equation is an equation relating one or more unknown functions to their derivatives. In applications, functions usually represent physical quantities, derivatives represent rates of change, and differential equations define the relationship between them. These relationships are common.

Now,

Given differential equation is

y''' - 2y'' +y' = 2- 24eˣ +40e⁵ˣ                 ------------ (1)

Auxiliary equation is m³ - 2m² +2m = 0

Now,

   m(m² - 2m +2) = 0

⇒ m(m-1)² = 0

Therefore, m = 0,1,1

Therefore,

\(y_{c} = c_{1}+ c_{2} e^{x} + c_{2}x e^{x}\)

Now, we have to find the particular solution by method of undetermined coefficient.

   \(y'_{y} = a + b(x^{2} e^{x} +2xe^{x} ) +5ce^{x}\)

⇒ \(y''_{p} = a + bx^{2} e^{x} +2bxe^{x} +5ce^{x}\)

⇒ \(y''_{p} = b(x^{2} e^{x} +2xe^{x}) + 2b(ex^{x}+ e^{x} +25ce^{x}\)

⇒ \(y'''_{p} = bx^{2} e^{x} +6bxe^{x} +6be^{x} +125ce^{5x}\)

Putting these values in differential equation (1), we get:

y'''(0) = 13/2

Complete Question:

Solve the given initial-value problem. y''' ? 2y'' + y' = 2 ? 24ex + 40e5x, y(0) = 1 2 , y'(0) = 5/ 2 , y''(0) = ? 13/ 2

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The numbers of pears and apples bought are 16 and 20 respectively

let

x = number of pears

y = number of apples

He bought 4 more apples than pears. Therefore,

He bought a number of pears and apples and paid $128 for them. Therefore,

y - x = 4

4y + 3x = 128

Therefore,

3y - 3x = 12

4y + 3x = 128

7y = 140

y = 140 / 7

y = 20

Therefore,

20 = x + 4

x = 20 - 4

x = 16

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The term that can be added to the list so that the greatest common factor of the three terms  12h3 36h3, 12h6, is 48h5

A group of numbers' greatest common factor (GCF) is the biggest factor that all the numbers have in common. For instance, 12, 20, and 24 all share two characteristics.

The term that  can fit in to the list so the GCF is 12h3 would be 48h5, this is so because 48 is first divisible by 12  without any  fraction, and we can remove upon dividing 3 h's from this term as it contains a total of 5 h's.

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Answer:

(7,3.5)

Step-by-step explanation:

Midpoints

x = (x1 + x2)/2 = (9 + 5)/2 = 14/2 = 7

y = (y1 + y2)/2 = (2 + 5)/2 = 7/2 = 3.5

Step-by-step explanation:

The last option 45 and 46

Answer:

its 4-5 not 45-46 \

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given a chord of distance of 15cm, if it is 9cm from the center of a circle, this means that the 9cm length will be projecting from the centre of the circle perpendicular to the chord and passing through its centre.

Since the radius of a circle is a line that is drawn from the centre of a circle to ts circumference, the set up will form a right angles triangle within the circle with the hypotenuse as the radius and the other two sides as the opposite and adjacent respectively. Using the Pythagoras theorem to get the length of the radius (hypotenuse);

hyp² = opp² + adj²

Let the opposite be the 9cm length

Adjacent will be half of the chord length = 15/2 = 7.5cm

Substituting this values into the formula we will have;

hyp² = 9² + 7.5²

hyp² = 81+56.25

hyp² = 137.25

hyp² = √137.25

hyp = 11.72

Hence the radius of the circle is approximately 11.72 cm long

Answer: To calculate the expected value, we need to multiply each possible outcome by its probability and then add up the results.

The probability of selecting a gold marble is 3/41, the probability of selecting a silver marble is 8/41, and the probability of selecting a black marble is 30/41.

The winnings/losses associated with each outcome are $3 for gold, $2 for silver, and -$1 for black.

Step-by-step explanation:

Therefore, the expected value can be calculated as follows:

(3/41) x $3 + (8/41) x $2 + (30/41) x (-$1)

= $0.073

The expected value is $0.073, which means that on average, you can expect to win $0.073 per game if you play this game many times.

Therefore, if you play this game, you can expect to win a small amount of money on average, but it is not a guaranteed win.

References:

Grinstead, C.M. and Snell, J.L. (2006). Introduction to Probability. American Mathematical Society.

"Expected Value," Investopedia, accessed May 14, 2023, https://www.investopedia.com/terms/e/expectedvalue.asp.

Answer:

Step-by-step explanation:

\(72.46387 = 72\)

4 is not up to 5

Your answer would be C.

He did not go insane

Answer:

FV= $38,735.32

Step-by-step explanation:

Giving the following information:

Monthly deposit= $100

Number of periods= 18*12= 216 months

The interest rate is confusing. I will assume an interest rate of 6%. If it is not correct, just change it in the formula.

Monthly interest rate= 0.06/12= 0.005

To calculate the future value, we need to use the following formula:

FV= {A*[(1+i)^n-1]}/i

A= monthly deposit

FV= {100*[(1.005^216) - 1]} / 0.005

FV= $38,735.32

The correct answer is: O Yes, distance and angle measure are preserved.

When a triangle ABC is reflected across the line y = x, the pre-image and image are congruent.

This is because the line y = x is the perpendicular bisector of the segment joining each corresponding point of the pre-image and image.

Reflection across the line y = x is a type of transformation known as an isometry, which preserves both distance and angle measure.

Here's why:

Distance preservation:

When a point is reflected across the line y = x, the distance between the original point and its reflection remains the same.

This holds true for all corresponding points of the triangle.

Therefore, the distance between any two corresponding points in the pre-image and image triangle will be equal, resulting in distance preservation.

Angle preservation: When a line segment is reflected across the line y = x, the angle between the line segment and the line y = x is preserved. This means that the corresponding angles in the pre-image and image triangle will be congruent.

Since both distance and angle measure are preserved during reflection across the line y = x, the pre-image and image triangles are congruent.

It's important to note that congruence under reflection across a line holds only when the line of reflection is the same for both the pre-image and image.

If the line of reflection were different, the triangles would not be congruent.

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Answer:

8500

Step-by-step explanation:

When compounded continuously the future value,  FV , of your initial investment,  PV , is determined with the the equation

\(FW = PV\) ×\(e^{rxt}\)

where  r  is the norminal interest rate, expressed as a decimal, and  t  is the investment period in years.

Plugin the values in this equation gives

\(FW = $7,500\) × \(e^{0.015x8} =$8,456.23\)

Round to nearest hundred dollars = 8500

Answer:

the c.o.p is 14.25

Step-by-step explanation:

ANSWER: You can make 16 refrigerator magnets.

If you divide 10 by 5/8, you multiply by the reciprocal of 5/8 which is 8/5. You have 8/5 x 10. Cross simplify and you have 16.

Answer:

I think that is 26y

Step-by-step explanation:

Answer:

the answer for y-18 =7y + 9 - 10y

Step-by-step explanation:

Answer:

can we get a picture

Step-by-step explanation:

Word Problem:

Take a number, x, double it and then take that result away from 10.

Expression:

\(10-(2x)\)

Answer: C. The measures of variation reveal nothing about the pattern over time.

Step-by-step explanation:

Given the following :

10 17 10 16 11 3 8 5 4 4 17 5 8 17

Range of hurricane data = 16

The standard deviation of sample data = 5.5 hurricanes

The variance of the sample data is 30.3 hurricane^2.

The measures of variation described above only shows the spread of the hurricane such as the range, that is the highest and lowest recorded.

The variance explains how spread out the data is and the standard deviation explains how values of a data differs from the mean value. The data fails to give time related information or pattern.

Answer:

4.2.1)  R140 000

4.2.2)  R144 758.28

4.2.3)  Option 2

Step-by-step explanation:

To calculate the return on Ayanda's investment using Option 1, we can use the simple interest formula.

\(\boxed{\begin{minipage}{7 cm}\underline{Simple Interest Formula}\\\\$ I =Prt$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)

Given values:

Substitute the given values into the formula and solve for I:

\(I=200000 \cdot 0.12 \cdot 6\)

\(I=24000 \cdot 6\)

\(I=144000\)

Therefore, the return on Ayanda's investment using Option 1 is R144000.

\(\hrulefill\)

To calculate the return on Ayanda's investment using Option 2, we can use the compound interest formula.

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

Given values:

Substitute the given values into the formula and solve for I:

\(I=200000(1+0.095)^6-200000\)

\(I=200000(1.095)^6-200000\)

\(I=200000(1.72379142...)-200000\)

\(I=344758.28426...-200000\)

\(I=144758.28426...\)

\(I=144758.28\)

Therefore, the return on Ayanda's investment using Option 2 is R144758.28.

\(\hrulefill\)

Comparing the returns from both options, we find that Option 1 offers a return of R144000, while Option 2 offers a return of R144758.28. As R144758.28 > R144000, then Option 2 will render the most money for Ayanda's investment.

Answer:

D

Step-by-step explanation:

Whatever angle you pick the three possibilities must add to 180.

a) adds to 150

b) 32 + 59 + 79  =  170. Close but not close enough

c) c has three 5s. The total will end in 5. Not the answer.

d) d does add to 180. It's the answer.

Which set of measures could be the measures of the interior angles of a triangle?

a.30°, 90°, 30°

b.32°, 59°, 79°

c.35°, 65°, 75°

d.22°, 37°, 121°

In this question we are asked to find out which one could be the measures of the interior angles of a triangle. Add the three measure angles given if you get 180° then those angles can be the interior angles of a triangle.

We know that,

\( \bull \: \small\boxed{ \rm{ Sum \: of \: all \: interior \: angles \: of \: a \: triangle = 180°}}\)

a) 30°, 90°, 30°

→ 30° + 90° + 30° = 180°

→ 150° ≠ 180°

Option a) is not the correct answer.

b) 32° , 59° , 79°

→ 32° + 59° + 79° = 180°

→ 170° ≠ 180°

Option b) is not the correct answer.

c) 35° , 65° , 75°

→ 35° + 65° + 75° = 180°

→ 175° ≠ 180°

Option c) is not the correct answer.

d) 22° , 37° , 121°

→ 22° + 37° + 121° = 180°

→ 180° = 180°

Hence, opition d) is the correct answer

9514 1404 393

Answer:

  c.  3 to 4

Step-by-step explanation:

There are 3 oranges and 4 apples in the bowl, so the ratio is ...

  oranges/apples = 3/4 or 3 to 4

Answer:

(x,y)= (-92/35,233/70)

Step-by-step explanation: