Simplify the expression to a polynomial in standard form:
(x + 3)(2x" + 3x + 7)

Answer: 14 degrees F.

Step-by-step explanation:

        To see how many degrees it much rise to reach 0F, we will subtract -14 from 0 to find our answer.

o - - 14 = 0 + 14 = 14 degrees F

Answer:the simplified form of the expression (10x-5/6)-x+4/3 is 9x - 1.

Step-by-step explanation: To simplify the expression (10x-5/6)-x+4/3, you can start by applying the order of operations, which dictates that you should perform operations within parentheses or brackets first.

The expression (10x-5/6) can be simplified as follows:

(10x-5/6) = 10x - (5/6)

= 10x - (5*6)/6

= 10x - 5

= 10x - 5

Next, you can simplify the remaining terms of the expression:

(10x-5) - x + 4/3

= (10x-5) - (x3)/3 + 4/3

= (10x-5) - x + (43)/3

= (10x-5) - x + 4

= 10x - 5 - x + 4

= 10x - x - 5 + 4

= 9x - 1

Therefore, the simplified form of the expression (10x-5/6)-x+4/3 is 9x - 1.

Based on the given information , the proof of triangle RST ≅ triangle VUT is shown below .

In the question ,

two triangles are given where ;

it is given that side  ST ≅ UT

and  ∠SRT ≅ ∠UVT .

we have to prove that ΔRST congruent  ΔVUT .

In triangle RST and triangle VUT .

side ST = side UT              .....given that ST ≅ UT ;

angle SRT = angle UVT    ....given that  ∠SRT ≅ ∠UVT ;

angle RTS = angle VTU    .....because they are vertically opposite angles .

Hence by ASA congruence , triangle RST ≅ triangle VUT .

Therefore , it is proved that triangle RST ≅ triangle VUT  .

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The minimum and the maximum values are 0 and 1/27, respectively.

The extreme values of a function are the minimum and the maximum values of the function.

The function is given as:

f(x, y, z) = x²y²z²

x² + y² + z² = 1

Subtract 1 from both sides of x² + y² + z² – 1

x² + y² + z²-1=0

Using Lagrange multiplies, we have:

L(xy.z. λ) f(x. y.z) + λ(0)

Substitute f(x.y. z) = x³y²z² and x² + y² + z² − 1 = 0

L(x, y, λ) = x²y²z² + λ(x² + y² + 2² – 1)

Differentiate

Lx = 2xy²z² + 2λx

Ly = 2x²yz² + 2λy

Lz = 2x²y³z + 2λz

Lλ = x² + y² + z²

Equate to 0

2xy²z² + 2λx = 0

2x²yz² + 2λy = 0

2x²y²z+ 2λz = 0

x² + y² + z²-1=0

Factorize the above expressions

2xy²z²+2λx = 0

2x(y²z² + λ) = 0

2x = 0 or y²z²+λ=0

x=0 or y²z² = -λ

2x²yz² + 2λy = 0

2y(x²z² + λ) = 0

2y=0 or x²z²+λ=0

y = 0 or x²z² = -λ

2x²y²z+λz = 0

2z(x²y² + λ) = 0

2z = 0 or x²y² +λ=0

z = 0 or x²y² = -λ

So, we have:

x = 0 or y²z² = -λ

y=0 or x²z² = -λ

z = 0 or x²y² = -λ

Because

-λ= -λ

The above expressions become:

x=y=z=0

x²z² = y²z²

x² = y²

x = ±y

Also, we have:

x²y² = x²z²

y² = z²

y = tz

Also:

y²z² = x²y²

z² = x²

z = ±x

So, we have:

x = ±y

y = ±z

z = ±x

This means that:

x=y=z

Recall that: x² + y² + z² = 1

So, we have:

x² + x² + x² = 1

3x² = 1

Divide through by 3

x² = 1/3

Take square roots of both sides

x=±[tex]\frac{1} \sqrt{3}[/tex]

So, we have:

x=y=z=±[tex]\frac{1} \sqrt{3}[/tex]

So, the critical points are:

x=y=z=0

x=y=z=±[tex]\frac{1} \sqrt{3}[/tex]

Substitute the above values in f(x, y, z)=x²y²z²

f(0,0,0) = 0² × 0² × 0² = 0

f(±[tex]\frac{1} \sqrt{3}[/tex],±[tex]\frac{1} \sqrt{3}[/tex],±[tex]\frac{1} \sqrt{3}[/tex]) = (±±[tex]\frac{1} \sqrt{3}[/tex])² × (±±[tex]\frac{1} \sqrt{3}[/tex])² × (±±[tex]\frac{1} \sqrt{3}[/tex])² =[tex]\frac{1}{27}[/tex]

Considering the above values, we have:

Minimum 0

Maximum =      1/27

Hence, the minimum and the maximum values are 0 and 1/27, respectively.

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The equation of line that passes through the given point and is (a) parallel  to given line is 4x + y - 16 =0

(b) perpendicular to given line is 4x - y -8 =0

According to the question,

The required line is passing through given points and is

(a) parallel (b) perpendicular to given line

Let the equation of required line be (y - y') = m'(x - x')

(a) Parallel

If two lines are parallel to each other then their slopes are equal

Slope of given line : m = y2 - y1 / x2-x1

This line passes through (2,2) and (1,6)

=> m = 6 - 2 / 1 - 2

=> m = -4

Therefore , the slope of required line will be -4 also,

Required line passes through (4,3)

Equation of required line = (y - 4) = -4(x - 3)

=> y - 4 = -4x + 12

=> 4x + y - 16 =0

(b) Perpendicular

If two lines are perpendicular to each other then the product of their slope is -1

So, m × m' = -1

=> -4 × m' = -1

Dividing by -4

=> m' = 4

Therefore , equation of required line =>  (y - 4) = 4(x - 3)

=> y - 4 = 4x - 12

=> 4x - y -8 =0

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The number of the adult will be 77

The number of the child will be 160.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

237 peoples used the public swimming pool.

And, The daily prices are $1.75 for children and $2 for adult.

Now,

Let The number of the adult = x

The number of the child = y

So, We can formulate;

237 peoples used the public swimming pool.

⇒ x + y = 237 ..(i)

And, The daily prices are $1.75 for children and $2 for adult.

⇒ 2x + 1.75y = 444  ..(ii)

From (i);

⇒ x + y = 237

⇒ x = 237 - y

Substitute above value in (ii), we get;

⇒ 2x + 1.75y = 444

⇒ 2 (237 - y) + 1.75y = 444

⇒ 474 - 2y + 1.75y = 444

⇒ 474 - 444 = 0.25y

⇒ 40 = 0.25y

⇒ y = 160

And, from (i),

⇒ x + y = 237

⇒ x + 160 = 237

⇒ x  = 77

Thus, The number of the adult = 77

The number of the child = 160.

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The ratio of the length of the altitude to the length of one side of the triangle is equal to the ratio of the length of the hypotenuse to the length of the other side.1) AD/AB = BC/AC is true

In the accompanying diagram of right triangle ABC, altitude BD is drawn to hypotenuse AC. This means that the length of BD is equal to the length of the altitude from the vertex of the right angle to the hypotenuse. This also means that the length of BD is a right triangle's altitude. In a right triangle, the altitude of a right triangle is the line segment connecting one vertex of the right angle to the hypotenuse, and is perpendicular to the hypotenuse. This also means that the ratio of the length of the altitude to the length of one side of the triangle (AD/AB) is equal to the ratio of the length of the hypotenuse to the length of the other side (BC/AC). This statement must always be true, regardless of the size of the triangle or its specific shape. This is because the ratio of the length of the altitude to the length of one side of the triangle is always equal to the ratio of the length of the hypotenuse to the length of the other side.

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Answer:

Read below

Step-by-step explanation:

The equation for the volume of water in the bowl after a certain amount of time can be represented by the formula: y = k * x, where k is the constant of proportionality. This constant represents the rate at which water is dripping into the bowl, in milliliters per second.

To find the constant of proportionality, you need to know the rate at which the water is dripping into the bowl. If you know the rate, you can plug it into the formula above to find the equation that represents the volume of water in the bowl over time. For example, if the water is dripping into the bowl at a rate of 1 milliliter per second, the equation would be: y = 1 * x. This means that after 1 second, the bowl would contain 1 milliliter of water, after 2 seconds it would contain 2 milliliters of water, and so on.

It's important to note that the constant of proportionality will change if the rate at which the water is dripping into the bowl changes. For example, if the water is dripping into the bowl at a rate of 2 milliliters per second, the equation would be: y = 2 * x. This means that after 1 second, the bowl would contain 2 milliliters of water, after 2 seconds it would contain 4 milliliters of water, and so on.

In summary, the equation for the volume of water in the bowl after a certain amount of time can be represented by the formula: y = k * x, where k is the constant of proportionality, which represents the rate at which water is dripping into the bowl. To find the equation, you need to know the rate at which the water is dripping into the bowl, and plug that value into the formula as the value of k.

The set S is composed of the integers that are between -5 and -1; with -5 being included. Rewriting this set by using the Roster Method gives us an answer of,

S = {-5, -4, -3, -2}

The term "roster method" refers to a method of displaying a set's components by listing them in bracketed lists. The set can be modeled most easily using the roster form. The components of a set are listed in row format in roster form, with commas between them.

The components of a set are listed in row format in roster form, with commas between them.

A set in mathematical form is simply represented mathematically using the roster notation. The elements (or members) in this approach are listed in a row between curly brackets. When there are multiple elements in a set, there is a comma between every pair of elements.

Based on the given above, the set T is composed of the integers that are between -5 and -1; with -5 being included. Rewriting this set by using the Roster Method gives us an answer of,

S = {-5, -4, -3, -2}

The complete question is:

Rewrite the set S by listing its elements. Make sure to use the appropriate set notation. S = {[ z| z is an integer and -5 ≤ x < -1}

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a) The standard error of the mean is equal to the standard deviation divided by the square root of the sample size. In this case, the standard error of the mean would be equal to 23.65/sqrt(8) = 6.61.

b) Using the central limit theorem, we can say that the probability that the mean of the eight plots would be within 1 standard error of the mean is approximately equal to 68%. This is because, under the central limit theorem, the distribution of the sample means approaches a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size. Therefore, in this case, we would expect that 68% of the sample means would be within 1 standard deviation of the population mean.

c) The probability that we calculated in (b) might not be very accurate because the central limit theorem assumes that the underlying population is normally distributed. However, it is not clear from the histogram whether the number of live maples per plot is normally distributed. If the distribution of the number of live maples per plot is not normal, then the central limit theorem would not be applicable and the probability we calculated might not be accurate.

Hence we get the required answer.

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If v1,...,vp is linearly dependent in V, then there exist scalars c1,...,cp such that c1v1 + ... + cpvp = 0.

Applying the linear transformation T to both sides of this equation, we get T(c1v1 + ... + cpvp) = T(0). Since T is a linear transformation, T(c1v1 + ... + cpvp) = c1T(v1) + ... + cpT(vp).

Therefore, Tv1,...,Tvp is linearly dependent in W. This shows that if a linear transformation maps a set v1,...,vp onto a linearly independent set Tv1,...,Tvp, then the original set v1,...,vp must be linearly independent as well, because if it were linearly dependent, then Tv1,...,Tvp would also be linearly dependent.

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A:

The return from opening the office building under the assumption that it is leased would be the difference between the net income generated by the increase in sales and the expenses associated with opening the new office, including the cost of leasing the office space.

To calculate the net income generated by the increase in sales, we first need to calculate the total cost of goods sold. Since the cost of goods sold is estimated to be 40 percent of sales, the cost of goods sold for the new office would be 40 percent x $2.6 million = $<<40*.01*2.6=1.04>>1.04 million.

Subtracting the cost of goods sold from the increase in sales, we find that the net income generated by the increase in sales would be $2.6 million - $1.04 million = $<<2.6-1.04=1.56>>1.56 million.

Next, we need to calculate the expenses associated with opening the new office, including the cost of leasing the office space. Since the corporate overhead would increase by $306,500, the total up-front costs associated with opening the new office would be $306,500 + $2.6 million = $<<306.5+2.6=2.906>>2.906 million.

To calculate the cost of leasing the office space, we need to multiply the annual lease payment by the number of years in the lease term. Since the annual lease payment is $645,000 and the lease term is 15 years, the total cost of leasing the office space would be $645,000 x 15 years = $<<645000*15=9675000>>9.675 million.

Subtracting the total up-front costs and the cost of leasing the office space from the net income generated by the increase in sales, we find that the return from opening the office building under the assumption that it is leased would be $1.56 million - $2.906 million - $9.675 million = $<<1.56-2.906-9.675=-9.020>>-9.020 million. This means that the corporation would incur a loss of $9.020 million by opening the new office and leasing the office space.

B:

C:

To calculate the return on the incremental cash flow from owning versus leasing, we need to subtract the cash flow from leasing the office space from the cash flow from owning the office space.

First, let's calculate the cash flow from leasing the office space. We already know that the total cost of leasing the office space would be $9.675 million. To calculate the cash flow from leasing the office space, we need to subtract the real estate operating expenses from the total cost of leasing the office space. Since the real estate operating expenses are estimated to be 50 percent of the lease payments, the real estate operating expenses would be 50 percent x $645,000 = $<<50*.01645=322500>>322,500 per year. Since the lease term is 15 years, the total real estate operating expenses would be $322,500 x 15 years = $<<322.515=4837.5>>4,837,500. Subtracting the real estate operating expenses from the total cost of leasing the office space, we find that the cash flow from leasing the office space would be $9.675 million - $4.837.5 million = $<<9.675-4.837.5=4.837.5>>4,837,500.

Next, let's calculate the cash flow from owning the office space. We already know that the total up-front costs associated with opening the new office would be $2.906 million. To calculate the cash flow from owning the office space, we need to subtract the total annual operating expenses from the net income generated by the increase in sales. Since the net income generated by the increase in sales is $1.56 million and the total annual operating expenses are $217,774.36, the cash flow from owning the office space would be $1.56 million - $217,774.36 = $<<1.56-217774.36=1.34222564>>1,342,225.64.

Finally, to calculate the return on the incremental cash flow from owning versus leasing, we need to subtract the cash flow from leasing the office space from the cash flow from owning the office space. Therefore, the return on the incremental cash flow from owning versus leasing would be $1,342,225.64 - $4,837,500 = $<<1.34222564-4.837.5=-3.495.5>>-3,495,500. This means that the corporation would incur a loss of $3.495.5 million by choosing to own the office space instead of leasing it.

type of statistical inference should be used to answer each of the questions below.Two-sample t-test is there a difference in the amount of time people spend on social media between genders.

Two-sample t-test is a type of inferential statistic used to determine whether there is a significant difference between the means of two independent groups.

In this case, the two groups would be genders (male and female) and the type of data is the amount of time spent on social media.

Two-sample t-test is there a difference in the amount of time people spend on social media between genders.

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After solving the logical operations it can be determined that the correct answer is C) FALSE.

Logical operations are phrases that connect expressions to test if they are true or not.

The complement (') sign means that the opposite value of the variable is needed. For example if y is false, y' means true.

Let False = 0 and True = 1

= ((0 OR 0') AND (1' AND 0')) OR ((0 OR 0') AND (1 OR 0)')

= ((0 OR 1) AND (0 AND 1)) OR ((0 OR 1) AND (1)')

= (1 AND 0) OR (1 AND 0)

= 0 OR 0

= 0

Hence, the answer is C) FALSE

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Answer:

a) ending inventory:     11,850,000

  cost of goods sold: 25,200,000

 gross profit               25,200,000

b)

ending inventory:     1,800,000

cost of goods sold:  23,100,000

gross profit  50,400,000 - 23,100,000 =  27,300,000

5,200 at $600

4,100 at $700

6,200 at $800

purchase 29,000 at $900

-sold 28,000 grills

As we use LIFO we sale from the last purchase thus, 29,000 - 28,000 = 1,000 of this units are added as another layer for the inventory account

ending inventory

5,200 at $  600

4,100 at $   700

6,200 at $  800

1,000  at $  900

Total    $ 11,850,000

cost of good sold:

28,000 x $900 = $25,200,000

sales revenue

28,000 x 900 x 200% = $50,400,000

gross profit sales revenue less COGS

b) 5,200 at $600

4,100 at $700

6,200 at $800

purchase 15,500 at $900

-sold 28,000 grills

we check how many layer deep we go:

28,000 - 15,500 at 900= 12,500

12,500  -  6,200  at 800=  6,300

6,300 - 4,100 at 700      =  2,200  at 600

Ending Inventory

3,000 at $600 = $ 1,800,000

COGS:

15,500 x 900 + 6,200 x 800 + 4,100 x 700 + 2,200 x 600 = 23,100,000

Step-by-step explanation:

Let sn be the number of successes in n independent bernoulli trials, the probability of success for each trial is 1/2.

(a) 1 , (b) 0 ,(c) 0

(a) As n approaches infinity, the probability of having 2n - 3n successes in n trials is equal to the probability of having 2n + 3n successes in n trials. Since the probability of success for each trial is 1/2, the probability of having 2n - 3n successes is the same as the probability of having 2n + 3n successes. Therefore, the limit is 1.

(b) As n approaches infinity, the probability of having 2n - 4n successes in n trials is equal to 0, since the probability of success for each trial is 1/2. Similarly, the probability of having 2n + 4n successes in n trials is also equal to 0. Therefore, the limit is 0.

(c) As n approaches infinity, the probability of having 2n - 20 successes in n trials is equal to 0, since the probability of success for each trial is 1/2. Similarly, the probability of having 2n + 20 successes in n trials is also equal to 0. Therefore, the limit is 0.

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The missing values for the equivalent ratios in the order that they appear in this table include the following;

In Mathematics, a proportion can be defined as an expression which is typically used to represent (indicate) the equality of two (2) ratios. This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.

From column 1, we have:

Let the missing value be represented by x.

1/4/(1/2) = 3/4/x

2/4 = 3/4x

8x = 12

x = 12/8

x = 3/2

From column 2, we have:

Let the first missing value be represented by y.

1/4/(1/2) = y/3

2/4 = y/3

4y = 6

y = 6/4

y = 3/2.

From column 2, we have:

Let the second missing value be represented by z.

1/4/(1/2) = 5/z

2/4 = 5/z

2z = 20

z = 20/2

z = 10.

In conclusion, we can logically deduce that t 10/2, 5/(11/20), and 5/4.

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A: p not equal to the value will be  [tex]$$N=\left(\frac{n / 2}{x}\right)^x\left(\frac{n / 2}{n-x}\right)^{n-9} .$$[/tex]

B.Using the null distribution of X, show how the significance level corresponding to a rejection region |X - n/2| > k can be determined.

C. If n = 10 and k = 2, the significance level of the test = 0.11

D. Use the normal approximation to the binomial distribution of the significance level if n = 100 and k = 10 the value will be N(0.1).

1. The value of the generalized likelihood ratio test statistic will be

[tex]A=\frac{\left(\begin{array}{l}n \\x\end{array}\right)(1 / 2)^n}{m_0 x_{0 < p < 1}\left(\begin{array}{l}n \\x\end{array}\right) p^n(1-p)^{n-x}}[/tex]

As we know, the denominate will be maximized when [tex]$p=x / n$[/tex], the P under [tex]\Omega[/tex]

Hence [tex]$$N=\left(\frac{n / 2}{x}\right)^x\left(\frac{n / 2}{n-x}\right)^{n-9} .$$[/tex]

b)

[tex]$$\begin{aligned}\Lambda & =\left(\frac{n / 2}{x}\right)^x\left(\frac{n / 2}{n-x}\right)^{n-x} \\& =\left[\left(\begin{array}{c}2 x \\n\end{array}\right)^{-2 x / n}\left(2-\frac{2 x}{n}\right)^{-2+2 x / n}\right]^{n / 2} \\& =\left[y^{-y}(2-y)^{-(2-y)}\right]^{n / 2} \\& =\left[(1+v)^{-(1+v)}(1-v)-(1-v)\right]^{n / 2}\end{aligned}$$[/tex]

where [tex]y=2 x / n=1+0[/tex]

The last expression is symmetric about [tex]\theta=0+[/tex] is a maximum [tex]$\rightarrow t v=0$[/tex].

since the test rejects [tex]H_0[/tex] when [tex]$\wedge$[/tex] it is small.

If the only if [tex]$|0|=|1,2 \pi| n \mid$[/tex] is large.

This is equivalent to |x-n/2| is large

c) The significance level [tex]$\alpha$[/tex] of the test that rejects H_0 when [tex]$|x-n| 2 \mid > *$[/tex] is given by [tex]$$P\left(|x-n / 2| > k \mid H_0\right) \text {. }$$[/tex]

This probability can be determined using the pmf of the B(n, 0.5) distribution.

d) If n=10+k=2,

[tex]$$\begin{aligned}& P\left(|x-n|=| > k| H_0\right) \\= & P\left(|x-5| > 2 \mid H_0\right) \\= & P\left(x=0 \mid H_0\right)+P\left(x=1 / H_0\right)+P\left(x=2 \mid H_0\right)+P\left(x=8 / H_0\right) \\& +P\left(x=9 \mid H_0\right)+P\left(x=10\left(H_0\right)\right. \\= & 0.11 .\end{aligned}$$[/tex]

e) Using the normal approximation to the binomial distribution B(100,0.5), x is approximately n amply distributed with mean 50 * variance n p(1-p)=25.

Thus, the significant level of the test is

[tex]$$\begin{aligned}& P(|x-50| > 10) \approx P(|z| > 2)=0.046 . \\& \text { where } z \sim N(0,1) \text {. } \\&\end{aligned}$$[/tex]

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Probability provides information about the likelihood that something will happen.

The calculated probabilities are

0.5455

0.5909

0.4615

0.5556

a. The probability of the people that prefer sprite is

Probability = 60/110

= 0.5455

B. The probability that a person is between 21 and 40

probability = 65/110

= 0.5909

C. Probability of drinking lemonade given that age is between 21 and 40

Probability = 30/65

= 0.4615

d. Probability of sprite when under 21

25/45

= 0.5556

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I am closing 17 sales opportunities per day.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

The total number of sales = 26.

64% of sales are closing.

This means,

The number of closing sales.

= 64% of 26

= 64/100 x 26

= 0.64 x 26

= 16.64

Thus,

The number of closing sales is 17.

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If a ball is thrown in the air with a velocity of 52 ft/s, its height in feet t seconds later is given by y = 52t − 16t2.

Then the average velocity for the time period beginning when t = 2 and lasting for 0.5s,0.1s,0.05s,0.01s will be -20,-13.6,-12.8,-12.16 respectively

y=y(t)=52t-16t²

At t=2, y=52(2)-16(2)² =40

The average velocity between time 2 and 2+h is Vav. = [tex]\frac{y(2+h)-y(2)}{(2+h)-2}[/tex]

                                                                                      =[tex]\frac{-12h-16h^2}{h}[/tex]

                                                                                      = -12-16h

Now finding the average velocity for the period beginning when t = 3 and lasting-

(i)0.5 s is (2,2.5) , Vav. = -20.0 ft/s

(ii)0.1 s is (2,2.1), Vav = -13.6 ft/s

(iii) 0.05s is (2,2.05), Vav. = -12.8ft/s

(iv) 0.01s is (2,2.01) Vav.=-12.16ft/s

And at t=2 , h will approaches to zero so Vav= -12ft/s

Therefore, If a ball is thrown in the air with a velocity of 52 ft/s, its height in feet t seconds later is given by y = 52t − 16t2.

Then the average velocity for the time period beginning when t = 2 and lasting for 0.5s,0.1s,0.05s,0.01s will be -20,-13.6,-12.8,-12.16 respectively.

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The given inequality is y > x^2 + 1. To represent this inequality in a system of equations, we can subtract x^2 + 1 from both sides to get y - x^2 - 1 > 0. The inequality is nonstrict (i.e., it includes the equal sign), so we can represent it using an equation by setting y - x^2 - 1 = 0.

The additional constraints are y < x + 7 and x > 1. The first constraint can be represented by the inequality y - x - 7 < 0, which can be represented by the equation y - x - 7 = 0. The second constraint can be represented by the inequality x - 1 > 0, which can be represented by the equation x - 1 = 0.

Thus, the system of equations representing the situation is:

y - x^2 - 1 = 0

y - x - 7 = 0

x - 1 = 0

We can represent this system graphically by graphing each equation on a coordinate grid. The first equation, y - x^2 - 1 = 0, represents a parabola. The second equation, y - x - 7 = 0, represents a line with a slope of -1. The third equation, x - 1 = 0, represents a vertical line at x = 1.

One example of a height and side length that the obstacle course can use is a height of 6 feet and a side length of 2 feet. This satisfies all of the given constraints, and it can be seen in the graph as a point of intersection between the three lines.

we want that time to be less than equation or equal to 5 minutes start text, m, i, n, u, t, e, s, end text. therefore: 1[tex]5minutes[/tex]

Rate for ZZZ Zambonis × Time ≤ 5 minutes

Time ≤ 5 minutes/Rate for ZZZ Zambonis

To solve for the time needed to resurface one rink, we first need to set up an equation. We know that the number of rinks resurfaced by ZZZ Zambonis is equal to the rate for ZZZ Zambonis multiplied by the time. We want the time for 1 rink to be less than or equal to 5 minutes, so we need to solve for time in the equation. We can do this by dividing both sides of the equation by the rate for ZZZ Zambonis, resulting in the equation Time ≤ 5 minutes/Rate for ZZZ Zambonis. This equation gives us the maximum time needed to resurface one rink.

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The integral can be evaluated by interpreting it in terms of the area of the labeled regions in the figure. The integral is equal to the sum of the areas of the labeled regions, which is equal to a1.

1. The integral is given as an area under a graph.

2. The graph has labeled regions.

3. The integral can be evaluated by interpreting it in terms of the area of the labeled regions in the figure.

4. The integral is equal to the sum of the areas of the labeled regions, which is equal to a1.

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{48, 55, 73} and  {10, 23, 26} do not represent a right angle triangle.

If a² + b² < c² then it is an acute angle triangle.

If a² + b² = c² then it is a right-angle triangle.

If a² + b² ≥ c² then it is an obtuse angle triangle.

Now,

48² + 53² = 73².

2304 + 2809 = 5329.

5113 ≠ 5329 so do not represents a right-angle triangle.

Similarly,

39² + 80² = 89² represents a right-angle triangle.

42² + 56² = 70² represents a right-angle triangle.

10² + 23² ≠ 26²so do not represent a right-angle triangle.

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The instantaneous rate of change of daily receipts 13 weeks after the opening day is 1.

To find the instantaneous rate of change of daily receipts 13 weeks after the opening day, you can use the definition of the derivative. The derivative of a function at a point is defined as the limit of the average rate of change of the function over a small interval around that point, as the interval becomes smaller and smaller.

In this case, the function we are interested in is the function that represents the daily receipts of the movie "Avatar" as a function of the number of weeks after the opening day. Let's call this function f(x), where x represents the number of weeks after the opening day.

To find the derivative of f(x) at the point x = 13, we can use the following formula:

f'(x) = lim(h->0) [f(x+h) - f(x)]/h

Plugging in the values, we get:

f'(13) = lim(h->0) [f(13+h) - f(13)]/h

Since we are given the values of the function at various points, we can plug in the values to find the derivative. In this case, we have:

f'(13) = lim(h->0) [(4.027 + h) - 4.027]/h

Simplifying this expression, we get:

f'(13) = lim(h->0) h/h

Since the limit of h/h as h approaches 0 is 1, we can say that:

f'(13) = 1

It's important to note that this result tells us the rate of change of the function at a single point in time, rather than over a longer interval. If we were interested in the average rate of change over a longer interval, we would need to use a different approach.

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Complete Question:

The following table shows the daily receipts in millions of dollars of the movie "Avatar" for successive Fridays after its opening on Friday 18 December 2009. Weeks $Receipts 1 75.617 4 42.785 7 22.85 10 13.655 13 4.027 16 0.844 19 0.633 22 0.188 25 0.064 28 0.028 Estimate the instantaneous rate of change of daily receipts 4 weeks after the opening day. Round to four decimal places. - 1.1726 TIP Enter your answer as an integer or decimal number. Examples: 3,-4, 5.5172 Enter DNE for Does Not Exist, oo for Infinity Get Help:

given rate r = 5% compounded monthly r = 0.05/12 = 0.0041667

(1) monthly growth factor = 1.0041667 (2) monthly percent change = (1.0041667-1)*100%= 0.0041667*100% monthly percent change = 0.41667%

(B) given rate r = 6.9% compounded quarterly

r = 0.069/4 = 0.01725

(1) Quarterly growth factor = 1.01725

(2) Quarterly percent change = (1.01725-1)*100%= 0.01725*100% monthly percent change =1.725%

(C) given rate r = 3.4% compounded quarterly

r = 0.034/365 = 9.315 * 10 ^ - 5

(1) daily growth factor = 1 + 9.315 * 10 ^ - 5 = 1.00009315

(2) daily percent change = (1.00009315-1)*100%= 0.00009315*100% monthly percent change =0.009315%

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Answer:

c

Step-by-step explanation:

The number of exams that Gretchen has to take is 4 exams.

From the information illustrated, Gretchen spends 5.1 hours on Monday, 3/3/5 hours on Tuesday, and 5/3/10 hours on Wednesday studying for her final exams. The total hours that she used will be:

= 5.1 + 3 3/5 + 5 3/10

= 5.1 + 3.6 + 5.3

= 14 hours.

Since she spends 3/1/2 hours studying for each exam, the number of exams that she has to take will be:

= Number of hours / Hours used for each exam

= 14 / 3 1/2

= 4 exams

The number of exams are 4.

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