The formula s = StartRoot StartFraction S A Over 6 EndFraction EndRoot gives the length of the side, s, of a cube with a surface area, SA. How much longer is the side of a cube with a surface area of 1,200 square inches than a cube with the surface area of 768 square inches?

For this case we have the following expression:

[tex](c ^ 4) ^ 6 = c^{24}[/tex]

By definition of power properties we have to meet:

[tex](a ^ n) ^ m = a ^ {n * m}[/tex]

This property is known as "high power to power."

Answer:

The property shown is:

High power to power.

Final answer:

The expression for the total cost is (3 × $2.00) + (2 × $1.50). After performing the calculations, the total cost for Mark's pretzels and juice is $9.00.

Explanation:

To calculate the total cost of the pretzels and juice that Mark bought, we need to multiply the quantity of each item by its price and then add the totals for each item.

The expression for the pretzels is 3 bags × $2.00 per bag, which equals $6.00. For the juice, the expression is 2 bottles × $1.50 per bottle, which equals $3.00. The total cost is the sum of these two amounts, so we have:

Total Cost = Cost of Pretzels + Cost of Juice
= (3 × $2.00) + (2 × $1.50)
= $6.00 + $3.00
= $9.00

Therefore, the total cost for the pretzels and juice is $9.00.

Answer:

option B. 18,12,12

Step-by-step explanation:

perimeter= 60 units

(consider a rectangle with sides a,b,c & d in order)

a= 18 units (given)

c=18 units (since opp. sides of a rectangle are equal)

now the remaining length= 60-(18+18)

                                          = 60 - 36

                                          = 24

so the sum of the remaining sides, ie, b+d= 24

since b and d are equal (opp.sides of a rect.)

b=d=24/2=12

therefore, b=12; c=18; d=12

i really hope i'm clear...but if i'm not then please do ask...

Answer:

Step-by-step explanation:

Perimeter of a plane shape is the distance around the shape. The formula for determining the perimeter of a rectangle expressed as

Perimeter = 2(length + width)

The rectangle has for side. Two parallel and opposite sides are equal. There, if the length of one side of the rectangle is 18 units, it means that the length of the opposite side is also 18 units.

Since the perimeter of the rectangle is 60 units, it means that

2(18 + W) = 60

18 + W = 60/2 = 30

W = 30 - 18 = 12

Therefore, the lengths, in units, of the other three sides are 18 , 12 and 12 units

Answer:

Multiplying the mass of ice by the specific latent heat of fusion of ice

Step-by-step explanation:

The heat energy required to completely melt 100 grams can be calculated by multiplying the mass of ice (100g) by the specific latent heat of fusion of ice (336J/g)

Answer:

1) [tex]31 < p<37[/tex]

For this case the values that satisfy the inequality are: 32,33,34,35,36

And we can analyze one by one the number:

[tex] a=32= 16*2[/tex] so then is a composite number because 2>1 and 16>1

[tex] a=33= 11*3[/tex] so then is a composite number because 3>1 and 11>1

[tex] a=34= 17*2[/tex] so then is a composite number because 2>1 and 17>1

[tex] a=35= 7*5[/tex] so then is a composite number because 7>1 and 5>1

[tex] a=36= 6*6[/tex] so then is a composite number because 6>1 and 6>1

So then part 1 is correct and we can see that the statement is enough or sufficient all the values on 31<P<37 are composite numbers.

2) For this cas this statement is FALSE, since we have a counterexample on this case:

[tex]a=3=1*3[/tex] and 3 is not a composite number since 1 is not >1

And since we have one element that not satisfy the condition that's FALSE.

Step-by-step explanation:

For this question we need to use the following definition "If an integer p can b expressed as the product of two integers, each of which that is greater then 1, then the integer p can be considered as a composite number". And this number is not the same as prime number.

Part 1

[tex]31 < p<37[/tex]

For this case the values that satisfy the inequality are: 32,33,34,35,36

And we can analyze one by one the number:

[tex] a=32= 16*2[/tex] so then is a composite number because 2>1 and 16>1

[tex] a=33= 11*3[/tex] so then is a composite number because 3>1 and 11>1

[tex] a=34= 17*2[/tex] so then is a composite number because 2>1 and 17>1

[tex] a=35= 7*5[/tex] so then is a composite number because 7>1 and 5>1

[tex] a=36= 6*6[/tex] so then is a composite number because 6>1 and 6>1

So then part 1 is correct and we can see that the statement is enough or sufficient all the values on 31<P<37 are composite numbers.

Part 2

For this cas this statement is FALSE, since we have a counterexample on this case:

[tex]a=3=1*3[/tex] and 3 is not a composite number since 1 is not >1

And since we have one element that not satisfy the condition that's FALSE.

Answer:

17.37

Step-by-step explanation:

y varies inversely as the square root of x

Mathematically:

y = k.root x

We first find k here

To find k, we were made to know that y is 21 and x = 361

k = y/root.x

k = 21/root. 361

k = 21/19

now what is y when x = 247

From y = k.root x

y = 21/19 * root 247

y= 21/19 * 15.72

y = 17.37

Answer:

I think the answer is 3/52

Answer:the price of one adult ticket is $24.5

the price of one youth ticket is $20.5

Step-by-step explanation:

Let x represent the price of one adult ticket.

Let y represent the price of one youth ticket.

One family spends $131 on 2 adult tickets and 4 youth tickets at an amusement park. This means that

2x + 4y = 131 - - - - - - - - - -1

Another family spends $139 on 4 adult and 2 youth tickets at the same park. This means that

4x + 2y = 139 - - - - - - - - - - -2

Multiplying equation 1 by 4 and equation 2 by 2, it becomes

8x + 16y = 524

8x + 4y = 278

Subtracting

12y = 246

y = 246/12 = 20.5

Substituting y = 20.5 into equation 1, it becomes

2x + 4×20.5 = 131

2x + 82 = 131

2x = 131 - 82 = 49

x = 49/2 = 24.5

The intensity of sound is I=7.943 × 10⁻¹¹ Wm⁻²

Step-by-step explanation:

The intensity level in dB of a sound of intensity I is given as

(10dB)log₁₀ (I/I₀), where I₀ is the intensity of threshold of hearing

The intensity of threshold of hearing I₀= 1×10⁻¹² Wm⁻²

In this question;

I=?

I₀=1×10⁻¹² Wm⁻²

Sound intensity in dB = 19 dB

Substitute values in the equation

(10dB)log₁₀ (I/I₀)= 19

(10)log₁₀ (I/1×10⁻¹²)=19

log₁₀ (I/1×10⁻¹²) =19/10

log₁₀ (I/1×10⁻¹²) =1.9

(I/1×10⁻¹²)=10^1.9

(I/1×10⁻¹²)=79.43

(I/1×10⁻¹²)=79.43

I=79.43 * 10⁻¹²

I=7.943 *10⁻¹¹ Wm⁻²

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Answer:

12.47 is the correct answer

Answer:

Part 1) [tex]\frac{a^2}{b^2}=\frac{4}{9}[/tex]

Part 2) [tex]\frac{a}{b}=\frac{2}{3}[/tex]

Part 3) [tex]\frac{a^3}{b^3}=\frac{8}{27}[/tex]

Step-by-step explanation:

Part 1) Find the ratio Area I/Area II  

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

The ratio of the areas is equal to divide the surface area cylinder I by the surface area cylinder II

Let

a^2 -----> the surface area cylinder I

b^2 ----> the surface area cylinder II

we have

[tex]a^2= 8\pi\ in^2[/tex]

[tex]b^2= 18\pi\ in^2[/tex]

Find the ratio

[tex]\frac{a^2}{b^2}=\frac{8\pi }{18\pi}[/tex]

Simplify

[tex]\frac{a^2}{b^2}=\frac{4}{9}[/tex]

That means

[tex]\frac{a^2}{b^2}=\frac{4}{9}[/tex] --->[tex]4b^2=9a^2[/tex]

Four times area cylinder II is equal to nine times the surface area of cylinder  I.  

Part 2) Find the ratio a/b

we know that

If two figures are similar, then the ratio of its corresponding sides is equal to the scale factor.

In this problem

[tex]\frac{r_1}{r_2}=\frac{h_1}{h_2}=\frac{a}{b}[/tex] ----> scale factor

we have

[tex]\frac{a^2}{b^2}=\frac{4}{9}[/tex]

so

square root both sides

[tex]\frac{a}{b}=\frac{2}{3}[/tex]

That means

[tex]\frac{r_1}{r_2}=\frac{2}{3}[/tex] --->[tex]2r_2=3r_1[/tex]

Two times radius cylinder II (r_2) is equal to three times radius cylinder I (r_1)

[tex]\frac{h_1}{h_2}=\frac{2}{3}[/tex] --->[tex]2h_2=3h_1[/tex]

Two times height cylinder II is equal to three times height cylinder I

Part 3) Find the ratio Volume I/Volume II  

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

we have

[tex]\frac{a}{b}=\frac{2}{3}[/tex] ----> scale factor

[tex]\frac{Volume\ I}{Volume\ II}=\frac{a^3}{b^3}[/tex]

substitute the values

[tex]\frac{Volume\ I}{Volume\ II}=\frac{2^3}{3^3}[/tex]

[tex]\frac{Volume\ I}{Volume\ II}=\frac{8}{27}[/tex]

[tex]8Volume\ II=27Volume\ I[/tex]

8 times volume cylinder II is equal to 27 times volume cylinder I

Dana must pay $1238.75 upfront.

Step-by-step explanation:

Given,

Cost of car = $24,650

Sales tax = 3.5%

Amount of sales tax = 3.5% of cost of car

Amount of sales tax = [tex]\frac{3.5}{100}*24650[/tex]

Amount of sales tax = [tex]\frac{86275}{100}=\$862.75[/tex]

Amount of title and tag fees = $376

Total upfront amount = Amount of sales tax + Amount of title and tag fees

Total upfront amount = 862.75+376 = $1238.75

Dana must pay $1238.75 upfront.

Keywords: percentage, sales tax

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Answer:

[tex]y=-0.36x+12.6[/tex]

Step-by-step explanation:

we know that

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

we have

(10, 9) and (35, 0)

substitute the values in the formula

[tex]m=\frac{0-9}{35-10}[/tex]

[tex]m=-\frac{9}{25}=-0.36[/tex]

The equation of the line in slope intercept form is equal to

[tex]y=mx+b[/tex]

With the slope [tex]m=-0.36[/tex] and point (35,0) substitute in the equation and solve for b

[tex]0=-0.36(35)+b[/tex]

[tex]0=-12.6+b[/tex]

[tex]b=12.6[/tex]

therefore

The equation of the line in slope intercept form is

[tex]y=-0.36x+12.6[/tex]

Answer:the percent of increase in price is 7.69%

Step-by-step explanation:

The yearbook was sold for $26 at the beginning of the year. This means that the initial price of the year book was $26.

The price has increased to $28. The amount by which it was increased would be the current price - the initial price. It becomes

28 - 26 = $2

The percent of increase in price would be

Increase/initial price × 100

It becomes

2/26 × 100 = 7.69%

The question is incomplete. Here is the complete question:

Suppose your school is having a talent show to raise money for new music supplies. You estimate that 200 students and 150 adults will attend. You estimate $200 in expenses. Write an equation to find what ticket prices you should set to raise $1000.

Answer:

[tex]200x+150y=1200[/tex]

Step-by-step explanation:

Let 'x' be price per student ticket and 'y' be the price per adult ticket.

Given:

Number of students = 200

Number of adults = 150

Total fund to be raised = $1000

Expenses cost = $200

Now, price of ticket for 1 student = 'x'

Therefore, price of tickets of 200 students = [tex]200x[/tex]

Price of ticket of 1 adult = 'y'.

Therefore, price of tickets of 150 adults = [tex]150y[/tex]

Now, total fund raised will be equal to the total money obtained from selling the tickets minus the expenses estimated.

∴ Total fund raised = Total money from tickets - Expenses.

⇒ [tex]1000=200x+150y-200[/tex]

⇒ [tex]200x+150y=1000+200[/tex]

⇒ [tex]200x+150y=1200[/tex]

Therefore, the equation to find what ticket prices you should set to raise $1000 is given as:

[tex]200x+150y=1200[/tex]

Explanation:

Marginal distribution: This distribution gives the probability for each possible value of the Random variable ignoring other random variables. Basically, the values of other variables is not considered in the marginal distribution, they can be any value possible. For example, if you have two variables X and Y, the probability of X being equal to a value, lets say, 4, contemplates every possible scenario where X is equal to 4, independently of the value Y has taken. If you want the probability of a dice being a multiple of 3, you are interested that the dice is either 3 or 6, but you dont care if the dice is even or odd.

Conditional distribution: This distribution contrasts from the previous one in the sense that we are restricting the universe of events to specific condition for other variable, making a modification of our marginal results. If we know that throwing a dice will give us a result higher than 2, then to in order to calculate the probability of the dice being a multiple of 3 using that condition, we have two favourable cases (3 and 6) from 4 total possible results (3,4,5 and 6) discarding the impossible values (1 and 2) from this universe since they dont match the condition given (note that the restrictions given can also reduce the total of favourable cases).

The joint distribution calculates the probabilities for two different events (related to two different random variables) occuring simultaneously. If we want to calculate the joint probability of a dice being multiple of 3 and greater than 2 at the same time, our possible cases in this case are 3 and 6 from 6 possible results. We are not discarding 1 or 2 as possible results because we are not assuming, that the dice is greater than 2, that is another condition that we should met in the combination of events.

The concepts of conditional distribution, marginal distribution, and joint distribution are used in statistics to analyze relationships between two variables. The joint distribution represents frequencies or probabilities of different combinations of values, the marginal distribution focuses on each variable individually, and the conditional distribution focuses on subsets of the population based on a specific condition or value.

The conditional distribution, marginal distribution, and joint distribution are concepts used in statistics to analyze relationships between two variables in a dataset.

The joint distribution represents the frequencies or probabilities of different combinations of values for the two variables. It is typically presented in a two-way frequency table or as a joint probability function.

The marginal distribution focuses on the frequencies or probabilities of each variable individually, disregarding the other variable. It represents the disconditional distribution focuses on subsets of the population defined by a specific condition or value of one variable. It represents the tribution of one variable while ignoring the other.

The distribution of one variable within a specific condition or value of the other variable.

For example, in a two-way table with gender and favorite sport, the joint distribution represents the frequencies of males and females who prefer different sports. The marginal distribution represents the frequencies of males and females overall, ignoring their sport preferences. The conditional distribution represents the frequencies of different sports within each gender.

Answer:

the recommended number of caories for a 11 year old male = 220.

Step-by-step explanation:

it is given that frank consumes 660 calories during breakfast.

660 calories is the 30 percent of recommended calories for a day.

let the number of calories required for a day be x.

therefore 30 percent of x = 660

therefore [tex]\frac{30}{100}[/tex]×x = 660

30x= 660×100

x=660×[tex]\frac{100}{30}[/tex]

x= [tex]\frac{10}{3}[/tex]×660

x= 2200

solving the equation we get x= 2200

there the recommended number of caories for a 11 year old male = 220.

Answer:$1109.23 will be in the account after 9 years

Step-by-step explanation:

Initial amount deposited into the account is $400 This means that the principal

P = 400

It was compounded annually. This means that it was compounded once in a year. So

n = 1

The rate at which the principal was compounded is 12%. So

r = 12/100 = 0.12

It was compounded for 9 years. So

n = 9

The formula for compound interest is

A = P(1+r/n)^nt

A = total amount in the account at the end of t years. Therefore

A = 400 (1+0.12/1)^1×9

A = 400(1.12)^9 = 1109.23$

Answer:

  46°

Step-by-step explanation:

The exterior angle marked 69° is the sum of the remote interior angles 23° and x. So ...

  69° = 23° +x

  x = 69° -23°

  x = 46°

Answer:

46 degrees

Step-by-step explanation:

see attached

The cost of each order of fried crab claw is $4.5 and cost of each cup of gumbo is $3.5

Step-by-step explanation:

Let,

Cost of each fried crab claw = x

Cost of each gumbo = y

According to given statement;

4x+4y=32     Eqn 1

2x+y = 12.5   Eqn 2

Multiplying Eqn 2 by 2

[tex]2(2x+y = 12.5)\\4x+2y=25\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 3 from Eqn 1

[tex](4x+4y)-(4x+2y)=32-25\\4x+4y-4x-2y=7\\2y=7[/tex]

Dividing both sides by 2

[tex]\frac{2y}{2}=\frac{7}{2}\\y=3.5[/tex]

Putting y=3.5 in Eqn 2

[tex]2x+3.5=12.5\\2x=12.5-3.5\\2x=9[/tex]

Dividing both sides by 2

[tex]\frac{2x}{2}=\frac{9}{2}\\ x=4.5[/tex]

The cost of each order of fried crab claw is $4.5 and cost of each cup of gumbo is $3.5

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The price for each cup of gumbo is $3.5.

The student's question poses a system of linear equations problem where we need to determine the cost of each order of fried crab claws and each cup of gumbo. We can define two variables: let x be the price of an order of fried crab claws and y be the price of a cup of gumbo. The first condition gives us the equation 4x + 4y = 32, and the second condition gives us the equation 2x + y = 12.5. Solving the system of equations by multiplying the second equation by 4 and subtracting from the first one yields:

8x + 4y = 50

4x + 4y = 32

(8x + 4y) - (4x + 4y) = 50 - 32

4x = 18

x = 4.5

Thus, the price for each order of fried crab claws is $4.5. Now, substituting x in one of the equations to find y we get:

2(4.5) + y = 12.5

9 + y = 12.5

y = 12.5 - 9

y = 3.5

So, the price for each cup of gumbo is $3.5.

Answer:

The time that the hose can complete the job alone is 18.513 hour.

The time that the inlet pipe can complete the job alone is 17.513 hours.

Step-by-step explanation:

Let the number of hours required to fill the pond by hose alone = x

Then the number of hours required to fill the pond by inlet pipe alone = x-1

This means that in 1 hour, the hose alone can fill 1/x of the pond.

Similarly, in 1 hour, the inlet pipe can fill 1/(x-1) if the pond.

Taken together,in 1 hour, the hose and inlet pipe can together fill:

[tex]\[\frac{1}{x} + \frac{1}{(x-1)}\][/tex] of the pond.

But this actually corresponds to 1/9 of the pond.

[tex]\[\frac{1}{x} + \frac{1}{(x-1)} = \frac{1}{9}\][/tex]

Solving:

[tex]\[\frac{x-1+x}{x(x-1)} = \frac{1}{9}\][/tex]

=> [tex]\[18x-9 = x^{2}-x\] [/tex]

=> [tex]\[x^{2}-19x+9=0\][/tex]

=> x= 18.513,0.486 ( roots of the quadratic equation)

Of these values, x=18.513 is relevant since x-1 must be non-negative.

So, the number of hours required to fill the pond by hose alone is 18.513 hours

Similarly, the number of hours required to fill the pond by inlet pipe alone is 17.513 hours

The time that the hose can complete the job alone is (-9 + √(109))/18 hour. The time that the inlet pipe can complete the job alone is (-9 + √(109))/18 + 1 hours.

Let x be the time it takes for the hose alone to complete the job. Therefore, the inlet pipe can complete the job in x + 1 hour.

From the given information, we know that the inlet pipe and the hose together can fill the pond in 9 hours.

Using the formula for work done, we can set up the following equation:

1/((x + 1) + 1/((1/x)) = 1/9

Simplifying the equation, we get:

1/(x + 1) + x = 1/9

Multiplying all terms by 9(x + 1) to eliminate the fractions, we get:

9 + 9x(x + 1) = (x + 1)

Simplifying further, we get:

9 + 9x(x + 1) = (x + 1)

9x^2 + 9x - 7 = 0

Using the quadratic formula, we can solve for x:

x = (-b ± √(b^2 - 4ac))/(2a) = (-9 ± √(9^2 - 4(-7)))/(2(9))

Simplifying, we get:

x = (-9 ± √(81 + 28))/18 = (-9 ± √(109))/18

Since the time cannot be negative, we take the positive square root:

x = (-9 + √(109))/18

Therefore, the time that the hose can complete the job alone is (-9 + √(109))/18 hour.

The time that the inlet pipe can complete the job alone is (x + 1) = (-9 + √(109))/18 + 1 hours.

Answer: $21,000

Step-by-step explanation:

Cleaning expense is only related to the floor space occupied by the department.

If the company spend a total of $30,00 on cleaning each year.

And Department B occupies 70% of the company floor.

Therefore, the company spends 70% of their cleaning expense on department B

Hence, the cleaning expense on department B is given as;

= 70% of $30,000

= $21,000

Department B should be allocated $21,000 for cleaning expenses, as it occupies 70% of the floor space and the total cleaning expense is $30,000.

To determine how much cleaning expense should be allocated to Department B at Calico Company, you should consider the proportion of floor space occupied by the department. Since cleaning expenses are primarily based on vacuuming the carpet, it's reasonable to use floor space as the basis for allocation.

Department B occupies 70% of the company's floor space. With a total annual cleaning expense of $30,000, we can calculate Department B's share of the expense by multiplying the total expense by the percentage of space that Department B occupies:

Allocated expense to Department B = Total cleaning expense × Department B's percentage of floor space

Allocated expense to Department B = $30,000 × 70%

Allocated expense to Department B = $30,000 × 0.70

Allocated expense to Department B = $21,000

Therefore, $21,000 should be allocated to Department B for cleaning expenses.

Answer:

[tex]\Omega = \{ 1HH, 1HT, 1TH, 1TT, 2H, 2T, 3HH, 3HT, 3TH, 3TT, 4H, 4T,\\5HH , 5HT, 5TH, 5TT, 6H, 6T \}[/tex]

The probability is 3/12. The third option is correct.

Step-by-step explanation:

The sample space is

[tex]\Omega = \{ 1HH, 1HT, 1TH, 1TT, 2H, 2T, 3HH, 3HT, 3TH, 3TT, 4H, 4T,\\5HH , 5HT, 5TH, 5TT, 6H, 6T \}[/tex]

Note that this sample space is not equally probable.

The probability of getting a given number followed is the probability of getting an even number from the 6 numbers (3/6) multiplied by the probability of getting a head after getting that even number, that is 1/2, because is equally probable to get heads or tails from one single coin toss (note that we are assuming that the dice was even, thats why there is a single coin toss).

Therefore, the probability of getting an even number and a head is

P( D in {2,4,6} , H = 1) = P(D in {2,4,6}) * P(H=1 | D in {2,4,6}) = 3/6 * 1/2 = 3/12.

The sample space S can be constructed by listing all possible outcomes. The probability of getting an even number on the die followed by one head is 1/4.

The sample space S can be constructed by listing all possible outcomes. Since there are 6 possible outcomes for the die and 2 possible outcomes for the coin flip, the total number of outcomes is 6 * 2 = 12. The sample space S is {1HH, 1HTT, 2H, 2HTT, 3HH, 3HT, 4H, 4HTT, 5HH, 5HTT, 6H, 6HTT}.

The probability of getting an even number on the die followed by one head can be found by counting the number of favorable outcomes (even number on the die followed by one head) and dividing it by the total number of outcomes. From the sample space, we can see that there are 3 favorable outcomes: 2H, 4H, and 6H. Therefore, the probability is 3/12, which can be simplified to 1/4.

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Answer: The ratios are proportional

Step-by-step explanation:

Tony tacos is selling 15 sodas for 10 dollars.

Nicks nachos is selling 30 sodas for 20dollars. The ratio of the number sodas sold by Tony tacos to the number of sodas sold by Nicks nachos is 15/30 = 1/2

The ratio of the cost of sodas sold by Tony tacos to the cost of sodas sold by Nicks nachos is 10/20 = 1/2

So the number of sodas sold is proportional to the cost.

Answer:

B, C and D.

Step-by-step explanation:

3m=36-6m

9m=36

m=4

-1/3m+2=-1

-1/3m=-3

m=9

So not it

B, c and d is the same as they all equal to 4.

Answer:

The answer to your question is b, c and d

Step-by-step explanation:

Equation given

                        3m = 36 - 6m

                        3m + 6m = 36

                        9m = 36

                          m = 36/9

                         m = 4

Equation a

                        -1/3 m + 2 = -1

                        -1/3 m = -1 - 2

                        -1/3 m = -3

                               m = -3 x -3

                              m = 9

Equation b

                       -2(-4m - 6.4) = 44.8

                            -4m - 6.4 = 44.8/-2

                            -4m = -22.4 + 6.4

                            -4m = -16

                                m = -16/-4

                               m = 4

Equation c

                       8m - 5 - 2m + 1 = 20

                       6m = 20 + 4

                        6m = 24

                          m = 24/6

                         m = 4

Equation d

                       7m + 6 = 9m - 2

                       7m - 9m = -2 - 6

                             - 2m = -8

                                 m = -8/-2

                                 m = 4

Answer:

a) 4.387

b) Yes, because np & npq are greater than 10.

c) = 0.017          

Step-by-step explanation:

Give data:

p = 0.69

n = 90

a) a

E(X) = np = 62.1

[tex]SD(X) = \sqrt{(np(1-p))}[/tex]

          [tex]=\sqrt{90\times 0.69(1- 0.69)}[/tex]

          = 4.387

b)

np = 62.1  

q = 1 - p  = 1 - 0.69 = 0.31

npq = 19.251

Yes, because np & npq are greater than 10.

c.

[tex]P(X \geq 72   ) = P(X > 71.5)[/tex] [continuity correction]

[tex]=    P(Z> \frac{((71.5-62.1)}{ 4.387})[/tex]

= P(Z> 2.14 )      

= 1 - P(Z<2.14)              

= 1 - 0.983   (using table)          

= 0.017          

Final answer:

The tennis player is expected to have an average of 62.1 successful first serves with a standard deviation of 4.573 in 90 attempts. A normal model is appropriate for this distribution. The probability that she makes at least 7272 first serves is approximately [tex]\( 1 - 0.9908 \approx 0.0092 \)[/tex], or about 0.92%.

Explanation:

A certain tennis player makes a successful first serve 69% of the time. If the tennis player serves 90 times in a match, we can calculate the mean and standard deviation of the number of good first serves expected, and determine if a normal model can be used to approximate the distribution.

a) Mean and Standard Deviation

The mean (μ) of the number of successful first serves can be calculated using the formula μ = n*p, where n is the total number of serves, and p is the probability of success on each serve. For 90 serves with a 69% success rate, the mean is 90*0.69 = 62.1 serves.

The standard deviation (σ) can be calculated using the formula σ = √(n*p*(1-p)). Therefore, the standard deviation for our scenario is √(90*0.69*0.31) = 4.573.

b) Normal Model Appropriateness

To determine if a normal model can approximate the distribution, we check if np and n(1-p) are both greater than 10. Here, np = 62.1 and n(1-p) = 27.9, both of which are greater than 10, indicating a normal model is appropriate.

c) Probability of At Least 72 First Serves

Given the large number of trials (9090) and the high probability of success (0.6969), we can approximate the binomial distribution with a normal distribution using the central limit theorem. The mean of the binomial distribution is [tex]\( \mu = np = 9090 \times 0.6969 \approx 6340.8841 \)[/tex] and the standard deviation is [tex]\( \sigma = \sqrt{np(1-p)} = \sqrt{9090 \times 0.6969 \times (1-0.6969)} \approx 39.9549 \).[/tex]

Now, to find the probability that she makes at least 7272 first serves, we'll use the normal approximation with continuity correction. We'll first standardize X = 7272 to find the corresponding z-score:

[tex]\[ z = \frac{X - \mu}{\sigma} = \frac{7272 - 6340.8841}{39.9549} \approx 2.3333 \][/tex]

Using a standard normal distribution table or calculator, the probability associated with z = 2.3333 is approximately 0.9908.

Thus, the probability that she makes at least 7272 first serves is approximately [tex]\( 1 - 0.9908 \approx 0.0092 \)[/tex], or about 0.92%.

Answer:

The answer to your question is letter C. [tex]t = \frac{30}{7}[/tex]

Step-by-step explanation:

                               [tex]\frac{2}{3} t - \frac{1}{5} t = 2[/tex]

                               [tex]\frac{10t - 3t}{15} = 2[/tex]

                               [tex]\frac{7t}{15} = 2[/tex]

                                              7t = 30

                                                [tex]t = \frac{30}{7}[/tex]

Answer:

14.5

Step-by-step explanation:

PLS MARK BRAINLIEST

Answer:

  A: 6 and 24

  B: 4 times as great; the rate of change increases exponentially

Step-by-step explanation:

Part A: The average rate of change on the interval [a, b] is given by ...

  average rate of change = (h(b) -h(a))/(b -a)

On the interval [1, 2], the rate of change is ...

  (h(2) -h(1))/(2 -1) = (12 -6)/1 = 6

On the interval [3, 4], the rate of change is ...

  (h(4) -h(3))/(4 -3) = (48 -24)/1 = 24

For Section A, the average rate of change is 6; for Section B, the average rate of change is 24.

__

Part B: The ratio of the rates of change on the two intervals is ...

  (RoC on [3,4]) / (RoC on [1,2]) = 24/6 = 4

The average rate of change of Section B is 4 times that of Section A.

__

The rate of change is exponentially increasing, so an interval of the same width that starts at "d" units more than the previous one will have a rate of change that is 2^d times as much.

Answer:

A

[tex]h = -16t^2 + 192t[/tex]

B

Vertex=(6,576)

Step-by-step explanation:

The problem gives us the following data:

[tex]v_o=192\ ft/s,\ h_o=0[/tex]

A.

Thus the function is

[tex]h = -16t^2 + 192t[/tex]

The graph of h has the shape of an inverted parabola. Recall if the coefficient of the quadratic term is negative, the parabola is concave down, so it has a maximum value.

Part B

Let's take the function of h

[tex]h = -16t^2 + 192t[/tex]

Factoring by -16

[tex]\displaystyle h = -16(t^2 - 12t)[/tex]

Completing squares

[tex]\displaystyle h = -16(t^2 - 12t+36-36)[/tex]

[tex]\displaystyle h = -16(t^2 - 12t+36)+576[/tex]

Factoring

[tex]\displaystyle h = -16(t-6)^2+576[/tex]

Rearranging

[tex]\displaystyle h -576= -16(t-6)^2[/tex]

We can get the coordinates of the vertex from this standard form of the parabola.

Vertex=(6,576)

The maximum value means that at t=6 seconds, the firework will be 576 feet high and then it will start falling back to the ground.