expand and simplify (x+2)(x-2)-(x+3)²​

Hadey should open the park when the high temperature consistently reaches or exceeds 72°F and close it when it falls below.

To determine the best day to open and close the park each year, Hadey should consider the temperature patterns based on the given information. The temperature in Los Angeles peaked on September 9 at 102°F and reached a low approximately 6 months later, suggesting a periodic pattern.

To find the optimal opening and closing days, Hadey should look for the days when the high temperature is consistently above 72°F. This would ensure a good turnout for the amusement park. He should open the park when the high temperature consistently reaches or exceeds 72°F and close it when the high temperature consistently falls below this threshold. Using the temperature data from the most recent twelve months, Hadey should analyze the high temperature records for each day and identify the earliest day when the high temperature consistently reaches or exceeds 72°F. This would be the opening day of the park. Similarly, he should find the latest day when the high temperature consistently falls below 72°F, which would be the closing day.

It's important to note that Hadey's approach assumes that temperature patterns will remain consistent in the future. However, climate change and other factors can affect temperature variations, so it would be wise to consider long-term climate trends and consult with meteorological experts to ensure the park's success.

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The expected value (to you) of one raffle ticket is -$2.737.

The expected value (to you) if you purchase 12 raffle tickets is -$32.84.

The expected value (to the PTO) of one raffle ticket is $2.737.

Amount of money raised if 300 tickets are sold is $821.1.

Cost of a ticket = $3

P(winning a ticket) = 1/300

Winning amount = $76

Prize value = 1/300 × $76 = $0.253

Expected value (to you) for 1 ticket = $0.253 + (299/300 × -$3) = -$2.737

Expected value (to you) if you purchase 12 tickets = 12 × -$2.737

                                                                                   = -$32.84

Expected value (to the PTO) of raffle ticket = -$0.253 + (299/300 × $3)

                                                                       = $2.737

If they sell 300 tickets,

Expected value = 300 × $2.737 = $821.1

Amount raised = $821.1

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The empty space is -7.92 cm^3 (rounded to two decimal places).The result is negative, indicating that there is not enough space in the can to fit all the marbles.

To calculate the empty space in the can, we first need to calculate the volume occupied by the marbles and then subtract it from the total volume of the can.

The volume of each marble can be calculated using the formula for the volume of a sphere:

V_marble = (4/3) * π * r^3

where r is the radius of the marble.

Given that the radius of each marble is 1.2 cm, we can calculate the volume of one marble as follows:

V_marble = (4/3) * π * (1.2 cm)^3

≈ 7.238 cm^3 (rounded to three decimal places)

Since there are 5 marbles in the can, the total volume occupied by the marbles is:

V_total_marbles = 5 * V_marble

≈ 5 * 7.238 cm^3

≈ 36.19 cm^3 (rounded to two decimal places)

The volume of the can can be calculated using the formula for the volume of a cylinder:

V_can = π * r^2 * h

where r is the radius of the can and h is the height of the can.

Given that the radius of the can is 1.5 cm and the height of the can is 4 cm, we can calculate the volume of the can as follows:

V_can = π * (1.5 cm)^2 * 4 cm

≈ 28.27 cm^3 (rounded to two decimal places)

To find the empty space in the can, we subtract the volume occupied by the marbles from the total volume of the can:

Empty space = V_can - V_total_marbles

≈ 28.27 cm^3 - 36.19 cm^3

≈ -7.92 cm^3 (rounded to two decimal places)

The result is negative, indicating that there is not enough space in the can to fit all the marbles.

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There are 1026 went up for 1140 stocks went down.

We have to given that;

The stock market report says that 9 stocks went up for every 10 stocks that went down.

Since, We know that;

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Let us assume that,

Number of went up for 1140 stocks went down is, x

Hence, By definition of proportion, we get;

9 / 10 = x / 1140

x = 9 x 1140 / 10

x = 9 x 114

x = 1,026

Thus, Number of went up for 1140 stocks went down is, 1,026

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a) the demand equation in the form of p = f(Q) is p = -10/3Q + 14533.33

b) when the price per unit of calculators is Rs 1650, approximately 3865 calculators are demanded.

c) when 4500 calculators are demanded, the price per unit should be approximately Rs 3010.

To find the demand equation in the form of p = f(Q), we need to determine the relationship between the price per unit (p) and the quantity demanded (Q) based on the given information.

Let's use the two data points provided:

Point 1: Price (p1) = Rs 1200, Quantity (Q1) = 4000

Point 2: Price (p2) = Rs 1500, Quantity (Q2) = 3000

First, we calculate the slope of the demand equation using the formula:

Slope = (Q2 - Q1) / (p2 - p1)

Substituting the values, we get:

Slope = (3000 - 4000) / (1500 - 1200) = -1000 / 300 = -10/3

Next, we use one of the data points and the slope to find the y-intercept (b). Let's use Point 1:

p1 = Rs 1200, Q1 = 4000

Using the equation of a straight line (y = mx + b), we can rearrange it to solve for b:

b = y - mx

b = 1200 - (-10/3)(4000) = 1200 + 40000/3 = 1200 + 13333.33 = 14533.33

Therefore, the demand equation in the form of p = f(Q) is:

p = -10/3Q + 14533.33

To find the number of calculators demanded (Q) when the price per unit is Rs 1650, we can rearrange the equation and solve for Q:

1650 = -10/3Q + 14533.33

-10/3Q = 1650 - 14533.33

-10/3Q = -12883.33

Q = (-12883.33) / (-10/3)

Q = 12883.33 * 3/10

Q ≈ 3865

Therefore, when the price per unit of calculators is Rs 1650, approximately 3865 calculators are demanded.

Now, let's determine the price per unit (p) when 4500 calculators are demanded. We rearrange the equation and solve for p:

4500 = -10/3Q + 14533.33

-10/3Q = 4500 - 14533.33

-10/3Q = -10033.33

Q = (-10033.33) / (-10/3)

Q = 10033.33 * 3/10

Q ≈ 3010

Therefore, when 4500 calculators are demanded, the price per unit should be approximately Rs 3010.

By using the slope-intercept form of a linear equation and the given data points, we can determine the demand equation and solve for various scenarios, including finding quantities demanded at specific prices and determining the appropriate price for a given quantity demanded.

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Step-by-step explanation:

Cross multiply to get

8 (x-1) = 2 (x+2)

8x -8 = 2x + 4

6x = 12

x = 2

Step-by-step explanation:

Area of circle (pi r^2 ) - area of rectangle (W x H)   =  shaded area

      pi (4^2) -  (5 x 6 ) = 20.3 in^2

Answer:

1,-4(u+1)+6u=2(u+2)-8

Step-by-step explanation:

=-4u-4+6u=2u+4-8

=2u-4=2u-4

=2u-2u=-4+4

=0=0

2,2(y-1)+4y=3(y-1)+7

=2y-2+4y=3y-3+7

=6y-2=3y+4

=6y-3y=4+2

=3y/3=6/3=y=2

: all real numbers are solutions

To find the radius of the cylinder, we can use the formula for the volume of a cylinder:

V = πr²h

Given that the volume is 824 cubic inches, we can rearrange the formula to solve for the radius:

824 = πr²h

Since the height is not given, we cannot find the exact radius. However, we can still determine the relationship between the height and radius if the volume remains the same.

b. If the height of the cylinder is changed, but the volume stays the same, the radius will change inversely proportional to the height. This means that as the height increases, the radius will decrease, and vice versa. This relationship ensures that the volume remains constant.

Therefore, we cannot determine the exact radius without knowing the height, but we can conclude that the radius and height have an inverse relationship.

Answer:

To calculate the percent increase in the amount of interest paid between a household with a 740 credit score and one with a 730 credit score , we need to find the total amount paid for each score and then calculate the percent increase.

From the given table , we can see that the simple interest rate for a credit score of 740-799 is 15%, and the total number of payments is 33 . So, the total amount paid for a principal balance of $18,000 with a credit score of 740 is:

Principal + Total Interest = Total Amount Paid

$18,000 + ($18,000 * 15% * 33/12) = $20,700

Similarly, for a credit score of 730, we need to use the simple interest rate for a credit score of 670-739 , which is 18%, and the total number of payments is 38. So, the total amount paid for a principal balance of $18,000 with a credit score of 730 is:

Principal + Total Interest = Total Amount Paid

$18,000 + ($18,000 * 18% * 38/12) = $21,240

Now, to calculate the percent increase in the amount of interest paid , we can use the following formula:

Percent increase = |(New value - Old value) / Old value| * 100%

Plugging in the values, we get:

Percent increase = |($21,240 - $20,700) / $20,700| * 100%

Percent increase = 2.6%

Rounding to the nearest tenth, we get the final answer as:

Percent increase = 2.6% ≈ 2.5%   (rounded to the nearest tenth)

Therefore, the answer is O 2.5%.

Step-by-step explanation:

Answer:

How to calculate growth rate percentage?

To calculate the percentage growth rate, use the basic growth rate formula:

Subtract the original from the new value and divide the results by the original value. To turn that into a percent increase, multiply the results by 100.

Answer:

Sn = n÷2[2a+(n-1)d]

=18÷2[2(16)+(18-1)(-9)]

Sn=-1089

Step-by-step explanation:

First write out the formula for sum in arithmetic series

Then substitute the given information

Then punch everything as it is together with the signs to get the answer

Combining the information from the Latitude and longitude, we can conclude that Pretoria is situated in a north-eastern direction from Cape Town.

The general direction of Pretoria from Cape Town is North-East.

Cape Town is a coastal city located in the southwestern part of South Africa, while Pretoria is an inland city situated in the northeastern part of the country. To determine the general direction between the two cities, we consider their geographic coordinates.

Cape Town is approximately at a latitude of 33.9249° S and a longitude of 18.4241° E, while Pretoria is around 25.7479° S latitude and 28.2293° E longitude.

When we compare the latitude values, we see that Cape Town is situated further south than Pretoria. Therefore, the general direction from Cape Town to Pretoria is north.

Next, if we compare the longitude values, we observe that Cape Town has a significantly smaller longitude value compared to Pretoria. This indicates that Pretoria is situated more to the east.

Combining the information from the latitude and longitude, we can conclude that Pretoria is situated in a north-eastern direction from Cape Town.

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The passing grade should be set to 10 out of 15, which means a student needs to get at least 10 correct answers to pass the quiz.

Let X be the number of correct answers a student gets by guessing on each question. Since each question is true/false, the probability of guessing correctly is 0.5. Then, X follows a binomial distribution with parameters n = 15 and p = 0.5.

To find the passing grade, we need to find the minimum number of correct answers a student needs to pass the quiz. Let k be the passing grade. Then, the probability of passing by guessing is:

P(X ≥ k) = 1 - P(X < k)

Using the binomial probability formula, we can calculate:

P(X < k) = Σi=0k-1 (15 choose i) 0.5^15

We want to find the value of k such that P(X < k) is less than 0.1, or equivalently, P(X ≥ k) is greater than or equal to 0.9. We can use a calculator or a table to find that the smallest k that satisfies this condition is k = 10.

Therefore, the passing grade should be set to 10 out of 15, which means a student needs to get at least 10 correct answers to pass the quiz.

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Answer:

The total number of marbles is 10, the number of blue marbles is 3, and the red marbles are 4.

Step-by-step explanation:

have a nice day.

Check the picture below.

[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=\sqrt{a^2 + o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{AB}\\ a=\stackrel{adjacent}{6}\\ o=\stackrel{opposite}{6} \end{cases} \\\\\\ AB=\sqrt{ 6^2 + 6^2}\implies AB=\sqrt{ 36 + 36 } \implies AB=\sqrt{ 72 }\implies AB=6\sqrt{2}[/tex]

Answer:

D. 4, 5, 6, then 

H² = P² + B²

6² = 5² + 4²

36 = 25 + 16 

36 ≠ 41

This is not Pythagorean triple.

They plan to clean the street for 3 hours.

They plan to clean the park for 3 hours.

The first step is to set up a set of linear equations that describe the information in the question.

3p + 6s = 27 equation 1

6p + 8s = 42 equation 2

Where:

p = number of hours spent cleaning one park

s = number of hours spent cleaning on street

In order to determine the value of s, take the following steps:

Multiply equation 1 by 2

6p + 12s = 54 equation 3

Subtract equation 2 from equation 3

4s = 12

Divide both sides of the equation by 4

s = 12 / 4

s = 3 hours

Substitute for s in equation 1:

3p + 6(3) = 27

3p + 18 = 27

3p = 27 - 18

3p = 9

p = 9/3

p = 3

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Answer:

23552

Step-by-step explanation:

23, 92, 368...   is a geometric sequence.

first term = a = 23

common ratio = r = 2 term ÷ first term = 92 ÷ 23 = 4

nth term = [tex]ar^n^-^1[/tex]

6th term = [tex]23*(4)^6^-^1[/tex]

[tex]=23*4^5[/tex]

[tex]=23*1024[/tex]

[tex]=23552[/tex]

Hope this helps :)

Pls brainliest...

Answer:

The statement you provided describes a situation in which the cost of apples at a local market is directly proportional to the weight of the apples. This means that as the weight of the apples increases, the cost also increases at a constant rate. The graph mentioned in the statement would show this relationship between the weight of apples in pounds and the cost in dollars.

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Hello !

7          v

--    =   ---

5          6

v = 7 x 6 ÷ 5 = 8.4 (it's a decimal)

Answer:

8.4

Step-by-step explanation:

Make v the subject of the 'formula, by placing 6 towards the other side.

This can be done by multiplying 6 in both sides, so the left side of the formula is 7/5 * 6, while the right is remained with v/1 (since 1/6 * 6 is 1).

Now v = 7/5 * 6 which equals to: 8.4.

Question also says round to the nearest tenth, 8.4 is already rounded to the nearest tenth so the final answer is 8.4

Once you have the weight and length, you can use the formula:

BMI = weight (in kg) / height² (in meters²).

The weight from lb to kg and the length from inches to meters before applying the formula.

The specific Road to Health Chart contained in ANNEXURE G.

The Road to Health Chart and calculate BMI.

The age of a baby at a specific weight percentile:

To determine the age of a baby whose weight places her at the 75th percentile curve you would need to refer to the specific chart.

Locate the weight of 26 lb on the chart and find the corresponding age.

The chart typically provides a range of ages for each percentile curve, allowing you to estimate the age of the baby.

Calculating BMI:

To calculate the BMI (Body Mass Index) for Jay's baby you need both the weight and the length of the baby.

Since the length is given in percentile you would need to find the corresponding measurement value on the chart.

By plugging in the appropriate values you can calculate the BMI in the form of kg/cm².

Remember not to round off the answer as specified.

The specific Road to Health Chart in ANNEXURE G to obtain accurate information for these calculations.

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Considering the given information, we fail to reject the null hypothesis that the proportion of men who own cats is less than or equal to 23% at the 0.10 significance level.

The null and alternative hypotheses are as follows:

H o: p ≤ 0.23 (proportion of men who own cats is less than or equal to 23%)

H a: p > 0.23 (proportion of men who own cats is larger than 23%)

The test is right-tailed because the alternative hypothesis states that the proportion is larger than 23%.

Based on a sample of 40 people, with 15% of them owning cats, we can calculate the p-value.

To find the p-value, we need to use the binomial distribution and calculate the probability of observing a result as extreme or more extreme than the one obtained under the null hypothesis.

Let's calculate the p-value:

p = 0.15 (proportion of men in the sample who own cats)

n = 40 (sample size)

p-value = P(X ≥ 0.15 x 40) = P(X ≥ 6)

Using a binomial calculator or software, we can find that P(X ≥ 6) is approximately 0.162.

Since the p-value (0.162) is greater than the significance level of 0.10, we fail to reject the null hypothesis.

Therefore, based on the given information, we fail to reject the null hypothesis that the proportion of men who own cats is less than or equal to 23% at the 0.10 significance level.

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Step-by-step explanation:

Trapezium area = height   x   average of bases

the bases are the parallel sides   13 and 5

    average = (13+5) / 2 = 9 mm

Area = 10 mm * 9 mm = 90 mm^2  = .9 cm^2

The table of values when the missing parts are completed is

In      7    15    20    22   9        x      (y - 1)/3    2x        x + 3

Out  22   46   61    67   28   3x + 1      y         6x + 1    3x + 10

From the question, we have the following parameters that can be used in our computation:

The table of values

On the table of values, we can see that

The output value is 1 more than three times the input value

This can be expressed as

y = 3x + 1

When In = 22, we have

Out = 3 * 22 + 1 = 67

When Out = 28, we have

3 * In + 1 = 28

In = 9

When In = x, we have

Out = 3 * x + 1 = 3x + 1

When Out = y, we have

3 * In + 1 = y

In = (y - 1)/3

When In = 2x, we have

Out = 3 * 2x + 1 = 6x + 1

When In = x + 3, we have

Out = 3 * (x + 3) + 1 = 3x + 10

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Answer:

  65.12 m²

Step-by-step explanation:

You want the area of a trapezoid with bases 13.1 m and 5 m, and height 7.2 m.

The area of a trapezoid is given by the formula ...

  A = 1/2(b1 +b2)h

  A = 1/2(13.1 m + 5 m)(7.2 m) = 65.16 m²

The area is 65.16 m².

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The new gravitational force between the two planets, when they are moved to two million miles apart, is 250,000 N.

The new gravitational force between the two planets, when they are moved to two million miles apart, can be calculated using the inverse square law of gravity, resulting in a gravitational force of 250,000 N.

Let's denote the initial distance between the planets as d1 (1 million miles) and the corresponding gravitational force as F1 (1,000,000 N).

The final distance between the planets is denoted as d2 (2 million miles), and we need to find the new gravitational force, F2.

According to the inverse square law of gravity, the relationship between distance and gravitational force is as follows:

[tex]F1 / F2 = (d2^2) / (d1^2)[/tex]

Substituting the given values:

[tex]1,000,000 N / F2 = (2,000,000^2) / (1,000,000^2)[/tex]

Simplifying:

1,000,000 N / F2 = 4

Cross-multiplying:

F2 = 1,000,000 N / 4

F2 = 250,000 N.

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