The population of a city, P , in millions, is a function of ????, the number of years since 2010, so P = ???? (????). Explain the meaning of the statement ????(5) = 7 in terms of the population of this city.

Answer:

The given sums 11+17+23+29+35+41  can be written as in sigma notation is  [tex]\sum\limits_{i=1}^{6}5+6i[/tex]

Therefore 11+17+23+29+35+41=[tex]\sum\limits_{i=1}^{6}5+6i[/tex]

Step-by-step explanation:

Given series is 11+17+23+29+35+41

To find the given sum expressed in sigma notation :

11+17+23+29+35+41  can be written as the given sums in sigma notation is  [tex]\sum\limits_{i=1}^{6}5+6i[/tex]

That is

11+17+23+29+35+41=[tex]\sum\limits_{i=1}^{6}5+6i[/tex]

Now expand the sums and to verify that whether the summation is true or not :

[tex]\sum\limits_{i=1}^{6}5+6i=(5+6(1))+(5+6(2))+(5+6(3))+(5+6(4))+(5+6(5))+(5+6(6))[/tex]

[tex]=(5+6)+(5+12)+(5+18)+(5+24)+(5+30)+(5+36)[/tex]

[tex]=11+17+23+29+35+41[/tex]

Therefore 11+17+23+29+35+41=[tex]\sum\limits_{i=1}^{6}5+6i[/tex]

The sum can be expressed as [tex]\sum_{(i=1)}^6 = 5+6i[/tex].

As we can see in the following series,

Every number in the series can be expressed in the form of (5+6i) where i is the position of the series,

The sum can be verified by expanding the sum from i=1 to6.

[tex]\sum_{(i=1)}^6 = 5+6i\\\sum_{(i=1)}^6 = [5 + 6(1)]+[5 + 6(2)]+[5 + 6(3)]+[5 + 6(4)]+[5+ 6(5)]+[5 + 6(6)]\\\sum_{(i=1)}^6 = 11 + 17 + 23 + 29 + 35 + 41\\\sum_{(i=1)}^6 = 156[/tex]

therefore, the sum can be expressed as,

[tex]\sum_{(i=1)}^6 = 5+6i[/tex].

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Answer:

Explanation:

First, you must find the pattern behind the set of data in the table shown in the question.

It is said that this is a growing exponentially pattern. Thus, the data should be modeled by a function of the form P(x) = A(B)ˣ.

And you must find both A and B.

B is the multiplicative rate of change of the function which is a constant that you can find by dividing consecutive terms:

Thus, B = 1.55

So far, you know P(x) = A (1.55)ˣ

To find A, you can use P(0)=40, which drives to:

Thus, your function is P(x) = 40(1.55)ˣ

The population of moose after 12 years, is given by P(12):

Thus, round to the nearest whole number, those are 7,692 moose.

Answer: 3x -12y

Step-by-step explanation:

Hi, to answer this question we have to add both expressions, the times "from" and "to" school.

Total time spent: time to school + time from school

Mathematically speaking:

Adding alike terms:

In conclusion, the expression that represents the total time Henry spends commuting to and from school each day is 3x -12y.

Answer:

The answer to your question is (-∞, 3)

Step-by-step explanation:

Data

y(x) = -2x² + 3

v(x) = x

Process

1.- Evaluate y(x) in v(x)

   yov(x) = -2(x)² + 3

   yov(x) = -2x² + 3

2.- Graph the function

In the graph we observe that the posible values of "y" are from (-∞, 3) that is the range.

Answer:

Explanation:

The table that shows the pattern for this question is:

Time (year) Population

  0                   40

  1                     62

  2                    96

  3                   149

  4                   231

A growing exponentially pattern may be modeled by a function of the form P(x) = P₀(r)ˣ.

Where P₀ represents the initial population (year = 0), r represents the multiplicative growing rate, and P(x0 represents the population at the year x.

Thus you must find both P₀ and r.

1) P₀

  Using the first term of the sequence (0, 40) you get:

   P(0) = 40 = P₀ (r)⁰ = P₀ (1) = P₀

Then, P₀ = 40

 2) r

Take two consecutive terms of the sequence:

You can verify that, for any other two consecutive terms you get the same result: 96/62 ≈ 149/96 ≈ 231/149 ≈ 1.55

3) Model

Thus, your model is P(x) = 40(1.55)ˣ

4) Population of moose after 12 years

Answer:

bryan walked dogs for 5.8 hours

Step-by-step explanation:

if he had $52 and the walk per hour is $9

you have to divide 52/9

52/9 is 5.77777777777...

after you roud it to the nearest tenth that is 5.8

Bryan earned $9 per hour and had a $20 expense for flyers. After subtracting his expenses from his net income of $52, we can set up an equation to find the number of hours he worked, which is 8 hours.

Let h equal the number of hours Bryan walked dogs.

Calculate his earnings by multiplying h by the rate per hour, which is $9.

Subtract his expenses, which are $20 for the flyers, from his earnings to find his net income.

Set up the equation: 9h - 20 = $52.

Add $20 to both sides of the equation to isolate the term with h on one side: 9h = $52 + $20.

Simplify the right side of the equation: 9h = $72.

Divide both sides by 9 to solve for h: h = $72 ÷ 9.

Solve for h: h = 8.

Therefore, Bryan walked dogs for 8 hours to earn a net income of $52 after his $20 expense on flyers.

Answer: A) 0.99n + 9.9

B) the total cost is $11.88

Step-by-step explanation:

Let n represent the number of songs that Sophia purchases.

A) Sophia pays a $9.99 membership fee for Apple Music. If Sophia purchases n songs for $0.99 each,then an expression for the total cost would be

0.99n + 9.9

B) If she buys two songs from a new album at a price of $0.99 each, it means that the total cost would be

0.99 × 2 + 9.9

= 1.98 + 9.9

= $11.88

Answer:

Tara need to run 2 laps today.

Step-by-step explanation:

Number of laps in 1 mile = 3 laps

number of miles she wants to run today = [tex]\frac{2}{3}[/tex]

We need to find the number of lap she need to run today;

Solution:

Now we know that;

in 1 mile = 3 laps

In [tex]\frac{2}{3}[/tex] miles = number of laps in [tex]\frac{2}{3}[/tex] miles

By using Unitary method we get;

number of laps in [tex]\frac{2}{3}[/tex] miles = [tex]3\times\frac{2}{3} = 2\ laps[/tex]

Hence Tara need to run 2 laps today.

Option B

[tex]\frac{a^2b^7c^2}{a^2c^2} = b^7[/tex]

Solution:

Given that, we have to simplify the given expression

Given expression is:

[tex]\frac{a^2b^7c^2}{a^2c^2}[/tex]

We can simplify the expression by cancelling the common terms in numerator and denominator

Take the common terms out in given expression

[tex]\frac{a^2b^7c^2}{a^2c^2} = \frac{a^2c^2(b^7)}{a^2c^2}[/tex]

Cancel the common terms in numerator and denominator

[tex]\frac{a^2b^7c^2}{a^2c^2} = \frac{a^2c^2(b^7)}{a^2c^2} = b^7[/tex]

Thus the simplified form of given expression:

[tex]\frac{a^2b^7c^2}{a^2c^2}=b^7[/tex]

Thus option B is correct

==========================================

Explanation:

As you stated in problem 4, tan(angle) = opposite/adjacent

We'll use this idea to help find angle Z. First lets set up the proper tangent ratio for this problem

tan(Z) = XY/YZ

tan(Z) = 8/10

tan(Z) = 0.8

To isolate Z, we need to undo the tangent function. We will use the inverse tangent or the arctangent function to do this.

tan(Z) = 0.8

arctan( tan(Z) ) = arctan(0.8)

Z = 38.6598 which is approximate

This rounds to 38.66

Answer:

5/12

Step-by-step explanation:

For a coin

Number of sample space = 2

Probability of flipping a tail = 1/2

P(T) = 1/2

For a die

Number of sample space = 6

Let D be the event of rolling at least 2.

D = {2,3,4,5,6}

P(D) = 5/6

P(T) and P(D) = P(T) * P(D)

= 1/2 * 5/6

= 5/12

Answer:

1/12

Step-by-step explanation:

got it right

Answer: 1/5

Step-by-step explanation:

P(both are Orange)

P(at least one is orange)

By using conditional probability:

-The P(both are Orange) is (2C2)/4C2)=1/6

-at least one orange is 1 - 1/6=5/6

P(both are Orange / at least one is orange)=(1/6) / (5/6)

=6/30

=1/5

Given one ball has been established to be orange with no replacement, there are three possible outcomes left in the urn (OO, OB, BO). Only one outcome contains both balls as orange, hence, the probability is 1/3 or approximately 0.333.

Here, we already know that one ball selected is orange from an urn containing two orange and two blue balls. There was no replacement after the first draw, reforming the context of the problem and the counts of the balls in the urn for the second draw.

For the two-draw scenario under question, there are a total of six possible outcomes: (Orange, Orange), (Orange, Blue), (Blue, Orange), (Blue, Blue) - but since we know that at least one ball is orange, the (Blue, Blue) outcome is impossible, leaving us with three valid outcomes. Among these, only one outcome has both balls Orange.

Therefore, the probability that the other ball is also orange, given that at least one is Orange, is 1/3 or approximately 0.333, assuming that all outcomes are equally likely.

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Final answer:

The distribution of the sample means from samples of size n=600 is a normal distribution, according to the Central Limit Theorem, option C.

Explanation:

When samples of size n=600 are taken and the mean age is calculated from each sample, the distribution of sample means is best described by a normal distribution. This is due to the Central Limit Theorem which states that as the sample size becomes large (n ≥ 30 is a commonly used threshold), the sampling distribution of the sample means will tend to be normal regardless of the shape of the population distribution.

This property of the distribution of sample means applies as long as the samples are taken with replacement or if sampling without replacement, the population is at least ten times larger than the sample. In this case, with a sample size of 600, which is well above 30, we can confidently expect the distribution of sample means to follow a normal distribution.

Answer:

Hilang = 10%

(Di sini tanda negatif dihilangkan karena sudah ditetapkan sebagai hilang )

Step-by-step explanation:

Kami memiliki bahwa jika Rp 50.000.000 sama dengan 100%, berapa yang seharusnya mewakili Rp 45.000.000?

[tex]x=\frac{45.000.000Rp*100}{50.000.000Rp}=90[/tex]

90 ini adalah persentase yang mewakili 45.000.000, jadi kerugiannya dinyatakan sebagai:

h=(nilai jual /biaya )*100%-100% = (nilai jual /biaya -1)*100% = -10%

perhatikan: tanda negatif mewakili kerugian, keuntungan positif

Answer:

Aubrey tip $25.50 tip to the staff.

Step-by-step explanation:

Aubrey's dinner cost $ 85.

She tips the waitstaff 30%, percent for excellent service.

Now, to find the tip Aubrey pay to the staff.

Cost of dinner = $85.

Percent of tip = 30%.

So, to get the amount of tip:

30% of $85.

[tex]=\frac{30}{100} \times 85[/tex]

[tex]=0.30\times 85[/tex]

[tex]=\$25.50.[/tex]

Therefore, Aubrey tip $25.50 tip to the staff.

Final answer:

Aubrey tips the waitstaff $25.50 for excellent service on an $85 meal by converting the tip percentage to a decimal and multiplying it with the cost of her meal.

Explanation:

To calculate the tip that Aubrey would leave for excellent service, we first convert the tip percentage to a decimal by dividing by 100. A 30% tip becomes 0.30 in decimal form. Then, we multiply the decimal tip rate by the cost of her meal to find the amount of the tip.

For Aubrey's dinner which cost $85, the calculation would be as follows:

The exact calculation: $85 * 0.30 = $25.50.

Hence, Aubrey tips the waitstaff $25.50 for her $85 meal.

Final Answer:

The correct simplified ratio of US to British stamps is 25 : 2, which corresponds to answer choice E.

Explanation:

To determine the ratio of US to British stamps, we must use the given ratios of US to Indian and Indian to British stamps.

The given ratio of US to Indian stamps is 5 to 2. This means for every 5 US stamps there are 2 Indian stamps. We can represent this as:

US : Indian = 5 : 2

The given ratio of Indian to British stamps is 5 to 1. This implies that for every 5 Indian stamps, there is 1 British stamp. We can write this as:

Indian : British = 5 : 1

To find the ratio of US to British stamps, we need to combine these two ratios. To do this, we should express each ratio such that the Indian stamp part of each ratio is the same. Since the ratios already have the same number of Indian stamps (5 of them), we can directly multiply the US part by the British part across these ratios.

Thus, we multiply the number of US stamps (5 from the first ratio) by the number of British stamps (1 from the second ratio):

US to British = 5 (US) * 1 (British)
US to British = 5

Since we did not have to multiply the number of British stamps by anything (they were only multiplied by 1), the British part of the ratio remains unchanged.

Next, we multiply the Indian part of the first ratio by the British part of the second ratio:

Indian to British = 2 (Indian from the first ratio) * 5 (British from the second ratio)
Indian to British = 10

Now we can combine these two results to express the US to British ratio:

US to British = 5 (US) : 10 (British)

To simplify this ratio, we divide both sides by the common factor between them. In this case, that common factor is 5. So when we divide both numbers by 5, we have:

US to British = (5/5) : (10/5)
US to British = 1 : 2

However, this is not the option given in the question. Let's revisit the calculation and see if there was an error:

The correct approach to combining the ratios is to multiply the two ratios directly:

US : Indian = 5 : 2
Indian : British = 5 : 1

Multiplying across gives us:

US : British = (5 * 5) : (2 * 1)
US : British = 25 : 2
The correct simplified ratio of US to British stamps is 25 : 2, which corresponds to answer choice E.

Answer:

The equation representing the the scenario is [tex]72+6m=144[/tex].

It will take 12 month for the company to doubled the number of employees.

Step-by-step explanation:

Given:

Number of employees in the company =72

Number of employee increase per month = 6

We need to find the number of months required to double the number of employees.

Solution:

Doubled number of employees = [tex]2\times[/tex] Number of employees = 144

Let the number of months be 'm'

So we can say that;

Doubled number of employees is equal to Current number of employees in the company plus Number of employee increase per month multiplied by number of months.

framing in equation form we get;

[tex]72+6m=144[/tex]

Hence The equation representing the the scenario is [tex]72+6m=144[/tex].

On solving the above equation we get;

we will subtract both side by 72 we get;

[tex]72+6m-72=144-72\\\\6m=72[/tex]

Dividing both side by 6 we get;

[tex]\frac{6m}{6}=\frac{72}{6}\\\\m =12[/tex]

Hence It will take 12 month for the company to doubled the number of employees.

Answer:The new perimeter of the field is 2800 feet.

Step-by-step explanation:

The formula for determining the area of a square is expressed as

Area = 4L

Where L represents length of each side of the square.

The small farm field is a square measuring 350 ft on a side. This means that the perimeter of the field would be

Perimeter = 350 × 4 = 1400 feet.

If you double the length of each side of the field, the new length would be

350 × 2 = 700 feet.

The new perimeter of the field would be

700 × 4 = 2800 feet

Answer:

Bottles of soda filled on March 11.

Step-by-step explanation:

Population is usually constitutes of the set that contains the set of all possible observation in the undergoing study.

Here, sample known as the part of population consists of 80 bottles selected from the bottles of soda filled on March to check the calibration of filling machine. So, the population in the given scenario consists of the bottles of soda filled on March 11.

Answer:

Therefore, ' 19 ' smaller lawn mover and '11' larger lawn mover were sold.

Step-by-step explanation:

Given:

let the smaller lawn mover  be 'x'

let the larger lawn mower be 'y'

According to condition total mover will be

[tex]x+y=30\\x=30-y[/tex]................( 1 )

and total cost will be given as

[tex]249.99x+329.99y=8379.7[/tex]................( 2 )

To Find:

x =? and y =?

Solution:

Substituting equation 1 in equation 2 we get

[tex]249.99(30-y)+329.99y=8379.7\\7499.7-249.99y+329.99y=8379.7\\80y=880\\\\y=\dfrac{880}{80}\\\\y=11[/tex]

Substituting ' y 'in ( 1 ) we get

[tex]x=30-11=19\\x=19[/tex]

Therefore, ' 19 ' smaller lawn mover and '11' larger lawn mover were sold.

Answer:Robert's minimum age is 11 years.

Step-by-step explanation:

Let x represent George's age.

Let y represent Edward's age.

Let z represent Robert's age.

George is twice as old as Edward. It means that

x = 2y

Edward's age exceeds Robert's age by 4 years. It means that

z = y - 4

If the sum of the three ages is at least 56 years, it means that

x + y + z ≥ 56 - - - - - - - - - - 1

Substituting x = 2y and z = y - 4 into equation 1, it becomes

2y + y + y - 4 ≥ 56

4y - 4 ≥ 56

4y ≥ 56 + 4

y ≥ 60/4

y ≥ 15

z = y - 4 = 15 - 4

z ≥ 11

Final answer:

To find Robert's minimum age, we need to calculate the ages of Edward, George, and Robert based on the given information.

Explanation:

Minimum Age Calculation:

Let's denote the age of Edward as E, George as 2E (twice as old as Edward), and Robert as E - 4 (Edward's age exceeds Robert's by 4 years).

The sum of their ages is at least 56, so E + 2E + (E - 4) ≥ 56.

Solving the inequality, we get E ≥ 20, George's age (2E) is at least 40, and Robert's minimum age (E - 4) is at least 16.

Answer:

0.5

Step-by-step explanation:

Probability is the possibility of an event happening,

probability = number of required outcomes/ number of possible outcomes

number of red marbles = 10

number of blue marbles = 15

The selection of two marbles  is done without replacement.

Pr( of same color) = RR or BB

which means; (the first is red and second is red) or (the first is blue and the second is blue)

OR in probability means adition while AND means multiplication.

Pr( of same color) = [tex](\frac{10}{25}*\frac{15}{24})+(\frac{15}{25}*\frac{10}{24})[/tex]

                    =[tex]\frac{1}{4} +\frac{1}{4}[/tex]

      =0.5

Probabilities are used to illustrate the chances of an event

The probability that marbles of the same color are picked is 0.50

The numbers of marbles are given as:

[tex]\mathbf{Red =10}[/tex]

[tex]\mathbf{Blue =15}[/tex]

[tex]\mathbf{Total =25}[/tex]

The probability that marbles of the same color are picked is:

[tex]\mathbf{Pr = (Red\ and\ Red) + (Blue\ and\ Blue)}[/tex]

So, we have:

[tex]\mathbf{Pr = (10/25 \times 9/24) + (15/25 \times 14/24)}[/tex]

[tex]\mathbf{Pr = (0.15) + (0.35)}[/tex]

Add

[tex]\mathbf{Pr = 0.50}[/tex]

Hence, the probability that marbles of the same color are picked is 0.50

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Answer:

The equation use to find the value of R is [tex]55+R=110[/tex].

Step-by-step explanation:

Given:

Total Number of flowers = 110

Number of orange flowers = 55

Let the number of red flowers be represented by 'R'

We need to find the equation used to find the value of R.

Solution:

Now we know that;

Total Number of flowers is equal to sum of Number of orange flowers and Number of red flowers.

representing in equation form we get;

[tex]55+R=110[/tex]

Hence The equation use to find the value of R is [tex]55+R=110[/tex].

On Solving the above equation we get;

We will subtract both side by 55 using Subtraction property of equality.

[tex]55+R-55=110-55\\\\R=55[/tex]

Hence There are 55 red flowers in the garden.

Answer:

The answer to your question is

a) t₁ = 6 h

b) t₂ = 3h

Step-by-step explanation:

Data

v1 = 12 mph

v2 = 24 mph

total time = 9 h

Process

1.- Write equations to solve the problem

d₁ = v₁t₁    ------------------ Equation l

d₂ = v₂t₂

d₁ = d₂     because the distance is the same in both directions

t₁ = t₁

t₂ = 9 - t₁

d₂ = v₂(9 - t₁)  -------------- Equation 2

- Equal both equations

    v₁t₁ = v₂(9 - t₁)

- Substitute v₁ and v₂

   12t₁ = 24(9 - t₁)

- Solve for t₁

    12t₁ = 216 - 24t₁

    12t₁ + 24t₁ = 216

              36t₁ = 216

                  t₁ = 216 / 36

                  t₁ = 6 h

- Calculate t₂

t₂ = 9 - 6

t₂ = 3 h

Answer:

6 minutes

Step-by-step explanation:

Let the volume of the sink be Xm^3

The rate of filling the sink by the first faucet is R1 while the rate of draining the faucet is -R2(negative since it’s draining)

R1 = x/2

R2 = -x/3 ( negative as it is draining)

The time it would take both of them working at the same rate to fill the sink is as follows:

x/(R1 - R2) = T

x/( x/2 - x/3) = T

x = T(x/2 - x/3)

x = T( (3x - 2x)/6)

x = T(x/6)

x = Tx/6

6x = Tx

T = 6 minutes

We need more data about the box dimensions to calculate the savings. The formula involves multiplying the cost per square foot with the difference in surface areas and number of boxes. The idea of economies of scale isn't directly applicable in this context.

In order to answer this question, we would require additional information about the dimensions of the boxes and their surface areas. The cost difference between making boxes with different surface areas can be found by multiplying the difference in surface areas by the cost per square foot and then by the number of boxes.

The formula used would be: $1.10 (Cost per Square Foot) * Difference in Surface Areas * 900 (Number of Boxes).

In case of economies of scale, like the information provided about alarm clocks, the cost per box would decrease as the number of boxes produced increases. But this concept isn't directly applicable here as we're dealing with the material cost of the boxes, not the production cost.

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Answer:

Table 3

Step-by-step explanation:

The third one.

We have the function

                               [tex]h(x) = \sqrt[3]{-x+2}[/tex]

Now we will insert values of x in that definition o h(x) and see if the values we obtain match the corresponding y values in the table:

                  [tex]h(-6) = \sqrt[3]{-(-6)+2}= \sqrt[3]{6+2}= \sqrt[3]{8} = 2\\h(1) = \sqrt[3]{-1+2}= \sqrt[3]{1}= 1\\h(2) = \sqrt[3]{-2+2}= \sqrt[3]{0}= 0\\h(3) = \sqrt[3]{-3+2}= \sqrt[3]{1}= 1\\h(10) = \sqrt[3]{-10+2}= \sqrt[3]{-8}= -2[/tex]

We can see that the values match the table 3, so the table 3 represents points on the graph of h(x)

Answer:

C

Step-by-step explanation:

Answer:

The answer is -343.

Step-by-step explanation:

If a term doesn't have an exponent, it's considered that the exponent is 1 (so basically, (-7)² x (-7)^1.

Multiply the terms with the same base (by adding the exponents - (-7)²+1<- (as the exponential value) (couldn't find the sign so sorry.)

Add the numbers: (-7)³

A negative base raised to an odd power equals a negative: -7³

Write the problem out: -(7 x 7 x 7).

Multiply: -343

Answer:

her weekly allowance is $16

Step-by-step explanation:

Let x represent Imani's weekly allowance.

Imani spent half of her weekly allowance playing Mini-golf. This means that the total amount that she spent playing Mini-golf is x/2. The amount that she is left with would be

x - x/2 = x/2

In order to earn more money her parents let her wash the car for $4. This means that the total amount left with her is

x/2 + 4

if she ended with $12, it means that

x/2 + 4 = 12

x/2 = 12 - 4 = 8

x = 2 × 8 = $16