The Houston Astros fan population is 1,450,000 and is decreasing at an annual rate of 0.99% per year .Write an exponential equation to represent this situation after x years.

Answer:

a=16

Step-by-step explanation:

The distributive property states that

[tex]a(b+c)=ab+ac[/tex]

Therefore using the distributive property

[tex](y - 4x)(y ^ 2 + 4y + 16)[/tex]

=[tex]y(y ^ 2 + 4y + 16) - 4x(y ^ 2 + 4y + 16)[/tex]

Expanding the brackets

[tex]y ^ 3 + 4y^2 + 16y - 4xy ^ 2 - 16xy - 64x[/tex].....(i)

Comparing with the form

[tex]y ^ 3 + 4y ^ 2 + ay - 4x y ^ 2 - axy - 64x[/tex]-----(ii)

The coefficient of y in (i) is 16 which corresponds to a and the likewise the coefficient of xy

Therefore, a=16

Answer:

C.) 16

Step-by-step explanation:

Answer:

(a) 0.124

(b) 0.174

Step-by-step explanation:

We are given that 60% of the Valium users in the state of Massachusetts first took Valium for psychological problems.

The Binomial distribution probability is given by;

P(X = r) = [tex]\binom{n}{r}p^{r}(1-p)^{n-r}[/tex] for x = 0,1,2,3,.......

Here, n = number of trials(samples) which is 8 in our case

           r = no. of success

          p = probability of success which is probability of users who take  

                 Valium for psychological problems of 0.60 in our case

(a) Let X = users taking Valium for psychological problems

  So, P(X = 3) = [tex]\binom{8}{3}0.6^{3}(1-0.6)^{8-3}[/tex]

                      = [tex]56 * 0.6^{3}*0.4^{5}[/tex] = 0.124

(b) Since, it is given that 60% of the Valium users in the state of  Massachusetts first took Valium for psychological problems which means 40% of the Valium users in the state of Massachusetts take Valium for problems which are not psychological.

i.e., in this case p = 0.40

So, P(X >= 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8)

= [tex]\binom{8}{5}0.4^{5}(1-0.4)^{8-5} + \binom{8}{6}0.4^{6}(1-0.4)^{8-6} + \binom{8}{7}0.4^{7}(1-0.4)^{8-7} + \binom{8}{8}0.4^{8}(1-0.4)^{8-8}[/tex]

= [tex]56 * 0.4^{5} * (0.6)^{3} + 28 * 0.4^{6} * (0.6)^{2} + 8 * 0.4^{7} * (0.6)^{1} + 1 * 0.4^{8}[/tex]

= 0.174

Using the binomial probability formula, we can determine the probabilities requested in the question. For example, the probability that exactly 3 of the next 8 users began taking Valium for psychological problems is computed using the formula for binomial probability with n=8, k=3, and p=0.60, and the probability that at least 5 began taking Valium for other reasons is computed analogously with p=0.40.

This question relates to the concepts of binomial probability and combinatorics. It asks about the probability that certain conditions are met among a specific set of Valium users.

First, to find the probability that exactly 3 of the next 8 users began taking Valium for psychological problems, we would use the formula for binomial probability: P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k)). Here, n=8 (the total number of trials), k=3 (the number of successful trials we're looking for), and p=0.60 (the probability of a single successful trial).

Calculating, we get P(X=3) = C(8, 3) * (0.60^3) * ((1-0.60)^(8-3))

For the second part of the question, we want to find the probability that at least 5 out of the 8 users began taking Valium for reasons other than psychological issues. This is equivalent to 1 - the probability that 4 or fewer of the 8 users took it for non-psychological reasons.

The same binomial probability formula can be used, with n=8, p=0.40 (since the probability of a single user taking Valium for non-psychological reasons is 1 - 0.60 = 0.40), and k taking values from 0 to 4. The probabilities are computed for each k and then summed. The result is then subtracted from 1 to get our desired probability, given by: P(X>=5) = 1 - Σ [P(X=k) from k=0 to 4]

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Answer: the total square footage is

850 ft³

Step-by-step explanation:

The kitchen is 10 feet by 15 feet. This means that the volume of the kitchen would be

10 × 15 = 150 ft³

The living/dining combo is 20 feet by 25 feet. This means that the volume of the living/dining combo would be

20 × 25 = 500 ft³

The office and sunroom are each 10 feet by 10 feet. This means that the volume of the office would be

10 × 10 = 100 ft³

Also, the volume of the sunroom would be

10 × 10 = 100 ft³

Therefore, the total square footage is

150 + 500 + 100 + 100 = 850 ft³

Answer:

198,400,000

Step-by-step explanation:

Total Approximate Number of Residents in the United States = 320 million

38 per cent of the total number of residents live in the South

That means, as a percentage, 100%-38%=62% live in other areas of the Unjted States.

[tex]62 \% of 320 million[/tex] = [tex]\frac{62}{100}X320000000[/tex]=198,400,000.

Therefore a total of about 198,400,000 live in other areas of the United States.

Answer:

Cost of 3 bottles will be $7.5.

Step-by-step explanation:

Given:

According to double number line.

Cost of 4 bottles = $10

Based on this we need to find the cost of 3 bottles of water.

Solution:

Now we know that;

4 bottles = $10

1 bottle = Cost of 1 bottle

By using Unitary method we get;

Cost of 1 bottle = [tex]\frac{10}{4}=\$2.5[/tex]

So we can say that;

Cost of n bottles = [tex]\$2.5n[/tex]

Cost of 3 bottles = [tex]\$2.5\times 3 = \$7.5[/tex]

Hence Cost of 3 bottles will be $7.5.

Now we have drawn the double number line.

Bottom line(Line 1)  will be number of bottles:  

1   2   3   4   5   6  

Top line (Line 2) will be the cost of corresponding bottles:

2.5  5  7.5  10  12.5  15

Answer:

$7.5 Dollars

Step-by-step explanation:

The cost of 4 bottles is $10. So, 1 bottle is going to be $2.50.

Now, to find the cost of 3 water-bottles, we have to multiply.

$2.50 * 3 = $7.50.

So, the answer to this question is  3 bottles = $7.50

(Hope this helps!)

The area of the given rectangle is of the standard form option 1.[tex]2x^{2} + 3x - 20[/tex].

Step-by-step explanation:

Step 1:

The parameters needed to determine the area of a rectangle are the base length and the width.

The base length of this rectangle is [tex]2x-5[/tex] units while its width is [tex]x+4[/tex] units.

The area of a rectangle is determined by multiplying the base length with the width.

Step 2:

The area of the rectangle [tex]= (length)(width).[/tex]

Here length is [tex]2x-5[/tex] units and the width is [tex]x+4[/tex] units.

The area of the rectangle[tex]= (2x-5)(x+4) = 2x^{2} + 8x -5x-20 = 2x^{2} + 3x - 20.[/tex]

So the area of the given rectangle is of the standard form [tex]2x^{2} + 3x - 20[/tex] which is the first option.

To find the area of the rectangle, we need to multiply the expressions for the lengths of its sides. The sides are given as [tex]\(2x - 2\) and \(x + 4\).[/tex]

First, write the expressions for the sides of the rectangle:

- One side is[tex]\(2x - 2\)[/tex]

- The other side is[tex]\(x + 4\)[/tex]

To find the area, multiply these two expressions:

[tex]\[(2x - 2)(x + 4)\][/tex]

Use the distributive property (also known as the FOIL method for binomials) to expand this product:

[tex]\[(2x - 2)(x + 4) = 2x(x) + 2x(4) - 2(x) - 2(4)\][/tex]

Simplify each term:

[tex]\[= 2x^2 + 8x - 2x - 8\][/tex]

Combine like terms:

[tex]\[= 2x^2 + 6x - 8\][/tex]

So, the polynomial expression in standard form representing the area of the rectangle is:

[tex]\[2x^2 + 6x - 8\][/tex]

Given the options:

- 2x^2 + 3x − 20

- 2x^2 + 13x − 1

- 2x^2 + 13x − 20

- 2x^2 + 3x − 1

None of these options exactly match our result of [tex]\(2x^2 + 6x - 8\),[/tex] indicating a potential error in the problem statement or options provided. The correct simplified polynomial expression for the area, based on the given side lengths, is[tex]\(2x^2 + 6x - 8\).[/tex]

Answer:

0.323

Step-by-step explanation:

Number of mathematics instructors=8

Number of Computer Science instructors=13

Number of Statistics instructors=4

Number of Physics instructors=6

Total Attendance = 8+13+4+6=31

Probability of Getting a Physics Instructor=6/31

Probability of Getting a Statistics Instructor=4/31

Pr (Getting a Physics OR Statistics Instructor)

=Probability of Getting a Physics Instructor+

Probability of Getting a Statistics Instructor

=6/31+4/31=10/31=0.323

Answer:

Less than

Step-by-step explanation:

Sample variance is computed by dividing the Sum of Squares (SS) by the number of samples (n).

Population variance is computed by dividing the Sum of Squares (SS) by the difference between the number of samples and 1 (n-1).

After computing, it would be found that the sample variance is less than the population variance.

The average of sample variances, computed by dividing the Sum of Squares by sample size (n) from all possible samples, will be less than the population variance.

If sample variance is computed by dividing Sum of Square (SS) by sample size (n), then the average value of the sample variances from all possible random samples would be biased. In fact, it will be less than the actual population variance. This is commonly known as Bessel's correction in statistics. For an unbiased estimate of the population variance, we should rather divide the SS by degrees of freedom (n-1), not by the sample size n. So, when you average the sample variances, obtained by dividing by n from all possible samples, the result will be less than the population variance.

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Answer:

t=11 sec

Step-by-step explanation:

The position of the particle moving along the x-axis is given by:

[tex]s(t) = {t}^{3} - 18 {t}^{2} + 33t + 14[/tex]

The velocity is given by:

[tex]s'(t) = 3 {t}^{2} - 36{t} + 33[/tex]

If s'(t)>0 then the particle is moving right.

[tex]3 {t}^{2} - 36{t} + 33 \: > \: 0 \\ {t}^{2} - 12{t} + 11\: > \: 0[/tex]

[tex] \implies \: t \: < \: 1 \: or \: t \: > \: 11[/tex]

This means that the particle is moving left when

[tex]1 \: < \: t \: < \: 11[/tex]

The particle changes direction at time t=1 or t=11

Step-by-step explanation:

Hope it helps you in your learning process.

[tex]\frac{23\pi}{3}[/tex] corresponds to  [tex]\left(\frac{1}{2},-\frac{\sqrt{3}}{2}\right)[/tex].

[tex]-\frac{3\pi}{4}[/tex]  corresponds to [tex]\left(-\frac{\sqrt{2}}{2},-\frac{\sqrt{2}}{2}\right)[/tex].

-150 degree corresponds to  [tex]\left(-\frac{\sqrt{3}}{2},\frac{1}{2}\right)[/tex].

Rewrite as:

[tex]\frac{23\pi}{3}=\frac{18\pi+5\pi}{3}=6\pi+\frac{5\pi}{3}[/tex].

We know that [tex]\frac{5\pi}{3}[/tex] corresponds to [tex]\left(\frac{1}{2},-\frac{\sqrt{3}}{2}\right)[/tex]. So [tex]\frac{23\pi}{3}[/tex] also corresponds to  [tex]\left(\frac{1}{2},-\frac{\sqrt{3}}{2}\right)[/tex].

[tex]-\frac{3\pi}{4}[/tex] has same position as: [tex]-\frac{3\pi}{4}+2\pi=\frac{5\pi}{4}[/tex].

So the corresponding point to it is [tex]\left(-\frac{\sqrt{2}}{2},-\frac{\sqrt{2}}{2}\right)[/tex].

From unit circle 150 degree corresponds to [tex]\left(-\frac{\sqrt{3}}{2},\frac{1}{2}\right)[/tex].

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Answer:

Subtract the maximum and minimum values.

Step-by-step explanation:

The range of a data set is the interval that contains all values in the set and is determined as the difference between the maximum and the minimum values within the data set. Therefore, in order to find the range of a set of data, simply subtract the maximum and minimum values.

Answer:

Subtract the maximum and minimum values.

Step-by-step explanation:

Answer:

1350

Step-by-step explanation:

Initially 90 squirrels were tagged out of a total population of x squirrels.

Similarly, 42 squirrels out of a sample of 630 squirrels had tag

We can use ratio equality to find the total population x.

42:90=620:x

[tex]\frac{42}{90} =\frac{630}{x}[/tex]

Cross multiplying

42 X x = 630 X 90

Dividing both sides by 42

[tex]x=\frac{630 X 90}{42} \\=1350[/tex]

The total number of squirrels in the city park is 1350.

The total number of squirrels in the park is approximately 1350.

To estimate the total squirrel population in the park, we can use the Lincoln-Petersen method, which is a mark-recapture technique. The formula for this method is:

[tex]\[ N = \frac{(M \times n)}{m} \][/tex]

Given the data:

- ( M = 90 ) (the number of tagged squirrels),

- ( n = 630 ) (the total number of squirrels counted in the second sample),

- ( m = 42 ) (the number of tagged squirrels found in the second sample).

Plugging these values into the formula, we get:

[tex]\[ N = \frac{(90 \times 630)}{42} \] \[ N = \frac{56700}{42} \] \[ N = 1350 \][/tex]

Therefore, the total number of squirrels in the park is estimated to be 1350.

Answer:

C

Step-by-step explanation:

The slope = rise over run

If you count the blocks, you'll see it goes down 5 for every 6 to the right it goes.

Answer: c. price inelastic and supply is more price-inelastic.

Step-by-step explanation:

Inelastic price describes the consumers static habit of purchasing irrespective of the rise or fall in price.

Supply inelastic : This is a sitiuation when percentage change in supply is less than a percentage change in price.

Answer:

72

Step-by-step explanation:

3 x 4 = 12

12 x 6 = 72

hope i helped

Answer:

12.167[tex]cm^3[/tex]

Step-by-step explanation:

The volume of any solid shape is the quantity or capacity it can contain.  For example, if you have a closed tin of milf that is filled to the brim, the volume of the tin is the quantity of milk that is in the tin.

Given any cube with side length s, the Volume V=[tex]s^3[/tex]

If the cube has a side length of 2.3 centimeters

Volume=[tex]s^3[/tex]= s X s X s = 2.3 X 2.3 X 2.3=12.167[tex]cm^3[/tex]

Volume of the Cube = 12.167[tex]cm^3[/tex]

Answer: 12.167 cubic centimeters

Step-by-step explanation:

Answer:

1.4 units

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

I first went through starting with A and took 3-9 (since it’s in the first box) I got -6 . You then divide 3 and 9 by -6 and report your answer.

I got 3/-6 = -.5 and And 9/-6 = -1.5

I then moved onto 4 and 12, I took the difference 4-12 and got -11.

4/-11 = -0.36 and 12 /-11 = -1.09

Since these answers are not the all the same I moved onto B

I took 20-25 = -5

20/-5 = -4 and 25/-5 = -5

Next numbers

24-30 = -6

24/6 = 4 and 30/6= 5

Next number

32-40= -8

32/-8 = -4

40/-8 = -5

( when putting this in fraction form it would be -4/-5 and that turns positive.) making this table proportioned unlike the other ones

Answer: option B is the correct answer.

Step-by-step explanation:

If two variables are proportional, a change in the value of one variable would cause a corresponding change in the value of the other variable. This means that both variables are related by a constant of proportionality, k.

Looking at the given tables,

For table A,

9/3 = 12/4 but not equal to 20/5

The relationship is not proportional.

For table B,

25/20 = 30/24 = 40/32 = 1.25

The relationship is proportional.

For table C,

12/4 = 15/5 but not equal to 24/6

The relationship is not proportional.

For table D,

4/3 = 16/12 but not equal to 9/6

The relationship is not proportional.

Answer:

Step-by-step explanation:

False.  Asymptotes are the walls that the function can't get over.  This wall has no gaps or holes, nor does it have a gate.  The function has to stay on one side of the asymptote in order for it to be a legit asymptote.  Since our function is both above and below the dotted line, the dotted line is not an asymptote.

Answer:

Step-by-step explanation:

If you were talking about how many meters of fencing the school would need it would be 160 meters. The reason i say this is because if you were to divide the 3 sides of the playground by 48o meters of fencing you would get 160 meters of fencing. If this is not the answer your looking for than please state the question next time. THANK YOU

The function of area will be A(x) = x( 480 - 2x)

The area of the rectangle is the product of the length and width of a given rectangle.

The perimeter is given P = 480 meters

Since the one of the sides does not need fencing, the perimeter would be:

P = 2x + y

Make y the subject;

y = P -2x

Substitute 480 for P;

y = 480 - 2x

The area of a rectangular fence is:

Area = xy

Substitute ;

A = x( 480 - 2x)

Express as a function

A(x) = x( 480 - 2x)

Hence, the function of area will be A(x) = x( 480 - 2x)

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Answer:

At most 2 adult haircuts

Step-by-step explanation:

The equation given is:

[tex]0.75C+1.25A \leq 70[/tex]

This equation dictates the number of haircuts Horace gives in 7 hours.

Horace gave 5 child haircuts (C=5). So, that would make the equation:

[tex]0.75C+1.25A \leq 7\\0.75(5)+1.25A \leq 7\\3.75+1.25A \leq 7\\1.25A \leq 7 - 3.75\\1.25A \leq 3.25\\A \leq \frac{3.25}{1.25}\\A \leq 2.6[/tex]

This means Horace can give LESS THAN or EQUAL to 2.6 haircuts.

2.6 haircuts doesn't make sense, so the maximum would be "2" haircuts.

Atmost 2 adult haircuts

Title:

Step-by-step explanation:

Let the building contractor bought 1000 cement in total.

70% of 1000 = 700 cements were from A and (1000 - 700) = 300 cements were from B.

The number of undamaged bag from A was 95% of 700 = [tex]\frac{95}{100} \times700 = 7\times95 = 665[/tex] and the number of undamaged bags from B was 70% of 300 = [tex]\frac{70}{100} \times300 = 210[/tex].

Total undamaged bags were (665 + 210) = 870.

The probability that an undamaged bag is from A is [tex]\frac{665}{870} = \frac{133}{174}[/tex].

Answer:

  5

Step-by-step explanation:

Very early in your study of multiplication tables, you learned that ...

  5 × 2 = 10

Cathy must fill the 2-cup jar 5 times to transfer a total of 10 cups.

Final answer:

To fill a 10-cup bucket using a 2-cup jar, Cathy must scoop water from the pond 5 times, as 10 divided by 2 equals 5.

Explanation:

The question is how many times Cathy needs to scoop water from the pond with a 2-cup jar to fill her 10-cup bucket.

To find the answer, we simply divide the total capacity of the bucket by the capacity of the jar. So, the calculation would be:

Calculate the total number of cups needed: 10 cups (capacity of the bucket).

Calculate the number of cups per scoop: 2 cups (capacity of the jar).

Divide the total number of cups by the number of cups per scoop: 10 cups/ 2 cups per scoop

= 5 scoops.

Cathy needs to scoop water from the pond 5 times to fill her 10-cup bucket.

Answer:

Data-table is the correct approach of recording numerical information from an experiment

Step-by-step explanation:

A data-table is a group of related facts arranged in labeled rows and columns and is used to record information. Its purpose is to help sort, analyze and compare data gathered from a science experiment or research project. Knowing how to create a data table demonstrates skills in organizing information in a meaningful way and provides a learning base to progress to more sophisticated ways to track data.

Answer: It is C because if you organize the equation numerically the equation is 18x^3+30x^2+12x+10. So it is 18.

Answer:

66.7%

Step-by-step explanation:

Given that

Total population = 50 million

Adults = 30 million

Those not interested in working = 5 million

Those interested in working but given up on searching = 5 million

Those searching = 5 million

Those working part time = 5 million

Those working full time = 10 million

Recall that

Labour force participation rate = (number of people actively participating in labour ÷ total number of people eligible) × 100

Number of people actively participating in labour = employed + unemployed

Employed = 10 million full time + 5 million part time

= 15 million

Unemployed = 5 million. Those searching.

Thus,

People actively participating in labour = 15 + 5= 20 million.

Total number of eligible people = total number of adults = 30 million

Therefore

Labour participation rate = (20/30) × 100

= 0.66667 × 100

= 66.6667

Approximately 66.7%

Answer:

organizational

Step-by-step explanation:

organizational encoding iis process of categorizing information according to. the relationships among a series of items. Here the categorizing information are hearts, clubs, diamonds, and spades.

Hope it will find you well.

Moshe is using categorical encoding to group the cards that have already been played by suit

Moshe is using categorical encoding to group the cards that have already been played by suit. Categorical encoding is a type of semantic encoding, where information is organized and stored based on categories or groups. In this case, Moshe is categorizing the cards into the four suits: hearts, clubs, diamonds, and spades.

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Coefficient of [tex]x^2y^2[/tex] = 24

Solution:

Given that:

[tex](2x - y)^4[/tex]

We have to find the coefficient of [tex]x^2y^2[/tex] term

Use the following algebraic formula

[tex](a-b)^4 = a^4 - 4a^3b+6a^2b^2-4ab^3+b^4[/tex]

From given,

[tex](2x - y)^4[/tex]

Where,

a = 2x

b = y

Therefore, by using formula, we get,

[tex](2x - y)^4 = (2x)^4 - 4(2x)^3(y) + 6(2x)^2(y)^2 - 4(2x)(y)^3 + y^4\\\\Simplify\\\\(2x - y)^4 = 16x^4 - 32x^3y + 24x^2y^2-8xy^3 + y^4[/tex]

Find the coefficient of [tex]x^2y^2[/tex]

From above simplified expression,

coefficient of [tex]x^2y^2[/tex] = 24

Answer:

24

Step-by-step explanation:

The inverse of the equation y = 9x² − 4 is found by switching x and y and solving the equation for the new y. The correct inverse function after simplification is y = ±√(x / 9 + 4).

To find the inverse of the equation y = 9x2 − 4, you need to switch the roles of x and y and then solve for y once again. Here is a step-by-step explanation:

Comparing the result with the choices given, we find that y = ±√(x / 9 + 4) is the correct inverse function.

Answer:

(C)-262143

Step-by-step explanation:

For a geometric series, the nth term

[tex]A_n=ar^{n-1}[/tex] where a= first term, r=common ratio.

If [tex]A_1=a=-3[/tex] , r=4 and [tex]A_n=-196608[/tex]

then from [tex]A_n=ar^{n-1}[/tex]

-196608=-3 X [tex]4^{n-1}[/tex]

[tex]4^{n-1}=\frac{-196608}{-3} =65536\\4^{n-1}=4^8[/tex]

Since the bases are the same, the powers are equal

n-1=8

n=8+1=9

Therefore the Sum of the geometric series

[tex]S_n=\frac{a(r^n-1)}{r-1}[/tex] (This form is used because r>1)

[tex]S_n=\dfrac{-3(4^{9}-1)}{4-1}[/tex]

[tex]S_n=\dfrac{-3(262144-1)}{3}=\dfrac{-3(262143)}{3}=-262143[/tex]