Consider points R, S, and T.

Point S is in the middle. Point R is below and to the left of point S. Point T is below and to the right of point S.

Which statement is true about the geometric figure that can contain these points?

No line can be drawn through any pair of the points.
One line can be drawn through all three points.
One plane can be drawn so it contains all three points.
Two planes can be drawn so that each one contains all three points.

Answer:

The balance on the loan f(p) = $100 - $20 × p

Step-by-step explanation:

The parameters of the question are;

The loan amount = $100

The amount of monthly payment for the loan = $20

The function rule for the balance of the function f(p) where p is the number of payments is given as follows;

The balance on the loan, f(p) = The loan amount less the total amount paid

The total amount payment Jeania has made = Amount of monthly payment × Number of months paid, p

The total amount payment Jeania has made = $20 × p

∴ The balance on the loan, f(p) = $100 - $20 × p

Which gives;

f(p) = $100 - $20 × p.

Answer:

The answer is below

Step-by-step explanation:

The z score is a measure used in statistic to determine the number of standard deviations by which the raw score is above or below the mean. . The z score is given by:

\(z=\frac{x-\mu}{\sigma}\\ where\ \mu \ is \ the\ mean, \sigma\ is\ the\ standard\ deviation\ and\ x \ is\ the\ raw\ score\)

(a) Z = -0.12 and Z = 0.12

From the normal distribution table, Area between z equal -0.12 and z equal 0.12  = P(-0.12 < z < 0.12) = P(z < 0.12) - P(z < -0.12) = 0.5478 - 0.4522 = 0.0956 = 9.56%

b) The area that lies between Z = - 0.35 and Z=0

From the normal distribution table, Area between z equal -0.35 and z equal 0  = P(-0.35 < z < 0) = P(z < 0) - P(z < -0.35) = 0.5 - 0.3594 = 0.1406 = 14.06%

c) The area that lies between Z = 0.02 and Z = 0.82

From the normal distribution table, Area between z equal 0.02 and z equal 0.82  = P(0.02 < z < 0.82) = P(z < 0.82) - P(z < 0.02) = 0.7939 - 0.5080 = 0.2859 = 28.59%

The length of diagonal AB is approximately 24.4 inches.

We have,

If we assume that the pennant is a right triangle with one of the legs being 14 inches (the short edge) and the other leg is unknown, we can use the Pythagorean theorem to find the length of the diagonal.

According to the Pythagorean theorem,

14² + x² = 24²

where x is the length of the other leg (the one we are trying to find).

Solving for x,

x² = 24² - 14²

x² = 400

x = 20

The length of the other leg of the triangle is 20 inches, and using the Pythagorean theorem, we can find the length of the diagonal:

AB = √(14² + 20²) = √(596) ≈ 24.4 inches

Thus,

The length of diagonal AB is approximately 24.4 inches.

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The probability that the dealership will make a profit if 4 customers enter on Friday is approximately 24.01%.

a. You can estimate the Hypergeometric Distribution with the Binomial Distribution under the following conditions:
1. The sample size (n) is relatively small compared to the population size (N).
2. The probabilities of success (p) and failure (q) remain approximately constant throughout the sampling process.

In this case, since we're assuming sampling with replacement, identical cars, and independent trials with constant probability, it's appropriate to use the Binomial Distribution.

b. To calculate the probability that the dealership will make a profit if 4 customers enter on Friday, we can use the Binomial Distribution formula:

P(X = k) = (nCk) * (p^k) * (q^(n-k))

Where:
- P(X = k) is the probability of exactly k successes (cars sold)
- nCk is the number of combinations of n items taken k at a time
- p is the probability of success (car sold)
- q is the probability of failure (car not sold)
- n is the number of trials (customers)
- k is the number of successes (cars sold)

Here, n = 4, p = 0.70, and q = 1 - p = 0.30. We need to find the probability of selling at least 4 cars (k ≥ 4) to make a profit:

P(X ≥ 4) = P(X = 4)
P(X = 4) = (4C4) * (0.70^4) * (0.30^0)
P(X = 4) = 1 * (0.2401) * (1)
P(X = 4) = 0.2401

Therefore, the probability that the dealership will make a profit if 4 customers enter on Friday is approximately 24.01%.

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The general solution to the given differential equation is

y = ± √(1 / (2ln|t| + 4/t - C2))

To solve the given differential equation, we can use the method of separable variables. Let's go through the steps:

Rearrange the equation to separate the variables:

t^2y' + 2ty - y^3 = 0

Divide both sides of the equation by t^2:

y' + (2y/t) - (y^3/t^2) = 0

Now, we can rewrite the equation as:

y' + (2y/t) = (y^3/t^2)

Separate the variables by moving the y-related terms to one side and the t-related terms to the other side:

(1/y^3)dy = (1/t - 2/t^2)dt

Integrate both sides of the equation:

∫(1/y^3)dy = ∫(1/t - 2/t^2)dt

To integrate the left side, let's use a substitution. Let u = y^(-2), then du = -2y^(-3)dy.

-1/2 ∫du = ∫(1/t - 2/t^2)dt

-1/2 u = ln|t| + 2/t + C1

-1/2 (y^(-2)) = ln|t| + 2/t + C1

Multiply through by -2:

y^(-2) = -2ln|t| - 4/t + C2

Now, take the reciprocal of both sides to solve for y:

y^2 = (-1) / (-2ln|t| - 4/t + C2)

y^2 = 1 / (2ln|t| + 4/t - C2)

Finally, taking the square root:

y = ± √(1 / (2ln|t| + 4/t - C2))

Therefore, the general solution to the given differential equation is:

y = ± √(1 / (2ln|t| + 4/t - C2))

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Answer:

There is no picture

Step-by-step explanation:

The angle between the stick and the base of the box is 77. 9 degrees

To determine the angle between the stick and the base, we have to know the trigonometric identities.

These identities are;

From the information given, we have;

sin A = FB/AB

Given that;

GB = 14.5cm

AB = 18. 6cm

substitute for the length of the sides, we have;

sin A = 14.5/18. 6

Divide the values, we have;

sin A = 0. 7796

Find the inverse sine

A = 77. 9 degrees

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The velocity of money (V) by the quantity equation  is 4.

Money exchange rates in an economy are gauged by the concept of velocity of money. The quantity equation is expressed as:

M * V = P * Y

where:

M = Quantity of money (in this case, 3,000 Billions of Dollars)

V = Velocity of money (to be estimated)

P = Price level (in this case, 1.0)

Y = GDP or output (in this case, 12,000 Billions of Dollars)

To estimate the velocity of money (V), we rearrange the equation:

V = (P * Y) / M

Substituting the given values:

V = (1.0 * 12,000) / 3,000

V = 12,000 / 3,000

V = 4

Therefore, the estimated velocity of money (V) is 4.

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Answer:

b

Step-by-step explanation:

C

The mistake the arrangers made is in the second inequality. They considered the number of caps to be bought should be at least 5 times greater than the number of blouses, not the other way around. The correct inequality should be C

The correct answer is D) The first inequality should be s + h ≤ 1800.

The organizers made an error in the first inequality. The given inequality 10s + 8h ≤ 1800 represents the total cost of buying shirts (10s) and hats (8h) should be less than or equal to $1800. However, this does not take into account the fact that the organizers want to buy at least 5 times as many shirts as hats, as indicated by the second inequality h ≥ 5s.

The correct way to represent this constraint is by using the equation s + h ≤ 1800, which ensures that the total number of shirts and hats purchased does not exceed $1800 in cost. This is because the organizers want to make sure that the total cost of shirts and hats combined does not exceed the budget of $1800.

Answer:

63 =  EHF

Step-by-step explanation:

We know that EHG is a right angle which is 90 degrees

FHG is 27 degrees

EHG = FHG + EHF

90 = 27+  EHF

90-27 = EHF

63 =  EHF

Mathematics → Solid Figures → Volume

The volume of a cylinder is:

In this question,

r = 2 ft (4/2 =2)

h = 5 ft

Then, the volume of the cylinder is (Vc):

Using π = 3:

The volume of a rectangular prism (Vr) is:

In this question:

l = 9 ft

w = 5 ft

h = 5 ft

Then, the volume of the rectangular prism is:

The volume of the object (V) is the sum of the volumes:

Answer: 285 ft³.

Answer:

See below

Step-by-step explanation:

To find the mean, you take each data point, add them together, and divide it by the number of data points.

Problem 1

Mean of High Temperatures = (65+67+54+52+63+69+75)/7 = 445/7 = between 63 and 64

Problem 2

Mean of Low Temperatures = (61+55+37+29+34+42+54)/7 = 312/7 = between 44 and 45

Answer:

x = 20 , y =43

Step-by-step explanation:

1- 7x-3 + 3x-17 = 180

10x = 200, x = 20

Y = 3x-17  x is 20 so Y=60-17=43

Answer:

Rectangle

ABCD

LMNO

PQRS

Area

8 sq. cm

12 sq. cm

6 sq. cm

Length

4 cm

4 cm

2 cm

Breadth

2 cm

3 cm

3 cm

Length × Breadth

4 cm × 2 cm = 8 cm2

4 cm × 3 cm = 12 cm2

2 cm × 3 cm = 6 cm2

In each case we observe the length × breadth = Area of the rectangle.

Therefore, area of rectangle = length × breadth = l × b sq. units

From the above multiplication, we get the following facts:

Length of the rectangle = Area of the RectangleBreadth of the Rectangle

Breadth of the rectangle = Area of the RectangleLength of the Rectangle

Answer:

\(x^{3}-\frac{8}{7} xy^{2} -\frac{7}{8}x^{2}y+y^{3}\)

Step-by-step explanation:

\((\frac{1}{7} x -\frac{1}{8} y)*(7x^{2} - 8y^{2}) =\frac{1}{7} x*7x^{2} -\frac{1}{7} x*8y^{2}-\frac{1}{8} y*7x^{2} + \frac{1}{8} y*8y^{2}=\\\\=x^{3}-\frac{8}{7} xy^{2} -\frac{7}{8}x^{2}y+y^{3}\)

Answer: 13

Step-by-step explanation: 17-4=13

Answer:

Step-by-step explanation:

The distance formula is d=√x2 - x1²+ y2 - y1².

The first thing to do is substitute the numbers we have into this formula.

d=√9 - 9²+ 4 - -7²

d=√0² + 11²

d = d=√0 + 121

d = d=√121

d = 11

The measure of length AB equals to 5 cm.

Congruent triangles have both the same shape and the same size.

Given is a triangle ΔABC.

Now, we can write that in ΔABD and ΔCBD as -

AD = DC        {Given}

∠ADB = ∠CDB = 90°

BD = BD         {Common}

So, we can write that ΔABD ≅ ΔCBD. So, we can write -

AB = BC = 5 cm

Therefore, the measure of length AB equals to 5 cm.

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Answer:

200000+60000+8000+700+40+1

Step-by-step explanation:

268,741

2 is in the hundred thousands place  200000

2 is in the ten thousands place  60000

8 is in the  thousands place  8000

7 is in the hundreds place 700

4 is in the tens place  40

1 is in the one place  1

Add these together

200000+60000+8000+700+40+1

Answer:

\((2\times100000)+(6\times10000)+(8\times 1000)+(7\times100)+(4\times10)+(1\times1)\)

Step-by-step explanation:

So we want to write 268,741 in expanded form.

To do so, first take a look at what each digit means starting from the right.

268,741

This means 1 1s.

268,741

This means 4 10s.

268, 741

This means 7 100s.

268,741

This means 8 1000s.

268,751

This means 6 10,000s.

and 268,751.

This means 2 100,000s.

Therefore, 268,741 is 2 100,000s plus 6 10,000s plus 8 1000s plus 7 100s plus 4 10s plus 1 1s.

In expression form, this would be:

\((2\times100000)+(6\times10000)+(8\times 1000)+(7\times100)+(4\times10)+(1\times1)\)

Based on the sample of the 48 South African households collected from the Census At School survey project, the mean number of people living in a household will be 6.208, and the standard deviation is 2.576.

However, it is important to note that this sample only represents a small fraction of the total number of the households in South Africa, so we cannot make definitive conclusions about the entire population based on this sample alone.

To get a more accurate estimate of the number of people living in the South African households, a larger and the more representative sample would need to be collected.

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The domain of the function is all real numbers and  range is  y ≥ -1.

Since the vertex is at (1,-1), the axis of symmetry is x = 1.

This means that the domain of the function is all real numbers.

To find the range, we need to consider the y-values of the graph. Since the vertex is the lowest point of the graph, the range must be all y-values greater than or equal to -1.

However, since the parabola opens upwards, there is no upper bound on the y-values.

Therefore, the range is given by y ≥ -1.

Hence, the domain of the function is all real numbers and  range is  y ≥ -1.

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Answer:

Step-by-step explanation:

We need a picture of what you're talking about.

The system of inequalities represents the possible length, l, and the possible width, w, that her frame could have is l ≤ 12 and 2l + 2w < 30

The given parameters are

Length = Not more than 12 inches

Perimeter = Less than 30 inches

"Not more than" means less than or equal to

So, we have

l ≤ 12

The perimeter of a rectangle is

P = 2l + 2w

So, we have

2l + 2w = Less than 30 inches

"Less than" is represented with <

So, we have

2l + 2w < 30

Hence, the system of inequalities represents the possible length, l, and the possible width, w, that her frame could have is l ≤ 12 and 2l + 2w < 30

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Answer:

a. I ≤ 12
    2l + 2w < 30

Step-by-step explanation:

i got it right on edge.

Utilizing the Sieve of Eratosthenes method is simple. In order to encircle the remaining numbers, we must cancel all multiples of each prime number starting with 2 (including the number 1, which is neither a prime nor a composite).

The Sieve of Eratosthenes can be used to locate all prime numbers that are less than 100, as seen in the example below. In ten rows, start by writing the numbers 1 through 100.

Therefore, based on the preceding table, we can conclude that the prime numbers 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97 are. There are ten prime numbers between 50 and 100 in all. The required prime numbers are those that are surrounded.

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The net typing rate for experienced typists follows a normal distribution with a mean of 58 wpm and a standard deviation of 20 wpm.

In statistics, the normal distribution, also known as the Gaussian distribution, is a continuous probability distribution that is symmetrical around its mean. The given information states that the net typing rate for experienced typists can be approximated by a normal curve with a mean of 58 wpm and a standard deviation of 20 wpm.

The mean of 58 wpm represents the average typing rate for experienced typists. This means that the most common typing rate among this group is around 58 wpm. The standard deviation of 20 wpm indicates the spread or variability in the typing rates. A larger standard deviation suggests a wider range of typing speeds among experienced typists.

By knowing the properties of the normal distribution, such as the mean and standard deviation, we can make probabilistic statements about the net typing rate of experienced typists. For example, we can calculate the probability of a typist typing at a certain rate or within a specific range of rates. Additionally, we can use this information to compare and evaluate individual typists' performance or assess the effectiveness of typing training programs.

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Answer:

over the five years Mr. Amari will have gained 30$

Step-by-step explanation: