Blake walked 7/8 of a mile in 1/5
of an hour. If Blake continued walking at the same rate, what is the distance he would travel in one hour?

Answer:

\(A=2513.27\ cm^2\)

Step-by-step explanation:

The radius of semicircle window, r = 40 cm

The area of semicircle is given by :

\(A=\dfrac{\pi r^2}{2}\)

Substitute all the values in the above formula.

\(A=\dfrac{\pi \times 40^2}{2}\\\\A=2513.27\ cm^2\)

So, the area of the window is equal to \(2513.27\ cm^2\).

The correct matching of positive and negative number according to the situation is given by,

An increase in altitude of 6 miles.→ +6

6 degrees below zero.→-6

Taking 12 steps back.→-12

Going up 12 stairs.→+12

Depositing $2,000 →+2000

A withdrawal of $2,000→ -2000.

The left hand side statement representing the situation of right hand side are as follow,

An increase in altitude of 6 miles represents the positive value of 6 as it increases.

+ 6.

6 degrees below zero represents the negative value of 6 as below zero numbers are negative.

-6.

Taking 12 steps back represents the negative value of 12 as moving back is negative direction.

-12.

Going up 12 stairs represents the positive value of 12 as moving up is always positive.

+12.

Depositing $2,000 represents the positive value of 2000 as it increases the amount.

+2000

A withdrawal of $2,000 represents the negative value of 2000 as it decreases the amount.

-2000.

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Answer:

y=2/3+5

Step-by-step explanation:

Answer:

y=2/3+5

Step-by-step explanation:

Answer:

A: 25

B: 800

C: 2,400

Step-by-step explanation:

Hopes this helps. :) ( Unless you have already solved ) Just have a good day.

Answer:

A: 25

B: 800

C: 2,400

Step-by-step explanation:

Answer:

\(y=11\)

Step-by-step explanation:

So we have the function:

\(g(x)=|x-4|+8\)

First, note that this is an absolute value function.

The standard form of an absolute value function is:

\(y=|mx-b|+c\)

Where m is the slope and the vertex point is (b/m, c).

Let's determine our vertex first. B is 4, m is 1, and c is 8. So:

\((4/1,8)=(4,8)\)

So, our vertex is at (4,8).

Also, note that there is no negative in front of our absolute value, so this is going upwards.

Now, recall that an absolute value function has the general shape of a V. Since this is a positive absolute value, all x-values to the left of the vertex will be decreasing, while all x-values to the right of the vertex will be increasing.

In other words, from negative infinity to 4, the function will be decreasing.

And from 4 until positive infinity, the function will be increasing.

We want to find the minimum value of the function between [-2,1].

Since [-2,1] is to the left of the vertex, this means that the function is decreasing.

So, to find the minimum value, we just need to use the x-value closest to the vertex, in this case, x=1.

So, to find the minimum value, we just need to substitute 1 into g(x). So:

\(g(1)=|1-4|+8\)

Subtract:

\(g(1)=|-3|+8\)

Absolute Value:

\(g(1)=3+8\)

Add:

\(g(1)=11\)

Therefore, our minimum value of the g(x) on the interval [-2,1] is y=11.

We can graph the function to verify our answer. As we can see, the minimum value on the interval [-2,1] (black line) is indeed y=11.

Answer:

25√3mm

Step-by-step explanation:

this might be the answer..

Answer:

\(25\sqrt{3}\)

Step-by-step explanation:

\(\frac{10^2*\sqrt{3} }{4}\)

Answer:

11

Step-by-step explanation:

4 times 11 is 44

Answer:B- 11

Step-by-step explanation:

To find the slope of a graphed line, use rise/run. Count how many units you have to rise and run to get to from one point to the other. Up and right means positive slope, down and left means negative slope.

So from (-4,-2) to (2,2).

Now count how many units you're going up and right.

I counted 4 up and 2 right. So the slope is 4/2 or can be simplified to 2/1 or 2.

If you have to find the slope intercept equation, all you're missing is b, the y-intercept. You can find the y-intercept by looking at where the line crosses the y-axis, which in this problem is 6.

The slope intercept formula is y=mx+b

m is the slope, and b is the y-intercept.

So if you put the slope and the y-intercept in the equation, the slope intercept for this graph is:

y=2x+6

Hope this helped!

The arrival rate is found to be 30 emails per hour and the service rate is calculated to be 45 emails per hour.

It has been mentioned in the question that in every 2 minutes, customers send emails to a help desk of an online retailer, on an average, and the standard deviation of the inter-arrival time is also given to be 2 minutes. The online retailer has three employees for answering those emails.

It takes almost 4 minutes to write a response email to the customer, on average. The standard deviation (SD) of the service times is 2 minutes. This is a g/g/k type queue.

Therefore the arrival rate per hour is given by the following relation:

Arrival rate in 1 hr = No. of minutes in an hr / inter arrival time of email taken in minutes

Given here,

No. of minutes in an hour = 60 minutes

Inter arrival time of the email taken in minutes = 2 minutes

∴ Arrival rate in 1 hr = 60 / 2

                                = 30 emails / hr

Hence the arrival rate is 30 emails per hour.

Now for finding out the service rate we have the following formula:

Service rate = No. of minutes in an hr x No. of employes answering/ average time that is required to write response email

Given here,

No. of minutes in an hr = 60 minutes

No. of employes answering = 3

Average time that for writing response email = 2 minutes

∴ Service rate = 60 * 3 / 4

                       = 45 emails / hr

Hence the service rate is 45 emails per hour.

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The factors of the polynomial are (x - 4)(x - 4)(x + 7), and the polynomial is completely factored.

For the polynomial x³ - 7x² - 16x + 112, the following statements are true:

1. The factors of the polynomial are (x - 4)(x - 4)(x + 7).

2. The polynomial is completely factored.

To factor the polynomial completely, we can use different factoring techniques such as grouping, factoring by grouping, or synthetic division.

In this case, we observe that the number 4 is a root of the polynomial since when we substitute x = 4 into the polynomial, we get zero.

Using synthetic division or long division, we can divide the polynomial by (x - 4) twice to obtain the factored form (x - 4)(x - 4)(x + 7).

Hence, the factors of the polynomial are (x - 4)(x - 4)(x + 7), and the polynomial is completely factored.

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As per the given question,

width of a goal is 24 inches times the diameter of the puck

Diameter of the puck = smallest odd prime no. = 3

Now ,

width of the goal is;

= 24 * 3                         (three times of the puck)

= 72 inches.

Converting 72 inches into feet ;

Ans = 6 feet.

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If 09 people can complete the job in 75 days then 25 people needs 45 days to complete the job.

Let T be the time and L be the Labor (Number of people working on the bridge).

T ∞ 1/√L  (Inverse relationship)

T = K/√L                   ----------------------------- (1)

Since, Constant "K" is introduced once the variation sign (∞) changes to equality (=) sign.

According to the question,

Time (T) = 75 days    and

labor (L) = 09

From the equation (1), we get,

    T = K / √L

⇒ 75   = K/√9

⇒ 75= K/3

⇒ K= 225

First, the relationship between these variables is:

                       T = 225/√L

Therefore, how long it will take 25 people to do it means that we should look for the time.

                           T=225/√L

                      ⇒  T= 225/√25

                      ⇒  T= 225/5

                      ⇒  T= 45 days.

therefore, 25 people needs 45 days to complete the job.

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Based on the amount predicted to be spent, the hypotheses Null Hypothesis = $1,007.24 and Alternate Hypothesis ≠ $1,007.24

The null hypothesis, or H0, in statistics science is the exact reverse of what the researcher wants to investigate. Generally, unless there is compelling proof to the contrary, the null hypothesis is taken to be correct. Another theory that will demonstrate the area one wants to investigate and be reflected by H1 must be developed.

The forecast is confirmed by the null hypothesis, which in this instance is that the typical consumer will indeed spend $1,007.24. According to the Alternate Hypothesis, the predicted occurrence won't occur, so in this instance, the shopper wouldn't spend $1,007.24. In conclusion, the variant contradicts the null hypothesis and supports it.

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Answer:

6

Step-by-step explanation:

Integers are just whole numbers.

So between 1.25 and 7.1 there is...

2,3,4,5,6,7

These are 6 integers.

\(oOoBrainlyPrincessoOo\)

Integers are positive and negative numbers.

So integers between 1.25 and 7.1 are : 2, 3, 4, 5, 6, and 7.

That's a total of 6 integers.

Hope it helps!

\(GraceRosalia\)

ΣX for the sample with n=8 and mean M=12 is 96.

The value of ΣX represents the sum of all the individual scores in a sample.

To calculate ΣX, we multiply the sample size (n) by the sample mean (M). In this case, we have a sample size of n=8 and a mean of M=12.

ΣX = n * M = 8 * 12 = 96.

Therefore, the value of ΣX for this sample is 96.

In the second scenario, we have a sample of n=15 scores with a mean of M=6. We add one more score with a value of X=22 to the sample.

To find the new sample mean, we need to calculate the sum of all the scores in the new sample and divide it by the new sample size.

The sum of the scores in the original sample can be calculated as ΣX = n * M = 15 * 6 = 90.

When we add the score X=22 to the sample, the new sum of scores becomes ΣX = 90 + 22 = 112.

The new sample size is n + 1 = 15 + 1 = 16.

To find the new sample mean, we divide the sum of the scores by the new sample size:

New sample mean = ΣX / (n + 1) = 112 / 16 = 7.

Therefore, the value for the new sample mean is 7.

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Answer:

w = (0, 15)

Step-by-step explanation:

w²-15w =0

w(w-15)=0

w=0 , w=15

if w=0

0(0-15)=0

0(-15)=0

0=0

if w=15

15(15-15)=0

15(0)=0

0=0

Answer:

n=-6

Step-by-step explanation:

2(n+5)=-2

2n+10=-2 (distribute the 2)

2n=-12 (subtract 10 from left, add it to right)

n=-6

a) pV_m = RT(1 + ((-RT / a) - b)V_m - (a / V_m) - b^2 / V_m)  this equation can be written in the form of a virial equation of state in powers of 1/V_m.

b) a ≈ 1.673 cm^6·atm·mol^(-2)

c) The Boyle-temperature for argon can be estimated using the calculated van der Waals constants as V_m approaches infinity.

Step by step:

(a) To show that the van der Waals equation can be written in the form of a virial equation of state, we start with the given van der Waals equation:

p = (RT / (V_m - b)) - (a / V_m^2)

We can rewrite this equation by multiplying both sides by V_m:

pV_m = RT - bV_m - (a / V_m)

Now, let's substitute B and C in terms of a and b:

B = b - (RT / a)

C = b^2

Substituting these values into the equation, we have:

pV_m = RT - (RT / a)V_m - (a / V_m) - bV_m - b^2 / V_m

Rearranging terms, we get:

pV_m = RT(1 + ((-RT / a) - b)V_m - (a / V_m) - b^2 / V_m)

This equation can be written in the form of a virial equation of state in powers of 1/V_m.

(b) Given that B = -21.7 cm^3·mol^(-1) and C = 1.200×10^3 cm^6·mol^(-2), and using R = 8.2057×10^(-2) dm^3·atm·K^(-1)·mol^(-1), we can substitute these values into the equations for B and C:

-21.7 = b - (8.2057×10^(-2) / a) (Equation 1)

1.200×10^3 = b^2 (Equation 2)

From Equation 2, we can solve for b:

b = ±√(1.200×10^3)

Since b cannot be negative according to the van der Waals equation, we take the positive square root:

b = √(1.200×10^3) = 34.64 cm^3·mol^(-1)

Now, substituting this value of b into Equation 1, we can solve for a:

-21.7 = 34.64 - (8.2057×10^(-2) / a)

Solving for a, we find:

a = (8.2057×10^(-2)) / (34.64 + 21.7)

a ≈ 1.673 cm^6·atm·mol^(-2)

(c) To estimate the Boyle temperature, we use the condition:

d(1/V_m) / dZ = 0

At Boyle temperature, V_m approaches infinity. Taking the derivative, we have:

d(1/V_m) / dZ = (2a / V_m^3) - b = 0

Solving for V_m, we get:

V_m = (2a / b)^(1/3)

Substituting the values of a and b that we calculated earlier, we can find V_m:

V_m = (2(1.673) / (34.64))^(1/3)

V_m ≈ 2.519 dm^3·mol^(-1)

Therefore, the Boyle temperature for argon can be estimated using the calculated van der Waals constants as V_m approaches infinity.

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The real numbers can be classified as either rational or irrational numbers.

1. Rational Numbers:
Rational numbers can be expressed as the ratio (or fraction) of two integers. They can be written in the form p/q, where p and q are integers and q is not equal to zero. Rational numbers can be positive, negative, or zero. Some examples of rational numbers include 1/2, -3/4, and 5.

2. Irrational Numbers:
Irrational numbers cannot be expressed as the ratio of two integers. They are non-repeating and non-terminating decimals. Irrational numbers can be positive or negative. Some examples of irrational numbers include √2, π (pi), and e (Euler's number).

It is important to note that the set of real numbers contains both rational and irrational numbers. Every rational number is a real number, but not every real number is a rational number. This means that there are real numbers that cannot be expressed as a fraction.

In summary, the classification of real numbers as rational or irrational depends on whether they can be expressed as a ratio of integers (rational) or not (irrational). The set of real numbers contains both rational and irrational numbers, providing a comprehensive representation of all possible values on the number line.

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Answer:

71+112+48+x=360

231+x=360

x=360-231

x=129

the measure for the missing angle is 129

The area of the rectangle is 3\(\sqrt{56}\)

Given,

A rectangle has a length of √7 and a width of 3√8.

We need to find the area of the rectangle.

The area is given by:

Area = Length x width

Find the length and width of a rectangle.

Length = \(\sqrt{7}\)

Width = 3\(\sqrt{8}\)

Find the area of the rectangle.

Area =  Length x width

       = \(\sqrt{7}\) x 3\(\sqrt{8}\)

When there are two different square roots we multiply them together under one root.

\(\sqrt{a\times b} ~~=~~\sqrt{a}\times\sqrt{b}\)

Now,

       = 3\(\sqrt{7\times8}\)

       = 3\(\sqrt{56}\)

Thus the area of the rectangle is 3\(\sqrt{56}\)

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Answer: C 24

Step-by-step explanation:

The measure of the length of EF in a right-angle triangle is 24 units, then the correct option is C.

It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function. The Pythagoras is the sum of the square of two sides is equal to the square of the longest side.

The right-angle triangle is shown in a diagram. Then by the Pythagoras theorem, we have

P² = H² - B²

P² = 25² - 7²

P² = 625 - 49

P² = 576

 P = 24

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An iterative rule, aₙ to model the sequence formed by the number of seats in each row is: aₙ = 7n + 11

The row that has 102 seats is: 13th row

The general formula to find the nth term of an arithmetic sequence is:

aₙ = a + (n - 1)d

where:

a is first term

d is common difference

n is position of term

We are given:

First row = 18 seats

Second row = 25 seats

Common difference = 7

Thus:

aₙ = 18 + (n - 1)7

aₙ = 18 + 7n - 7

aₙ = 7n + 11

The row that has 102 seats is:

102 = 7n + 11

7n = 102 - 11

7n = 91

n = 91/7

n = 13

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Answer:

8

Step-by-step explanation:

8 is the third digit meaning it's in the thousands

Answer:

x >= 1/5

Step-by-step explanation:

2 + 5x >= 3

5x >= 1

x >= 1/5

The recurrence relation for the amount of water in the bird bath at the end of day n is W(n) = (2/3) * W(n-1) + 1, where n > 0.

5) Recurrence Relation for Water in the Bird Bath:

Let W(n) represent the amount of water in the bird bath at the end of day n.

At the end of day 0, the bird bath contains 8 gallons of water, so we have W(0) = 8.

Each day, one-third of the water evaporates, and Andrew adds one gallon. This means that the amount of water at the end of day n is equal to two-thirds of the water at the end of the previous day, plus one gallon added.

Therefore, the recurrence relation for W(n) is:

W(n) = (2/3) * W(n-1) + 1, where n > 0.

At the end of day n, the amount of water is obtained by taking two-thirds of the water at the end of the previous day (W(n-1)) and adding one gallon (since Andrew adds one gallon each day).

For example, to find the amount of water at the end of day 1 (W(1)), we substitute n = 1 in the recurrence relation:

W(1) = (2/3) * W(0) + 1

    = (2/3) * 8 + 1

    = 5.33 + 1

    = 6.33 gallons.

This relation allows us to calculate the amount of water in the bird bath for any given day based on the previous day's amount, taking into account evaporation and the addition of one gallon each day.

6) Recurrence Relation for Spread of a Virus:

(a) Recurrence Relation:

Let V(n) represent the number of infected people on day n.

On day 1, one person is infected, so we have V(1) = 1.

On each subsequent day, each infected person gives the cold to two others. This means that the number of infected people on day n is twice the number of infected people on the previous day.

Therefore, the recurrence relation for V(n) is:

V(n) = 2 * V(n-1), where n > 1.

Starting from day 1, the number of infected people doubles each day because each infected person infects two others.

For example, to find the number of infected people on day 3 (V(3)), we substitute n = 3 in the recurrence relation:

V(3) = 2 * V(2)

    = 2 * (2 * V(1))

    = 2 * (2 * 1)

    = 4.

This means that on day 3, there are 4 infected people.

(b) Limitations of the Model:

- This model assumes that each infected person will always infect exactly two others. In reality, the rate of transmission may vary depending on various factors such as social interactions, hygiene practices, and preventive measures.

- The model does not consider factors such as recovery or immunity. It assumes that once a person is infected, they remain infected and continue to spread the virus indefinitely, which is not realistic.

- It assumes a homogeneous population, where every individual has an equal chance of being infected. In reality, the spread of a virus may be influenced by various factors such as age, pre-existing health conditions, and geographical location.

- The model does not consider external factors such as vaccination campaigns, quarantine measures, or changes in behavior due to awareness and education.

The recurrence relation for the spread of the virus is V(n

) = 2 * V(n-1), where n > 1. However, this model has limitations as it oversimplifies the spread of a virus by assuming constant transmission rates, neglecting recovery or immunity, and ignoring other influential factors. Real-world virus spread is much more complex and influenced by various factors that this model does not account for.

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To determine which payment plan the real estate investor would prefer, we need to compare the present value of each payment option. Assuming a discount rate of 0%, meaning no time value of money is considered, we can directly compare the payment amounts.

1. Payment of $2,000 at the first of each month: This results in a total payment of $24,000 over the 12-month lease.

2. Upfront payment of $24,000: This option requires paying the full amount at the beginning of the lease.

3. Payment of $2,000 at the end of each month: Similar to option 1, this results in a total payment of $24,000 over the 12-month lease.

4. Upfront payment of $12,000 and $12,000 half-way through the lease: This option requires paying $12,000 at the beginning of the lease and another $12,000 halfway through the lease.

Since all the payment options have a total cost of $24,000, the real estate investor would likely prefer the payment plan that offers more flexibility or matches their cash flow preferences. Options 1 and 3 provide the investor with the option to pay monthly, while options 2 and 4 require a larger upfront payment. The choice would depend on the investor's financial situation and preferences.

Answer:

Step-by-step explanation:

y-intercept:5

slope:-½

linear equation slope intercept form:y=mx+b

therefore

y=-½x+5

our answer is D

Answer:

250

Step-by-step explanation: