f(3) = 3x² +b For the function, f, defined above, f(4) = 49. What is the value of b?
​

Given:

Total number of girls in her class = 16

Total number of boys in her class = 14

To find:

The number of different ways of choosing one girl and one boy.

Solution:

We have,

Total number of girls = 16

Total number of boys = 14

So,

Total number of ways to select one girl from 16 girls = 16

Total number of ways to select one boy from 14 boys = 14

Now, number of different ways of choosing one girl and one boy is

\(16\times 14=224\)

Therefore, the required number of different ways is 224.

a. The number of  different ways of choosing one girl and one boy is 226

Total number of ways to select one girl from 16 girls = 16

Total number of ways to select one boy from 14 boys = 14

So, the number should be

\(= 16 \times 14\)

= 224

Find out more information about the Number here : https://brainly.com/question/17429689?referrer=searchResults

The average rate of change of f(x) = x^2 + 10 over the interval -2 ≤ x ≤3 is 1.

We know that the formula to calculate the average rate of change of a function over an interval is

Average Rate of Change = (f(b) - f(a)) / (b - a)

Where, a and b are the initial and final values of x respectively.

f(x) = x^2 + 10

Between the interval [-2, 3], a = -2 and b = 3.

Substituting the values in the formula:

Average Rate of Change = (f(b) - f(a)) / (b - a)= (f(3) - f(-2)) / (3 - (-2))

Now, let's find f(3) and f(-2)

f(3) = 3^2 + 10 = 19

f(-2) = (-2)^2 + 10 = 14

Substitute the values:

Average Rate of Change = (f(3) - f(-2)) / (3 - (-2))= (19 - 14) / (3 + 2)= 5/5= 1

Hence, the average rate of change is 1.

To learn more about average rate of change  visit : https://brainly.com/question/8728504

#SPJ11

Answer:

24 cm

Step-by-step explanation:

We can set up a ratio of 18 m / x cm = 3 m / 4 cm because we know that it's a scale.

Cross multiplying, we get 3x = 72. Divide both sides by 3 and we have x = 24 cm.

We can also consider it by just dividing 18 m by 3 m to find the scale factor, which is 6. We then multiply the 4 cm by 6 to get 24 cm as well.

Answer:

B

Step-by-step explanation:

Don't know how to type those here so see attachment

Answer:

x = √29

Step-by-step explanation:

a^2 + b^2 = c^2

5^2 + 2^2 = c^2

25 + 4 = c^2

29 = c^2

√29 = √c^2

√29 = c

x = √29

n=4 is the degree maclurins polynomial is required so that the error in the approximation is less than 0.001.

Given that,

The expression is

e⁰⁵=1+0.5+0.5²/2!+0.5³/3!+.....

We have to find what degree maclurins polynomial is required so that the error in the approximation is less than 0.001.

We know that,

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

√e=1.64872

Pₙ( x)= e⁰⁵=1+0.5+0.5²/2!+0.5³/3!+.....

P₂=1+0.5+0.5²/2!=1.625

P₃= P₂+0.5³/3!=1.6458

P₄= P₃+0.5⁴/4!=1.648404

√e - P₄ = -0.0003158

Therefore, n=4 is the degree maclurins polynomial is required so that the error in the approximation is less than 0.001.

To learn more about approximation visit: https://brainly.com/question/15696262

#SPJ4

Answer:

not sure if they want 19 or 19.00

Answer:

the answer is A. 64:343.

Step-by-step explanation:

The ratio of the volumes of two similar figures is equal to the cube of the ratio of their corresponding side lengths. Since the scale factor of the two cylinders is 4:7, the ratio of their corresponding radii is 4:7 and the ratio of their heights is also 4:7.

So, the ratio of their volumes is (4/7)^3 = (64/ 343) = 64:343

So, the answer is A. 64:343.

The average selling price of a ticket at the Algal Rhythms concert is $25

The given parameters are:

75% of the tickets were sold for $30.

The remaining 25% were sold for $10.

The average selling price of a ticket at the Algal Rhythms concert is calculated using

Average = Sum of (Price * Percentage)

So, we have

Average = 30 * 75% + 10 * 25%

Evaluate the expression

Average = 25

Hence, the average selling price of a ticket at the Algal Rhythms concert is $25

Read more about average at:

https://brainly.com/question/20118982

#SPJ1

The proportion of trick-or-treaters who were not dressed as cowboys is 10/13.

If three out of every thirteen trick-or-treaters were dressed as cowboys, it means that the proportion of trick-or-treaters dressed as cowboys is 3/13.

To find the proportion of trick-or-treaters who were not dressed as cowboys.

we subtract the proportion dressed as cowboys from 1 (since the total proportion of trick-or-treaters must sum to 1).

Proportion not dressed as cowboys = 1 - Proportion dressed as cowboys

Proportion not dressed as cowboys = 1 - (3/13)

Proportion not dressed as cowboys = (13/13) - (3/13)

Proportion not dressed as cowboys = 10/13

Therefore, the proportion of trick-or-treaters who were not dressed as cowboys is 10/13.

To learn more on Ratios and Proportions click:

https://brainly.com/question/1504221

#SPJ4

Answer:

\(\frac{-3}{7}\)

Step-by-step explanation:

The explicit rule for the geometric sequence 3, 12, 48,... is:

f(n) = \(3 \times 4^{(n-1)\). B.

The explicit rule for the geometric sequence 3, 12, 48,... need to determine the common ratio, r.

We can do this by dividing any term by the previous term:

r = 12/3

= 48/12

= 4

Now that we know the common ratio can use the formula for the nth term of a geometric sequence:

\(a_n\) = \(a_1 \times r^{(n-1)\)

where:

\(a_n\) is the nth term

\(a_1\) is the first term (3 in this case)

r is the common ratio (4 in this case)

n is the term number

Substituting these values into the formula, we get:

\(a_n\) = \(3 \times 4^{(n-1)\)

So, the explicit rule for the geometric sequence 3, 12, 48,... is:

f(n) = \(3 \times 4^{(n-1)\)

For similar questions on geometric sequence

https://brainly.com/question/1509142
#SPJ11

1. For the differential equation 3.1, the general solution is y = (C₁ + C₂e³x) + (1/2)e¹x - (1/2)cos 2x, where C₁ and C₂ are arbitrary constants.

2. For the differential equation 3.2, the general solution is y = (C₁cos(2x) + C₂sin(2x))e^(−x) + (1/5)sin 2x + (1/10)cos 2x, where C₁ and C₂ are arbitrary constants.



1. To find the general solution for equation 3.1, we first determine the characteristic equation by replacing D² with r², D with r, and solving r² - 5r + 6 = 0. The roots are r₁ = 2 and r₂ = 3. Thus, the homogeneous solution is y_h = C₁e²x + C₂e³x, where C₁ and C₂ are constants.

Next, we find the particular solution for the inhomogeneous term e¹x + sin 2x. Assuming y_p = Ae¹x + Bcos 2x + Csin 2x, we substitute it into the differential equation and equate coefficients. Solving the resulting equations, we find A = 1/2, B = -1/2, and C = 0. Therefore, the particular solution is y_p = (1/2)e¹x - (1/2)cos 2x.

Finally, the general solution is y = y_h + y_p, giving y = (C₁ + C₂e³x) + (1/2)e¹x - (1/2)cos 2x.

2. For equation 3.2, the characteristic equation is r² + 2r + 4 = 0, which has complex roots r₁ = -1 + 2i and r₂ = -1 - 2i. The homogeneous solution is y_h = (C₁cos(2x) + C₂sin(2x))e^(-x), where C₁ and C₂ are constants.

To find the particular solution for e²sin 2x, we assume y_p = (Acos 2x + Bsin 2x)e^(-x). Substituting it into the differential equation and solving the resulting equations, we obtain A = 1/10 and B = 1/5. Thus, the particular solution is y_p = (1/10)cos 2x + (1/5)sin 2x.

Combining the homogeneous and particular solutions, the general solution is y = y_h + y_p, giving y = (C₁cos(2x) + C₂sin(2x))e^(-x) + (1/5)sin 2x + (1/10)cos 2x.

To learn more about arbitrary constants click here

brainly.com/question/29093928

#SPJ11

Answer:

A. $107.20

Step-by-step explanation:

dont know sorry

Answer:

a. 4.00

b. 3.00

I hope this helps

The no. of ways to select the 2 blue balls and 2 orange balls from the urn is 0.4545

No. of Blue balls in the urn = 6

No. of Orange balls in the urn = 6

Total no. of balls in the urn = No. of blue balls + No. of orange balls

                                            = 6 + 6

                                           = 12 balls

No. of blue balls to be selected = 2

No. of orange balls to be selected = 2

No. of balls to be selected = 4

The total. no of ways 4 balls can be selected =\(^{12}C_{4}\)

The No. of ways 2 blue balls can be selected = \(^{6}C_{2}\)

The No. of ways 2 orange balls can be selected =    \(^{6}C_{2}\)

Therefore, No. of ways to select 2 blue balls and 2 orange balls from the urn

                      =  \(^{6}C_{2} \times ^{6}C_{2} /^{12}C_{4}\)

Probability = No. of ways to select blue balls x No. of ways to select orange balls / Total no. of ways to select balls

                         P = (15×15)/495

                             = 225 / 495

                          P = 0.4545

Therefore,  the no. of ways to select blue and orange balls is 0.4545

Learn more about the probability at

brainly.com/question/11234923

#SPJ4

The probability that a baseball player has exactly 5 hits in his next 7 at bats =  0.0034

In this question we have been given a baseball player has a batting average of 0.19

We need to find the probability that he has exactly 5 hits in his next 7 at bats.

We know that the formula for the binomial distribution:

P(x) = nCx p^x q^(n - x)

From given information:

p = 0.19

q = 1 - p

  = 1 - 0.19

  = 0.81

n = 7 and x = 5

Using binomial distribution formula the probability would be,

P = nCx p^x q^(n - x)

P = 7C5 * (0.19)^5 * (0.81)^(7 - 5)

P = 21 * (0.19)^5 * (0.81)^2

P = 0.0034

Therefore, the required probability is:  0.0034

Learn more about probability here;

https://brainly.com/question/30034780

#SPJ4

Answer:

\(x(t) = 54t\)  and \(y(t) = 134(t - 3)\)

Step-by-step explanation:

Represent the swimmers with A and B

For Swimmer A:

\(Rate = 54m/min\)

For Swimmer B:

\(Rate = 134m/min\)

Required:

Write a parametric equation

For Swimmer A:

If swimmer A covers 54 meters in 1 minutes, then the swimmer covers 54t in t minutes

So, the function is:

\(x(t) = 54t\)

For Swimmer B:

If swimmer A covers t minutes, swimmer B swims for (t - 3) minutes because swimmer B starts 3 minutes later.

If in 1 minutes, swimmer B covers 134 minutes; In (t - 3) minutes, the swimmer covers 134(t - 3)

So, the rate is:

\(y(t) = 134(t + 3)\)

Hence, the parametric functions are:

\(x(t) = 54t\) and

\(y(t) = 134(t - 3)\)

Answer:

A on Edge

Step-by-step explanation:

9514 1404 393

Answer:

  x = 7

Step-by-step explanation:

Put -3 where g(x) is and solve the resulting equation for x.

  g(x) = -x +4

  -3 = -x +4

  x -3 = 4 . . . . . . add x (so we can work with a positive coefficient

  x = 7 . . . . . . . . add 3

Answer:

x=-7 i guess

Step-by-step explanation:

To construct a Deterministic Finite Accepted M such that L(M) = L(G), the language generated by grammar G = ({S, A, B}, {a, b}, S , {S -> abS, S -> A, A -> baB, B -> aA, B -> bb} ), the following steps should be followed:

Step 1: Eliminate the Null productions from the grammar by removing productions containing S. The grammar, after removing null production, becomes as follows.{S -> abS, S -> A, A -> baB, B -> aA, B -> bb}

Step 2: Eliminate the unit productions. The grammar is as follows. {S -> abS, S -> baB, S -> bb, A -> baB, B -> aA, B -> bb}

Step 3: Now we will convert the given grammar to an equivalent DFA by removing the left recursion. By removing the left recursion, we get the following productions. {S -> abS | baB | bb, A -> baB, B -> aA | bb}

Step 4: Draw the state diagram for the DFA using the following rules: State diagram for L(G) DFA 1. The start state is the initial state of the DFA. 2. The final state is the final state of the DFA. 3. Label the edges with symbols on which transitions are made. 4. A table for the transition function is created. The table for the transition function of L(G) DFA is given below:{Q, a} -> P{Q, b} -> R{P, a} -> R{P, b} -> Q{R, a} -> Q{R, b} -> R

Step 5: Construct the DFA using the state diagram and transition function. The DFA for the given language is shown below. The starting state is shown in green and the final state is shown in blue. DFA for L(G) -> ({Q, P, R}, {a, b}, Q, {Q, P}) Where, Q is the starting state P is the first intermediate state R is the second intermediate state.

To know more about deterministic finite: https://brainly.com/question/33237093

#SPJ11

A big sample that should the experimenter take from the population is 256 and if the standard deviation and the width of the confidence interval are both doubled then the sample is also 256.

In the given question,

The confidence level = 99%

Given width = 0.5

Standard deviation of resistance(\(\sigma\))= 1.55

We have to find a big sample that should the experimenter take from the population and what happens if the standard deviation and the width of the confidence interval are both doubled.

The formula to find the a big sample that should the experimenter take from the population is

Margin of error(ME) \(=z_{\alpha /2}\frac{\sigma}{\sqrt{n}}\)

So n \(=(z_{\alpha /2}\frac{\sigma}{\text{ME}})^2\)

where n=sample size

We firstly find the value of ME and \(z_{\alpha /2}\).

Firstly finding the value of ME.

ME=Width/2

ME=0.5/2

ME=0.25

Now finding the value of \(z_{\alpha /2}\).

Te given interval is 99%=99/100=0.99

The value of \(\alpha\) =1−0.99

The value of \(\alpha\) =0.01

Then the value of \(\alpha /2\) = 0.01/2 = 0.005

From the standard table of z

\(z_{0.005}\) =2.58

Now putting in the value in formula of sample size.

n\(=(2.58\times\frac{1.55}{0.25})^2\)

Simplifying

n=(3.999/0.25)^2

n=(15.996)^2

n=255.87

n≈256

Hence, the sample that the experimenter take from the population is 256.

Now we have to find the sample size if the standard deviation and the width of the confidence interval are both doubled.

The new values,

Standard deviation of resistance(\(\sigma\))= 2×1.55

Standard deviation of resistance(\(\sigma\))= 3.1

width = 2×0.5

width = 1

Now the value of ME.

ME=1/2

ME=0.5

The z value is remain same.

Now putting in the value in formula of sample size.

n\(=(2.58\times\frac{3.1}{0.5})^2\)

Simplifying

n=(7.998/0.5)^2

n=(15.996)^2

n=255.87

n≈256

Hence, if the standard deviation and the width of the confidence interval are both doubled then the sample size is 256.

To learn more about confidence interval link is here

brainly.com/question/24131141

#SPJ4

Answer: 200 seats

Step-by-step explanation:

There are 96 students and 34 adults in a concert. The total number of people present is therefore:

= 96 + 34

= 130 people

These 130 people only fill 65% of the seats. Assume the total number of seats is x:

130 = 65% * x

x = 130/65%

x = 200 seats

James will fully clear the loan after approximately 12 years when the remaining balance reaches zero.

To determine the number of years it will take for James to fully clear the loan, we need to calculate the remaining balance after each payment and divide the initial loan amount by the annual payment until the remaining balance reaches zero.

The loan amount is 9000 euros, and James pays off 770 euros each year. Since the interest is charged at a rate of 3% of the original amount per annum, the interest for each year will be \(0.03 \times 9000 = 270\) euros.

In the first year, James pays off 770 euros, and the interest on the remaining balance of 9000 - 770 = 8230 euros is \(8230 \times 0.03 = 246.9\)euros. Therefore, the remaining balance after the first year is 8230 + 246.9 = 8476.9 euros.

In the second year, James again pays off 770 euros, and the interest on the remaining balance of 8476.9 - 770 = 7706.9 euros is \(7706.9 \times 0.03 = 231.21\) euros. The remaining balance after the second year is 7706.9 + 231.21 = 7938.11 euros.

This process continues until the remaining balance reaches zero. We can set up the equation \((9000 - x) + 0.03 \times (9000 - x) = x\), where x represents the remaining balance.

Simplifying the equation, we get 9000 - x + 270 - 0.03x = x.

Combining like terms, we have 9000 + 270 = 1.04x.

Solving for x, we find x = 9270 / 1.04 = 8913.46 euros.

For more such questions on loan

https://brainly.com/question/25696681

#SPJ8

50 different ways. Do I have to list them? Could I also have brainliest?

Answer:

600

Step-by-step explanation: