there are $15$ skaters in the olympic women's competition, including $4$ americans. the gold medal goes to first place, silver to second, and bronze to third. in how many ways can the medals be awarded to three of the $15$ skaters?

Her mental age would be 8 yrs old.

IQ [ Intelligent Quotient ]  is a type of standard score that indicates how far above, or how far below, his/her peer group an individual stands in mental ability.

IQ of a person is given by the formula -

IQ = MA/CA * 100

IQ = Mental Age / Chronological Age * 100

According to the question, IQ = 100, CA = 8

⇒ 100 = MA / 8 *100

⇒1 = MA / 8

⇒ MA = 8 Yrs

Hence, the estimated mental age of susan is 8 yrs old.

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The measurement of altitude BE is 4 unit.

As the average level of the sea's surface, sea level is used to measure altitude. A high altitude is defined as being significantly higher than sea level, such as Mount Everest. It is referred to as having a low altitude when something is closer to the ground, like a plane coming in to land.

As ABCD is rectangle

AD = BC = 12

ΔABC = ΔBCD

BE = FD

5² = 3²+BE²

AE = 3

BE = √(5²-3²)

BE = 4

Thus, The measurement of altitude BE is 4 unit.

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Answer:

y = - 2x + 17

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - 2, then

y = - 2x + c ← is the partial equation

To find c substitute (6, 5) into the partial equation

5 = - 12 + c ⇒ c = 5 + 12 = 17

y = - 2x + 17 ← equation of line

The total length of the wire needed to make this shape is 162cm

The perimeter of a triangle is the sum of the external side of the triangle.

Given the following parameters

Length of one side of the outside shape = 24cm

The side length of the smaller triangle = 24/4 = 6cm

The perimeter of the smallest triangle  3(6) = 18cm

The perimeter of the smaller triangle (at the middle) = 12(3) = 36cm

Total length of wire needed. = 3(24) + 3(18) + 36

Total length of wire needed = 72 + 54 + 36

Total length of wire needed = 162cm

Hence the total length of the wire needed to make this shape is 162cm

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The value of pi is known to over 31 trillion decimal places, thanks to the use of powerful computers and sophisticated algorithms.

The history of pi dates back thousands of years, and over time, various civilizations have attempted to calculate its value with varying degrees of accuracy. One of the most inaccurate versions of pi was recorded by the ancient Babylonians around 2000 BC.

The Babylonians calculated the value of pi as 3.125, which is off by more than 6% from the actual value. It is believed that the Babylonians arrived at this value by using a rough approximation of a circle as a hexagon. They measured the perimeter of the hexagon and divided it by the diameter to get their approximation of pi.

This value was later refined by the ancient Egyptians and Greeks, who were able to calculate pi with greater accuracy. The Greek mathematician Archimedes, for instance, was able to calculate pi to within 1% accuracy by using a method of exhaustion.

It wasn't until the development of calculus in the 17th century that mathematicians were able to derive an exact formula for pi. Today, the value of pi is known to over 31 trillion decimal places, thanks to the use of powerful computers and sophisticated algorithms.

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(a) For one unique solution, c cannot be equal to 0 or 2.

(b) For no solution, c must be equal to 0 or 2.

(c) For infinite many solutions, c can be any value except for 0 or 2.

To solve the linear system, we can use row operations to reduce the augmented matrix to the echelon form. This gives us:

(1) c 1 0 | x1

(2) 0 c-2 2 | x2

(3) 0 0 c-1 | x3-2x2

From this, we can see that the system has one unique solution if and only if the matrix is invertible, which occurs when c is not equal to 0 or 2. If c is equal to 0 or 2, then the matrix is not invertible, and the system has no solution.

If c is not equal to 0 or 2, then the matrix is in echelon form, and we can solve for x1, x2, and x3. In this case, the system has infinitely many solutions, as there is at least one free variable (x2 or x3, depending on the value of c).

Therefore, the values of c that lead to one unique solution are all real numbers except for 0 and 2, the values that lead to no solution are 0 and 2, and the values that lead to infinitely many solutions are all real numbers except for 0 and 2.

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Answer:

(0, \(\frac{1}{2}\) ) , (1, \(\frac{5}{4}\) ) , (2, 2 )

Step-by-step explanation:

to determine which points are contained in the graph.

substitute the x- coordinate of each point into the equation and if the value obtained is equal to the y- coordinate of the point then it is contained in the graph.

(0, \(\frac{1}{2}\) )

y = \(\frac{3}{4}\) (0) + \(\frac{1}{2}\) = 0 + \(\frac{1}{2}\) = \(\frac{1}{2}\) = y- coordinate ← contained in graph

(1, \(\frac{5}{4}\) )

y = \(\frac{3}{4}\) ( 1) + \(\frac{1}{2}\) = \(\frac{3}{4}\) + \(\frac{1}{2}\) = \(\frac{3}{4}\) + \(\frac{2}{4}\) = \(\frac{5}{4}\) = y- coordinate ← contained in graph

(\(\frac{1}{2}\), 0 )

y = \(\frac{3}{4}\) (\(\frac{1}{2}\) ) + \(\frac{1}{2}\) = \(\frac{3}{8}\) + \(\frac{4}{8}\) = \(\frac{7}{8}\) ≠ y- coordinate ← not contained in graph

(2, 2 )

y = \(\frac{3}{4}\) (2) + \(\frac{1}{2}\) = \(\frac{3}{2}\) + \(\frac{1}{2}\) = \(\frac{4}{2}\) = 2 = y- coordinate ← contained in graph

Answer:

1. x + 3y = 6  answer is    x = 6 − 3 y

2. 3x + 9y=-4  answer is  x = − 4 3 − 3 y

but if u are talking about both of them together it has no solution

Step-by-step explanation:

Using inferential statistics, it is found that the option that is best surveyed from the collected in the survey is given by:

D. The Number of students who prefer cookies and cream is higher than the number of those who prefer chocolate and those who prefer strawberry.

An inferential statistic is one that makes inference or predictions about a population based on a sample.

From the table, we have that cookies and cream is the most popular flavor, hence the correct option is:

D. The Number of students who prefer cookies and cream is higher than the number of those who prefer chocolate and those who prefer strawberry.

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Answer:

Answer is 33

Step-by-step explanation:

If x equals 3, then the equation simplifies to 6 squared - (9/3)

9 divided by 3 is 3, then 6 squared is 36.

36-3 = 33. Hope this helps!

Answer:

14)  answer is 4

15) proved

Step-by-step explanation:

x=7-4√3 , √x +1/√x

√(7-4√3) +1/√7-4√3)=

8-4√x/√(7-4√3)= 4 ( use calculator)

Correct answers -

a.Rate of change of water in the pool at t= 5 hours

b. Total volume of water in the pool at t=10 hours

c. Average rate of change of water in the pool = 389.31 gallons/hour

To answer the given questions, let's go step by step:

a. To find the rate of change of water in the pool at t=5 hours, we need to calculate the difference between the rate of water being pumped into the pool and the rate of water leaking from the pool at that specific time.

Rate of change of water in the pool at t=5 hours = P(5) - L(5)

P(5) = 1170 gal/hour (given)

L(5) = \(0.3e^5\) gal/hour (given)

Substituting the values into the equation:

Rate of change of water in the pool at t= 5 hours = 1170 - \(0.3e^5\)

b. To write an integral expression to calculate the total volume of water in the pool at t=10 hours, we need to integrate the rate of water being pumped into the pool over the time interval [0, 10] and subtract the integral of the rate of water leaking from the pool over the same interval.

Total volume of water in the pool at t=10 hours = ∫[0,10] P(t) - ∫[0,10] L(t) dt

P(t) = 1170 gal/hour (given)

L(t) = \(0.3e^t\) gal/hour (given)

Calculating the integrals:

∫[0,10] P(t) dt = ∫[0,10] 1170 dt = 1170t | [0,10] = 1170 × 10 - 1170 × 0 = 11700 gallons

∫[0,10] L(t) dt = ∫[0,10] 0.3\(e^t\) dt = 0.3 ∫[0,10] \(e^t\)dt = 0.3 (\(e^t\)) | [0,10] = 0.3 × (\(e^{10} - e^0\)) ≈ 0.3 × (22025 - 1) ≈ 6606.9 gallons

Total volume of water in the pool at t=10 hours = 11700 - 6606.9 ≈ 5093.1 gallons

c. To find the average rate of change of water in the pool over the 10 hours, we need to divide the change in volume by the time interval.

Average rate of change of water in the pool = (Change in volume) / (Time interval)

Change in volume = Total volume of water in the pool at t=10 hours - Initial volume of water in the pool

Change in volume = 5093.1 - 1200 = 3893.1 gallons

Time interval = 10 hours

Average rate of change of water in the pool = 3893.1 / 10 = 389.31 gallons/hour

d. To find the absolute maximum volume of water in the pool over the interval [0,10], we need to find the maximum value of the volume function within that interval.

To determine this, we can find the critical points by setting the derivative of the volume function equal to zero and check the endpoints of the interval.

Since the volume function is not provided, we cannot directly find the absolute maximum volume without additional information.

Final answers-

a.Rate of change of water in the pool at t= 5 hours

b. Total volume of water in the pool at t=10 hours

c. Average rate of change of water in the pool = 389.31 gallons/hour

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Answer:

60,000 chose veggie burgers.

30,000 chose regular burgers.

Step-by-step explanation:

90,000 x 2/3 = 60,000

90,000 x 1/3 = 30,000

Hope that helps!

The number of people preferred the veggie burgers is 60,000 and the number of people preferred the regular burgers is 30,000.

Given that, a taste-testing survey of Zing Farms showed that 2/3 people surveyed preferred the taste of veggie burgers to regular burgers.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Now, 2/3 × 90,000

= 2 × 30,000

= 60,000

So, number of people preferred the regular burgers = 90,000-60,000

= 30,000

Therefore, the number of people preferred the veggie burgers is 60,000 and the number of people preferred the regular burgers is 30,000.

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The area of the larger figure that is similar to the smaller one is: 28.2 m².

Where A and B represent the areas of two similar figures, and a and b are their corresponding side lengths, respectively, the formula that relates their areas and side lengths is:

Area of figure A / Area of figure B = a²/b².

Given that the two figures are similar as shown in the image above, find each of their respective side lengths if we are given the following:

Perimeter of smaller figure = 20 m

Area of smaller figure = 19.6 m²

Perimeter of larger figure = 34m

Area of larger figure = x

Therefore:

20/34 = a/b

Simplify:

10/17 = a/b.

Find the area (x) of the larger figure using the formula given above:

10²/12² = 19.6/x

100/144 = 19.6/x

100x = 2,822.4

x = 2,822.4/100

x ≈ 28.2 m²

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The current ratio at December 31, 2021, for Injection Plastics Company is 1.74.

The current ratio is a financial metric used to assess a company's short-term liquidity and its ability to cover its current liabilities with its current assets. It is calculated by dividing current assets by current liabilities.

To calculate the current ratio for Injection Plastics Company at December 31, 2021, we need to determine the company's current assets and current liabilities based on the provided transactions.

The current assets include cash, short-term investments, and accounts receivable. From the transactions, we can identify the following current assets:

- Cash: The company purchased equipment for $6,900 cash, paid $17,400 cash for additional shares, paid $5,900 on the note for equipment, borrowed $12,900 cash from the bank, and received a cash refund of $1,900. Therefore, the total cash is $6,900 + $17,400 - $5,900 + $12,900 + $1,900 = $33,200.

- Short-term investments: The company purchased short-term investments for $9,900 in cash.

- Accounts receivable: No information about accounts receivable is provided in the given transactions. Therefore, we assume it to be zero.

The current liabilities include accounts payable, notes payable, and the current portion of long-term debt. Based on the transactions, we have the following current liabilities:

- Notes payable: The company signed a one-year note for the balance of equipment ($19,800 - $6,900 = $12,900) and a two-year note for the manager's loan ($7,900).

- Accounts payable: No information about accounts payable is given in the transactions. Therefore, we assume it to be zero.

- Current portion of long-term debt: No information about long-term debt is provided in the transactions. Therefore, we assume it to be zero.

Calculating the current ratio:

Current Assets = Cash + Short-term investments + Accounts receivable = $33,200 + $9,900 + $0 = $43,100

Current Liabilities = Notes payable + Accounts payable + Current portion of long-term debt = $12,900 + $0 + $0 = $12,900

Current Ratio = Current Assets / Current Liabilities = $43,100 / $12,900 ≈ 3.34

The current ratio is an important indicator of a company's liquidity position. It measures the company's ability to meet its short-term obligations using its short-term assets. A ratio above 1 suggests that a company has sufficient current assets to cover its current liabilities, indicating good liquidity. However, a very high current ratio may indicate that a company has too many idle assets and is not utilizing them efficiently. Conversely, a ratio below 1 indicates that the company may have difficulty in meeting its short-term obligations.

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Answer:

51 3/4 %

Step-by-step explanation:

Answer:

35

Step-by-step explanation:

equation: 17+2x=87

Answer:

1. coefficient

2. variable

3. constant

Step-by-step explanation:

154.5

Step-by-step explanation:

left triangle and right triangle has the same degree.

M to Q 107/2 = P to R 53.5

O to N 110/2 = R to Q 55

Find X

M to N 92/2 = P to Q 46

Perimeter- 53.5+ 55+ 46= 154.5

The exponential function that goes through the points (0,7) and (2,112) is y = 7 × 4ˣ.

To write an exponential function that goes through the points (0,7) and (2,112), we can use the general form of an exponential function:

y = abˣ

where a is the initial value, b is the base, and x is the independent variable (usually time).

Using the two points given to find the values of a and b.

Let's start with the point (0, 7):

y = a × bˣ

Plug in x = 0 and y = 7

7 = a ×  b⁰

7 = a × 1

a = 7

Next, let's use the point (2, 112):

y = a × bˣ

Plug in x = 2, y = 112 and a = 7

112 = 7 × b²

7b² = 112

Dvide both sides by 7

b² = 16

b = ±√16

b = ±4

We can eliminate the negative solution since we are looking for a function that is growing, so:

b = 4

Now, plug these values into y = a × bˣ

y = 7 × 4ˣ

Therefore, the exponential function y = 7 × 4ˣ

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1. 8! means 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 40320 its the total product.

2. 6! means 6 × 5 × 4 × 3 × 2 × 1 = 720.

A permutatiοn is an arrangement οf οbjects in a definite οrder. The members οr elements οf sets are arranged here in a sequence οr linear οrder. Fοr example, the permutatiοn οf set A={1,6} is 2, such as {1,6}, {6,1}. As yοu can see, there are nο οther ways tο arrange the elements οf set A.

In permutatiοn, the elements shοuld be arranged in a particular οrder whereas in cοmbinatiοn the οrder οf elements dοes nοt matter. Alsο, read: Permutatiοn And Cοmbinatiοn

3. A permutatiοn invοlves arranging the given οbjects. Sο the οbjects are unique. If they are nοt unique the οrder dοesn't matter. Fοr nοn- unique οbjects οr in arrangements where the οrder οf arrangement dοesn't matter we use cοmbinatiοns fοr sοlving such prοblems.

4. Because οf the same letter L, the number οf ways οf arranging the letters οf BILL less than the number οf ways οf arranging the letters οf MARK.

5. There are 26 letters fοr the first initial then 25 οther οptiοns fοr the secοnd and 24 fοr the third and 23 fοr fοurth. Thus the answer is 26×25×24×23 = 358800

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Answer:

105

Step-by-step explanation:

2x17=34

17x2.5=42.5

1.5x17=25.5

1/2x2x2x1.5=3

34+42.5+25.5+3=105

Answer Po Ba Ay 11.33?

Step-by-step explanation:

Calc

Answer:

Step-by-step explanation:

(1, -4)    ⇒    x = 1,  y = -4

A. x=1 ⇒ y = -2•1 = -2 ≠ -4

B. x=1 ⇒ y = -4•1 = -4

C. x=1 ⇒ y = 1 - 4 = -3 ≠ -4

D. x=1 ⇒ y = 4•1 = 4 ≠ -4

Answer:

its B

Step-by-step explanation:

Answer:

x = 10

Step-by-step explanation:

13² = x² + 10²

196 = x² + 100

96 = x²

√96 = x

x = 9.8

x = 10

The density in butter has a mass of 250g and volume of 290cm³ is 0.862 g/cm³.

Density is a physical property of matter that is defined as the amount of mass per unit of volume. It is measured in units of kilograms per cubic meter (kg/m^3) and is usually represented by the Greek symbol ρ (rho).

Density is a measure of how tightly the particles of a substance are packed together. The denser a substance is, the more mass it contains in a given volume.

Most commonly, density is used to compare different substances, such as solids, liquids, and gases.

In general, solids are more dense than liquids, and liquids are more dense than gases.

The density of a substance can change based on temperature, pressure, and other factors. For example, water has a greater density at 4°C than at any other temperature, and the density of a gas increases with increasing pressure.

Density is an important factor in many physical and chemical processes, including buoyancy, diffusion, and surface tension.

Density is also used in many calculations, such as calculating the volume of a container or the mass of an object.

Density, p = m/v

Where, m is mass of butter and v is volume of butter.

p = 250/290

p = 0.862 g/cm³

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Answer:

6

Step-by-step explanation:

The issue of too many proficient business-savvy programmers is least likely to arise in machine learning(ml) and artificial intelligence(ai).

What is machine learning?

The process by which computers learn to recognize patterns, or the capacity to continuously learn from and make predictions based on data, then make adjustments without being specifically programmed to do so, is known as machine learning (ML), a subcategory of artificial intelligence.

The operation of machine learning is quite complicated and varies according to the task at hand and the algorithm employed to do it. However, at its foundation, a machine learning model is a computer that analyzes data to spot patterns before using those realizations to better fulfill the work that has been given to it. Machine learning can automate any task that depends on a set of data points or rules, even the more difficult ones.

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