Find a1, d, and the Explicit Rule for this arithmetic sequence: -3, 4, 11, 18, 25, ...
1.)a1 =-3, d=-7, an = -7n - 3
2.)a1 =-3, d = 7, an = 7n - 10
3.)21 = -3, d =-7, an = -7n - 10
4.)a1 = -3, d = 7, an = 7n - 3​

Answer:

0.91

Step-by-step explanation:

1 - P(both left handed)

1 - 0.3² = 0.91

Answer:

Step-by-step explanation:

Let us assume that she makes 10 minutes of call.

Telecorp has a flat rate of 7 cents per minute. If she uses this cell phone service, the amount that she would pay for 10 minutes of call is

0.07 × 10 = $0.7

America's charges 25cents per call. If she uses this cell phone service, the amount that she would pay for 10 minutes of call is $0.25

Phone busters charges 35 cents per call and 2 cents per min. If she uses this cell phone service, the amount that she would pay for 10 minutes of call is

0.35 + 10 × 0.02

= 0.35 + 0.2

= $0.55

The cheapest service is that of America's. Therefore, she should choose it.

Answer:

The Volume of the Shoebox is therefore  5884.7[tex]cm^3[/tex]

Step-by-step explanation:

The edges of a shoebox are measured to be 11.4 cm, 17.8 cm, and 29 cm.

We want to determine the volume of the box.

The Shoebox is in the shape of a Cuboid and;

Volume of a Cuboid=Length X breadth X height

Volume of the Shoebox= 11.4.X 17.8 X 29 =5884.68[tex]cm^3[/tex]

=5884.7[tex]cm^3[/tex] (correct to 1 decimal place)

The volume of the box is 5884.68 cubic cm.

Important information:

We need to find the volume of the box.

The volume of a cuboid is:

[tex]V=l\times b\times h[/tex]

Where [tex]l[/tex] is length, [tex]b[/tex] is breadth and [tex]h[/tex] is height.

The volume of the box is:

[tex]V=11.4\times 17.8\times 29[/tex]

[tex]V=5884.68[/tex]

Therefore, the volume of the box is 5884.68 cubic cm.

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Answer:

Given: ​ BD ​is an altitude of △ABC .

Prove: sinA/a=sinC/c

Triangle ABC with an altitude BD where D is on side AC. Side AC is also labeled as small b. Side AB is also labeled as small c. Side BC is also labeled as small a. Altitude BD is labeled as small h.

Statement Reason

​ BD is an altitude of △ABC .

Given △ABD ​ and ​ △CBD ​ are right triangles. (Definition of right triangle)

sinA=h/c and sinC=h/a

Cross multiplying, we have

csinA=h and asinC=h

(If a=b and a=c, then b=c)

csinA=asinC

csinA/ac=asinC/ac (Division Property of Equality)

sinA/a=sinC/c

This rule is known as the Sine Rule.

Answer:

For the people on Edge the answers are:

a/f

cf

c/b

cf + ec

c

Answer:

Population parameter

Step-by-step explanation:

We are given the following in the question:

74% of all instructors at your school teach 2 or more classes.

Parameter and statistic:

Population:

all instructors at your school

Parameter:

74% of all the instructors at your school teach 2 or more classes

Thus, 74% describes the population that takes two or more classes.

Hence, it is a population parameter.

Answer:

a) The maximum revenue is ​$312500

b) The maximum​ profit is $89000, the production level that will realize the maximum​ profit is 1800, and the price the company should charge for each television set is $160.

C) If the government decides to tax the company ​$55 for each set it​ produces, the sets should the company manufacture each month to maximize its​ profit is 1250. the maximum​ profit is $70825 What should the company charge for each​ set is $187.5

Step-by-step explanation:

a) Revenue R(x)

R(x) = p(x) * x = x * [tex](250-\frac{x}{20})[/tex] = [tex](250x-\frac{x^{2} }{20})[/tex]

For maximum revenue, the first derivative of R(x) = R'(x) = 0

R'(x) = [tex](250-\frac{2x}{20}) = 0[/tex]

[tex](250-\frac{2x}{20}) = 0\\[/tex]

[tex]250=\frac{2x}{20}[/tex]

x = 2500

the second derivative of R(x)=R''(x)

R''(x) = -1/10 which is less than 0.

Maximum revenue is at x = 2500

R(2500) = [tex](250*2500-\frac{2500^{2} }{20})=312500[/tex]

b) Profit P(x)

P(x) = R(x) - C(x) = [tex](250x-\frac{x^{2} }{20})-(73000+70x) = -73000+180x-\frac{x^{2} }{20}[/tex]

For maximum profit, the first derivative of P(x) = P'(x) = 0

P'(x) = [tex]180-\frac{2x }{20}=0[/tex]

[tex]180=\frac{2x }{20}[/tex]

x = 1800

the second derivative of P(x)=P''(x)

P''(x) = -1/10 which is less than 0.

For maximum profit, x = 1800

Therefore P(1800)[tex]=-73000+180*1800-\frac{1800^{2} }{20}[/tex] = 89000

The price the company should charge for each television set is  p(1800) =[tex](250-\frac{1800}{20}) = 160[/tex]

c) f the government decides to tax the company ​$55 for each set it​ produces, the new cost C(x) = 73000 + 125x

Profit P(x)

P(x) = R(x) - C(x) = [tex](250x-\frac{x^{2} }{20})-(73000+125x) = -73000+125x-\frac{x^{2} }{20}[/tex]

For maximum profit, the first derivative of P(x) = P'(x) = 0

P'(x) = [tex]125-\frac{2x }{20}=0[/tex]

[tex]125=\frac{2x }{20}[/tex]

x = 1250

the second derivative of P(x)=P''(x)

P''(x) = -1/10 which is less than 0.

For maximum profit, x = 1250 hence 1250 sets should the company manufacture each month to maximize its profit

Therefore P(1800) =[tex]-73000+125*1250-\frac{1250^{2} }{20}[/tex] = 70825

The price the company should charge for each television set is  p(1250) =[tex](250-\frac{1250}{20}) = 187.5[/tex]

The probable number of prople sent to US emergency rooms by 2090 can be between 22,050 and 23,100

Step-by-step explanation:

Total sent to US emergency room by 2010= 21000

The estimated increase in the rise of cases = 5 to 10% by 2090

Final numbers in 2090

Hence the final numbers in 2090 would be 5 to 10% more than the total cases in 2010

Lower limit= 5% of 21000= 1050

Hence lower limit of cases in 2090= 21000+1050= 22050

Upper limit of cases in 2090= 10% of 21000= 21000+2100= 23,100

The number would lie anywhere between 22050 and 23,100 in 2090

Answer:

T = 25 + 12 * h

Step-by-step explanation:

To find the rate of the tuner it is necessary to go to an equation:

First would be the full rate that has a value of 25. And for every hour that is 12.

That is to say:

T = 25 + 12 * h

h being the hours it takes to tune the piano. And this equation would reprehend what the piano tuner

Answer:

The probabilities are 3/8, 1/8 and 3/8 respectively

Step-by-step explanation:

The sample space for the provided case can be written as:

S= {(bbb, bbg, bgb, bgg, gbb, gbg, ggb, ggg)}

Here, boy child is denoted by "b" and girl child by "g".

Total number of outcomes are 8.

Number of outcomes that show exactly boys = 3.

Number of outcomes that show exactly 3 boys = 1

Number of outcomes that show exactly 1 boy = 3.

Thus, the required probabilities can be calculated as:

(a)

[tex]\\P( Exactly 2 boys) =\frac{3}{8}[/tex]

(b)

[tex]P( Exactly 3 boys) =\frac{1}{8}[/tex]

(c)

[tex]P(Exactly 1 boy)= \frac{3}{8}[/tex]

Thus, the required probabilities are 3/8, 1/8 and 3/8 respectively.

This is a problem in Mathematics, specifically probability, at the High School level. The student is asked to calculate the probability of certain gender distributions among three children. The outcomes are determined and the respective probabilities calculated: the probability for exactly 2 boys and 1 boy is found to be 3/8 each, while for exactly 3 boys it's 1/8.

This question pertains to the understanding of probability in a specific scenario: calculating the likelihood of certain outcomes when a couple has three children. Given that each child can be a boy or a girl (2 possibilities), and there are three children, there are 2^3 or 8 total possible outcomes.

a. To find the probability of having exactly 2 boys, we count the outcomes where that is the case: BBG, BGB, GBB. This is three outcomes, so the probability is 3/8.

b. There is only one outcome where all three children are boys (BBB), therefore the probability of exactly 3 boys is 1/8.

c. The outcomes with exactly 1 boy are BGG, GBG, GGB. This gives us three outcomes, hence the probability is also 3/8.

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Answer:

The larger surface area would be 756 [tex]Unit^2[/tex]

Step-by-step explanation:

Given the surface area of rectangular prism is 336 [tex]Unit^2[/tex] when its width is 4 [tex]Unit[/tex].

We need to compute the surface area when its width is 6 [tex]Unit[/tex].

Also, it was given that prisms are similar to each other.

Let us assume the [tex]l[/tex] is length [tex]b[/tex] is width and [tex]h[/tex] is the height of the prism.

So, the surface area would be

[tex]S=2(lb)+2(bh)+2(hl)[/tex]

[tex]336=2(4l)+2(4h)+2(hl)[/tex] Equation (1)

Now, the new width is 6 [tex]Unit[/tex]. That is 1.5 times the previous width. And those prisms are similar, which means other dimensions will also be 1.5 times the previous one.

We can write

[tex]b'=1.5\times b=1.5\times 4=6\\l'=1.5\times l\\h'=1.5\times h[/tex]

So, the new surface area would be

[tex]S'=2(l'b')+2(b'h')+2(h'l')\\S'=2(1.5\times l\times 1.5\times 4)+2(1.5\times4 \times 1.5\times h)+2(1.5\times h\times 1.5\times l)\\S'=2.25\times 2(l4)+2.25\times 2(h)+2.5\times 2(hl)[/tex]

[tex]S'=2.25[2(4l)+2(4h)+2(hl)][/tex]

From Equation (1) we can plug [tex]336=2(4l)+2(4h)+2(hl)[/tex]

[tex]S'=2.25\times 336=756\ Unit^2[/tex]

So, the larger surface area would be 756 [tex]Unit^2[/tex]

Answer:

2.79588001734

Step-by-step explanation:

If you use the log button on your calculator

log625 or log(625)

you get 2.79588001734

Answer:

2.79588001734

Step-by-step explanation: but you can solve for the nearest ten thousand just use a scientific calculator and input the numbers with or before log. Depends what type of scientific calculator you use.

Answer:

a) For the function [tex]48(1.25)^x[/tex], the parameter for the growth factor is 1.25

c) For the function [tex]28(0.5)^x[/tex], the parameter for the decay factor is 50%.

d) For the function y = 18x + 72, the parameter for the average rate of change is 18.

Step-by-step explanation:

We are given the following in the question:

a) the parameter for the growth factor is 1.25.

[tex]f(x) = 48(1.25)^x[/tex]

Comparing it to

[tex]y(x) = a(1+r)^x[/tex]

The growth factor is

[tex]1+r = 1.25[/tex]

Thus, the given statement is true

b) the parameter for the beginning value is 75.

We are given the equation

[tex]f(x) = 75x + 250[/tex]

The beginning value is given when x = 0. Putting value, we get

[tex]f(0) = 75(0) + 250 = 250[/tex]

Thus, the beginning value is 250.

Hence, the given statement is false.

c) the parameter for the decay factor is 50%.

[tex]f(x) = 28(0.5)^x[/tex]

Comparing it to

[tex]y(x) = a(1-r)^x[/tex]

The growth factor is

[tex]1-r = 0.5 = 50\%[/tex]

Thus, the given statement is true

d) the parameter for the average rate of change is 18.

[tex]y = 18x + 72[/tex]

Comparing to general form of equation:

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

where m is the slope and gives the average rate of change.

Thus, the average rate of change is 18.

Hence, the given statement is true.

Final answer:

The sample mean (μ) and standard deviation (σ) are calculated using the provided z-scores and corresponding sample values, resulting in a mean of 30 and a standard deviation of 10.

Explanation:

To solve for the sample mean and standard deviation using the given z-scores and sample values, we can employ the formula for calculating a z-score:

z = (X - μ) / σ

where X is the sample value, μ is the mean, and σ is the standard deviation. For X = 45 with a z-score of 1.50, the equation is:

1.50 = (45 - μ) / σ

For X = 40 with a z-score of 1.00, the equation becomes:

1.00 = (40 - μ) / σ

By solving these two equations simultaneously, we can find the values of μ and σ.

From the first equation, we have:

1.50σ = 45 - μ

From the second equation, we have:

1.00σ = 40 - μ

If we multiply the second equation by 1.5, it becomes:

1.50σ = 60 - 1.5μ

We can set the expressions for 1.50σ equal to each other:

45 - μ = 60 - 1.5μ

Solving for μ gives us the sample mean:

μ = 60 - 45 = 15 / (1.5 - 1) = 15 / 0.5 = 30

To find the standard deviation σ, we substitute μ = 30 into one of the original equations:

1.50σ = 45 - 30 = 15

Therefore, σ = 15 / 1.50 = 10

So, the sample mean (μ) is 30 and the sample standard deviation (σ) is 10.

Final answer:

The sample mean (μ) is 30 and the standard deviation (σ) is 10.

Explanation:

The question is asking to find the sample mean and standard deviation based on given z-scores for specific values in a normal distribution.

To find these parameters, we'll use the formula for calculating a z-score:

z = (X - μ) / σ, where z is the z-score, X is the value, μ is the mean, and σ is the standard deviation.

These two equations can be solved simultaneously to find the values of μ and σ.

Steps for solving them are:

Therefore, the sample mean (μ) is 30 and the standard deviation (σ) is 10.

Answer:

5f+3g=5.70

2f+10g=3.60

Step-by-step explanation:

Cost of 1 piece of fudge =f

Cost of 1 piece of bubble gum =g

If Chase bought 5 pieces of fudge and 3 pieces of bubble gum for a total of $5.70.

Chase's Cost:

For 5 pieces of Fudge, his cost is 5f

For 3 pieces of bubble gum, his cost is 3g

His Total, 5f+3g=$5.70

Sara bought 2 pieces of fudge and 10 pieces of bubble gum for a total of $3.60.

Sara's Cost:

For 2 pieces of fudge, her cost is 2f

For 10 pieces of bubble gum, her cost is 10g

Her Total, 2f+10g=$3.60

The system of equation that could be used to determine the cost of 1 piece of budge and bubblegum is then:

5f+3g=$5.70

2f+10g=$3.60

The equation is [tex]155p+225f=5050[/tex].

If p = 17, f = 13. This value is a reasonable value in this context.

If f = 28, p = -10. This value is not reasonable in this context.

Step-by-step explanation:

Step 1:

[tex]155p+225f=5050[/tex],

where p is the part-time memberships and f is the number of full-time memberships.

Kiri needs to make $5,050 a month from this rented space.

Each part-time membership costs $155 and each full-time membership costs $225.

Step 2:

We need to calculate the value of f when p = 17,

Substituting the value, p = 17 in the equation, we get;

[tex]125(17)+225f=5050[/tex], [tex]225f=5050-125(17),[/tex]

[tex]225f=2925, f = \frac{2925}{225}, f =13.[/tex]

The value of f = 13 and p = 17. This is a reasonable value in this context.

Step 3:

We need to calculate the value of p when f = 28,

Substituting the value, f = 28 in the equation, we get;

[tex]125p+225(28)=5050[/tex], [tex]125p=5050-225(28)[/tex]

[tex]125p=-1250, p = \frac{-1250}{125}, p=-10.[/tex]

The value of f = 28 and p = -10. This is not a reasonable value in this context. as the values of f and p cannot be negative for this given equation.

Answer:

C.  16 + 1/12

Step-by-step explanation:

5 + 1/2  =  11/2 =  66/12

6 + 1/3  =  19/3   =  76/12

4 + 1/4  =  17/4   =   51/12

66/12  +  76/12  +  51/12  =  193/12

193/12  =  16 +  1/12

Answer:

1. Stratified Random Sampling

Step-by-step explanation:

Sampling is a technique of drawing small number of representative units from population.

Stratified Random Sampling is when population is divided into : heterogenous (different) groups, homogeneous (identical) within themselves - known as Strata.

Process of drawing Sample from each such strata group is called Stratified Random Sampling. This sampling makes sample better representative of various groups in population. Eg : Dividing population in strata based on gender , religion etc & then drawing sample from each strata.

Researcher dividing students into - freshman, sophomores & other groups ; then drawing sample from each group is an example of Stratified Sampling. It creates representative sample of each student body in school .

The researcher is practicing stratified random sampling by dividing the students into groups based on their class standing and randomly selecting a sample from each group.

The researcher is practicing stratified random sampling.

In stratified random sampling, the population is divided into homogeneous groups called strata. The researcher then randomly selects a sample from each stratum to create a representative sample of the entire population.

In this case, the researcher divided the students into groups based on their class standing and randomly selected 50 students from each group.

This ensures that the sample includes students from all class standings and accurately represents the entire student body of the Scion School of Business.

Option C: [tex]\frac{4}{5}[/tex] is the slope of the line

Explanation:

The line passes through the points [tex](3,-1)[/tex] and [tex](-2,-5)[/tex]

We need to find the slope of the line.

The slope can be determined using the formula,

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Where the coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are [tex](3,-1)[/tex] and [tex](-2,-5)[/tex]

Let us substitute the points in the formula

Thus, we have,

[tex]m=\frac{-5-(-1)}{-2-3}[/tex]

Simplifying, we get,

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

Adding the numerator and denominator, we have,

[tex]m=\frac{-4}{-5}[/tex]

Cancelling the negative terms, we get,

[tex]m=\frac{4}{5}[/tex]

Thus, the slope of the line is [tex]m=\frac{4}{5}[/tex]

Therefore, Option C is the correct answer.

Answer:

int age;

age=18;

float weight;

weight=114.5F;

Step-by-step explanation:

int age; \\ it is declared as integer because 18 is an integer value

age=18; \\ initialized as 18 is stored in the variable 'age'

float weight; \\ weight is declared as float because it's value is floating or decimal value which cannot be declared as integer value

weight=114.5F; \\ F shows that it's single floating type value of 32 bits, if F is not written then it means it double floating type value which is 64 bits long

In order to declare and initialize two variables, one as an integer named 'age' initialized to '18' and the other named 'weight' initialized to '114.5', you'd write 'int age = 18;' and 'double weight = 114.5;' respectively.

To declare and initialize two variables in a programming language such as Java or C++, you would use the following syntax:

int age = 18;

double weight = 114.5;

The keyword 'int' declares an integer variable, and 'double' declares a variable for floating-point numbers. After the variable name, an equals sign ('=') is used to assign or initialize the variable to a specific value.

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Answer:

there are 5 animals in each pack.

Step-by-step explanation:

if you add 9+6= 15 then divide 15 by 3 you will get 5 as your answer

Answer: there were 5 animals in each pack.

Step-by-step explanation:

Let x represent the number of toy animals in each pack.

Josiah has 3 packs of toy animals. Each pack has the same number of animals. This means that the number of animals in the 3 packs is

3x

Josiah gives 6 animals to his sister stephanie. This is expressed as 3x - 6. If she has 9 left, it means that

3x - 6 = 9

3x = 9 + 6

3x = 15

x = 15/3

x = 5

Solution:

The circumference of a circle is given as:

[tex]\text{circumference } = 2 \pi r[/tex]

Where,

"r" is the radius of circle

We know that,

[tex]diameter = 2 \times radius\\\\d = 2 \times r\\\\d = 2r[/tex]

Thus the circumference can also written as:

[tex]\text{circumference } = 2 \pi r\\\\\text{circumference } = \pi \times d[/tex]

Thus, the circumference is found by multiplying Pi by the diameter is correct statement

The true statement about the circumference of a circle is: circumference is found by multiplying Pi by the diameter.

Therefore, the true statement about the circumference of a circle is: circumference is found by multiplying Pi by the diameter.

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Answer:

$1,579.44; yes

Step-by-step explanation:

The student will have saved $2500 over the two month period and will be able to afford the computer.

In order to calculate the amount saved over a two month period, we need to calculate the monthly savings. To do this, we subtract the monthly expenses from the monthly gross salary:

$2,500 - $1,250 = $1,250

So the monthly savings is $1,250. To find the savings over a two month period, we multiply the monthly savings by 2:

$1,250 x 2 = $2,500

The cost of the computer is $1,500 plus 5.1% sales tax. To find the total cost, we multiply $1,500 by 1.051:

$1,500 x 1.051 = $1,576.50

Since the savings over a two month period is $2,500, and the total cost of the computer is $1,576.50, the student will be able to afford the computer and have savings left over.

Answer:(x,-14) (x+6)

Step-by-step explanation:

I think correct me if I am wrong.

Answer:

6 and 15

Step-by-step explanation:

Answer:

6 and 15

Step-by-step explanation:

the factors of 90 are:

1   90

2   45

3   30

5   18

6   15

9   10

find the factors that =21

6+15=21 and 6 x 15=21

Answer:

3^2

Step-by-step explanation:

3^5/3^3=3^(5-3)=3^2

Answer:

[tex] \frac{ {3}^{5} }{ {3}^{3} } = {3}^{5 - 3} = {3}^{2} = 9[/tex]

Step by step explanation :

When dividing two fraction we subtract the powers if the bases are same.

Answer: the price of a bag of popcorn is $5.3

Step-by-step explanation:

Let x represent the price of one drink.

Let y represent the price of one bag of popcorn.

Robert spends a total of $65.25 on 4 drinks and 9 bags of popcorn. This is expressed as

4x + 9y = 65.25- - - - - - - - - - - - - - -1

Robert spends a total of $51.75 on 8 drinks and 3 bags of popcorn.

This is expressed as

8x + 3y = 51.75- - - - - - - - - - - - - - -2

Multiplying equation 1 by 8 and equation 2 by 4, it becomes

32x + 72y = 522

32x + 12y = 207

Subtracting, it becomes

60y = 315

y = 315/60

y = 5.25

Answer:

Therefore it has been draining 48 hours.

Step-by-step explanation:

Given that a water body is being drained it begins with 700 gallons of water.

Let after x hours the amount of water in the water body will 388 gallons.

The water body is draining 6.5 gallons each hour

It means

The amount of water that drain in 1 hour is 6.5 gallons.

The amount of water that drain in 2 hour is (6.5+6.5) gallons.

                                                                        =(2×6.5)gallons.

The amount of water that drain in 3 hour is( 6.5+6.5+6.5) gallons.

                                                                       =(3×6.5) gallons.

Therefore

The amount of water that drain = time ×6.5

The amount of water that drain in x hour is (x×6.5) gallons=6.5x gallons.                                                                        

Therefore the remaining water

= initial amount of water- drainage water

=(700-6.5x)gallons

According to the problem,

700-6.5x= 388

⇒ -6.5x = 388-700

⇒ - 6.5x = - 312

[tex]\Rightarrow x=\frac{-312}{-6.5}[/tex]

⇒ x= 48

Therefore it has been draining 48 hours.

Answer:

A

Step-by-step explanation:

FOIL:First,Inner,Outer,Last

After the polynomial operations are done we can see that A is the answer.

6g*8g=48g^2

6g*3h=18gh

8g*-5h=-40gh

-5h*3h=-15h

After combining like terms we get :

48g^2-22gh-15h^2

Step-by-step explanation:

[tex](f - g)(x) = f(x) - g(x) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = (2x - 4) - ( {x}^{2} + 3) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2x - 4 - {x}^{2} - 3 \\ \red{ \boxed{\therefore (f - g)(x) = - {x}^{2} + 2x - 7}}[/tex]