Identify the meaning of the variables in the point-slope form of a line.
m
(X1. Y1)
(x,y)
000
the slope of the line
any point on the line
a given point on the line

Answer:

The expression p−0.45p can be simplified to  0.55 p.

This means Phyllis can find the new price of a hat by finding  55 % of the original price.

Step-by-step explanation:

The given expression describes that the price of the Hat would be 55% of the original price.

Given that,
Hats are on sale for 45% off. Phyllis uses the expression p−0.45p to find the new price of a hat that originally cost p dollars.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
Given expression,
= p−0.45p
Simplify further,
= 0.55p
The above expression implies that the outcome is 55% of p, where p is the original price of the Hats.

Thus, the given expression describes that the price of the Hat would be 55% of the original price.

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Note:-

Graph must not be drawn to scale so taken imaginary coordinates most near to accurate

So the cordinates are

Mark the change between x and y

So

the relationship is

Option C

Answer:

C.  \(y=x+200\)

Step-by-step explanation:

Line of best fit (trendline) : a line through a scatter plot of data points that best expresses the relationship between those points.

All the given options for the line of best fit are linear equations.

Therefore, we can add the line of best fit to the graph (see attached), remembering to have roughly the same number of points above as below the line.

Linear equation:  \(y=mx+b\)

(where \(m\) is the slope and \(b\) is the y-intercept)

From inspection of the line of best fit, we can see that the y-intercept (where x = 0) is approximately 200.  So this suggests that either option C or option D is the solution.

We can also see that slope (gradient) is approximately 1, as for every +100 increase in x, y increases by +100.

\(\textsf{slope = rate of change}=\sf\dfrac{change \ in \ y}{change \ in \ x}=\dfrac{100}{100}=1\)

Therefore, this suggests that C is the solution and that the closest approximation to the line of best fit is \(y=x+200\)

Answer:

17.9

Step-by-step explanation:

Answer:

12 x 8 divided by 2 = 48cm

Step-by-step explanation:

Answer:Corporations step up their expansion plans and thus increase their demand for capital.

Step-by-step explanation:

Answer:

0.25cups

Step-by-step explanation:

if it is 1 cup then we are doubling the amount of onions so

1/8 x 2= 1/4= 0.25cups

There are two types of classifications for triangles, Classification according to internal angles and Classification according to the length of its sides.

A geometrical shape with three vertices, angles and sides, whose sum of internal angles is 180° is considered as a triangle.

Classification of triangles :-

There are two ways to classify triangles,

1) Based on the Angle :-

a) Acute Angled Triangle :- A triangle that has all three angles less than 90° is an acute angle triangle.

b) Right-Angled Triangle :- A triangle that has one angle that measures exactly 90° is a right-angle triangle.

c) Oblique Angled Triangle :- A triangle that has one angle that measures more than 90° is an obtuse angle triangle.

2) Based on the Sides :-

a) Scalene Angled Triangle :- A triangle that has all three sides of different lengths is a scalene triangle.

b) Isosceles Angled Triangle :- A triangle that has two sides of the same length and the third side of a different length is an isosceles triangle.

c) Equilateral Angled triangle :- A triangle that has all three sides of the same length is an equilateral triangle.

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Answer:

$9.01

Step-by-step explanation:

10 percent off of 15 is 8.5 and since sales tax is 6%, that means it adds 0.51 cents to the total, bringing the total to $9.01

Answer:

17.49

Step-by-step explanation:

15x0.10= 1.5
15+1.5= 16.5
16.5x0.06=0.99
16.5+0.99=

The value of radius of the circle is,

⇒ r = 7 units

Since, The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

We have to given that;

A circle is shown in figure.

Now, We ca formulate the value of radius of the circle is,

⇒ r = 8 - 1

⇒ r = 7 units

Thus, The value of radius of the circle is,

⇒ r = 7 units

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Answer:

The equation is;

2y = 5x-32

Step-by-step explanation:

Firstly, we find the mid-point segment

we can use the midpoint segment formula for this

Mathematically, we have this as:

(x,y) = (x1 + x2)/2, (y1 + y2)/2

(x,y) = (9-1)/2, (-8-4)/2

= (4,-6)

Let us find the slope of the given line segment

Mathematically, that will be;

m = (y2-y1)/(x2-x1) = (-4 + 8)/(-1-9) = 4/-10 = -2/5

Now, if two lines are perpendicular, the products of their slopes is equal to -1

so;

m1 * m2 = -1

-2/5 * m2 = -1

m2 = (-1 * 5)/-2

m2 = -5/-2 = 5/2

Since the perpendicular bisector is expected to pass through the midpoint,

we have the equation as slope 5/2 and point (4,-6)

so we use the point-slope equation form

That will be;

y-y1 = m(x-x1)

y+ 6 = 5/2(x-4)

2y + 12 = 5x - 20

2y = 5x -20-12

2y = 5x - 32

Based on the data given, the probability of the next roll of the die being a 4 is 30%.

what is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

To find the probability of rolling a 4 on the next roll, we need to divide the number of times 4 was rolled by the total number of rolls. In this case, 4 was rolled 9 times out of a total of 30 rolls.

So the probability of rolling a 4 on the next roll is:

9/30 = 3/10 = 0.3 = 30%

Therefore, based on the data given, the probability of the next roll of the die being a 4 is 30%.

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did the question tell you a specific year when was 19 years ago?

if it was 2003 then she would be 82 now in 2022

if it was 2002 then she would be 83 now in 2022

hoping you would give me a full explanation! : )

Yes, the average (arithmetic mean) of 5 different positive integers at least 30.

Statement 1: Each of the integers is a multiple of 10.

This statement tells us that all the integers in the set are divisible by 10. Let's assume the five integers are x₁, x₂, x₃, x₄, and x₅. Since each integer is a multiple of 10, we can express them as 10a₁, 10a₂, 10a₃, 10a₄, and 10a₅, where a₁, a₂, a₃, a₄, and a₅ are positive integers. Now, we can rewrite the sum of the five integers as follows:

10a₁ + 10a₂ + 10a₃ + 10a₄ + 10a₅ = 160

We can simplify this equation by factoring out 10:

10(a₁ + a₂ + a₃ + a₄ + a₅) = 160

Dividing both sides by 10, we have:

a₁ + a₂ + a₃ + a₄ + a₅ = 16

From this equation, we can observe that the sum of the positive integers a₁, a₂, a₃, a₄, and a₅ is 16. However, this information alone does not give us enough information to determine the value of the average or whether it is at least 30.

Statement 2: The sum of the 5 integers is 160.

This statement gives us the sum of the five integers directly. However, it doesn't provide any information about whether the integers are multiples of 10. We need to combine this statement with the first one to get a conclusive answer.

Combining both statements:

From statement 1, we know that each integer is a multiple of 10. Let's assume the integers are 10x₁, 10x₂, 10x₃, 10x₄, and 10x₅, where x₁, x₂, x₃, x₄, and x₅ are positive integers. Now, we can rewrite the sum of the five integers as follows:

10x₁ + 10x₂ + 10x₃ + 10x₄ + 10x₅ = 160

Simplifying this equation by factoring out 10, we have:

10(x₁ + x₂ + x₃ + x₄ + x₅) = 160

Dividing both sides by 10, we get:

x₁ + x₂ + x₃ + x₄ + x₅ = 16

Now, we have the same equation as in statement 1.

Therefore, the combined information from both statements gives us the same result.

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[First one, aka #13] is a

- If a 20-gallon bathtub is draining at a rate of 2.5 gallons, the max will be 20 gallons. Since it is water/etc, you cannot have negative water, so the least amount will be 0. We now have 0 ≤ ? ≤ 20

- What variable do we use? We are talking about gallons, so we will use g (gallons remaining) to get our answer of a, which is  0 ≤ g ≤ 20

[Second one, aka #11] is d

- I made the system

s - 18 = t

12s = 10t + 32

- Because one sport (s) has 18 less than one technology (t), so s - 18 = t. 12 sport (12s) has 32 more than 10 technology (10t) so if you add 32 to technology, you will get sport (12s = 10t + 32 )

Have a nice day!

  I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Answer:

7. cos(X) = 3/5 = 0.6

cos(Y) = 4/5 = 0.8

8. cos(X) = 15/17 ≈ 0.8824

cos(Y) = 8/17 ≈ 0.4706

9. cos(X) = 1/2 = 0.5

cos(Y) = (√3)/2 ≈ 0.8660

Step-by-step explanation:

The trigonometric ratio for cosine is given as follows;

\(Cos(\theta) = \dfrac{Adjacent\, side \, to\, angle}{Hypothenus\, side \, length \ of\, the \ triangle}\)

7. The adjacent leg length to ∠X = 27

The length of the hypotenuse side of the triangle = 45

∴ cos(X) = 27/45 = 3/5 = 0.6

Cos(X) = 3/5 = 0.6

The adjacent leg length to ∠Y = 36

∴ cos(Y) = 36/45 = 4/5 = 0.8

cos(Y) = 4/5 = 0.8

8. The adjacent leg length to ∠X = 15

The length of the hypotenuse side of the triangle = 17

∴ cos(X) = 15/17 ≈ 0.8824

The adjacent leg length to ∠Y = 8

∴ cos(Y) = 8/17 ≈ 0.4706

9. The adjacent leg length to ∠X = 13

The length of the hypotenuse side of the triangle = 26

∴ cos(X) = 13/26 = 1/2 = 0.5

Cos(X) = 1/2 = 0.5

The adjacent leg length to ∠Y = 13·√3

∴ cos(Y) = 13·√3/26 = (√3)/2 ≈ 0.8660

cos(Y) = (√3)/2 ≈ 0.8660.

In the given problem, we are provided with a p.d.f. for the random variable X as ce^(-6x) for x >= 0. Let's use this information to solve the questions:

(a) We know that the total area under the p.d.f. must be equal to 1. Therefore, we can set up the following integral and solve for c:

int0 to infinity = 1

=> c * int0 to infinity = 1

=> c * [(-1/6)*e^(-6x)] from 0 to infinity = 1

=> c * (0 - (-1/6)) = 1

=> c = 6

(b) To find the mean of Y, we first need to find the transformation function that relates X and Y. We know that Y = X^2, so we can use the transformation formula E(Y) = E(g(X)) = int(-infinity to infinity) (g(x) * f_X(x)dx) to find E(Y).

E(Y) = int(0 to infinity) (x^2 * 6e^(-6x)dx)

Using integration by parts, we can solve this integral to get E(Y) = 1/3.

To find the variance of Y, we use the formula Var(Y) = E(Y^2) - (E(Y))^2. We can use the formula for E(Y) that we just found, and also find E(Y^2) as:

E(Y^2) = int(0 to infinity) (x^4 * 6e^(-6x)dx)

Using integration by parts again, we get E(Y^2) = 1/9. Therefore, Var(Y) = 1/9 - (1/3)^2 = 2/27.

The squared coefficient of variation of X is defined as Var[X]/(E[X])^2. Using the mean and variance of X that we found in part (a), we get (Var[X]/(E[X])^2) = (1/36)/(1/36) = 1. Therefore, the squared coefficient of variation of Y is also 1.

(c) To compute Pr{X > 5}, we can use the p.d.f. that we were given. Since the p.d.f. is zero for x < 0, we only need to compute the integral from 5 to infinity:

Pr{X > 5} = int(5 to infinity) (6e^(-6x)dx)

= e^(-30)

(d) To compute Pr {X >5 | Y> 2}, we can use the formula for conditional probability:

Pr {X >5 | Y> 2} = Pr{X > 5 and Y > 2}/Pr{Y > 2}

Since Y > 2 implies X > sqrt(2), we can write the numerator as:

Pr{X > sqrt(2)} = int(sqrt(2) to infinity) (6e^(-6x)dx)

= e^(-3*sqrt(2))

To find the denominator, we can use the formula for the cumulative distribution function (c.d.f.) of Y:

F_Y(y) = Pr{Y <= y} = Pr{X^2 <= y} = Pr{-sqrt(y) <= X <= sqrt

A random variable is a numerical quantity that can take on different values based on the outcome of a random event. In this context, a probability density function (p.d.f.) describes the probability of observing different values of a random variable.

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The probability that a student who had a dog also had a cat would be = 7/25.

To calculate the possible outcome of the given event, the formula for probability should be used and it's given below as follows. That is;

Probability = possible outcome/sample space

possible outcome = 7

sample space = 7+2+3+13 = 25

Probability = 7/25

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Answer:

a.  He used an incorrect time ratio converting hours to minutes.

d. He incorrectly concluded that she is not running fast enough.

Step-by-step explanation:

Looking at the Coach's method of conversion when converting time, he assumed that an hour had 15 minutes instead of 60 minutes. He therefore did not use the correct time ratio to convert hours to minutes.

The coach's calculations yielded an answer of 34 ft/s. This is way faster than 8.8 ft/ s so his deduction that she was not running fast enough to beat her fastest time is incorrect because at that inhumane speed, she did.

Answer: A.)He used an incorrect time ratio converting hours to minutes.

D.)He incorrectly concluded that she is not running fast enough.

Step-by-step explanation: i hope this helps :)

The five-number summary is:

Minimum: 9

First Quartile: 16.5

Median: 25.5

Third Quartile: 39

Maximum: 51

3. Range = 42

4. Interquartile range = 22.5

Given the data for the lengths as, 36, 15, 9, 22, 36, 14, 42, 45, 51, 29, 18, 20, to find the five-number summary of the data set, we would follow the steps below:

1. The numbers in ordered from the smallest to the largest would be:

9, 14, 15, 18, 20, 22, 29, 36, 36, 42, 45, 51

2. The five-number summary for the lengths in minutes would be:

3. Range of the data = max - min = 51 - 9 = 42

4. The interquartile range for the data set = Q3 - Q1 = 39 - 16.5

Interquartile range for the data set = 22.5

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In this scenario, we are given the following information: sample size (n) is 49, sample mean (P) is 50, sample standard deviation (s) is 7, null hypothesis (H₀) states that the population mean (μ) is greater than or equal to 52, and the alternative hypothesis (Hₐ) states that the population mean is less than 52.

The test statistic for this situation is the t-statistic, which measures the difference between the sample mean and the hypothesized population mean, taking into account the sample size and the sample standard deviation. It is used to assess the evidence against the null hypothesis. In this case, since the alternative hypothesis states that the population mean is less than 52, we have a left-tailed test. To calculate the t-statistic, we use the formula:

t = (P - μ) / (s / √n)

Plugging in the given values:

t = (50 - 52) / (7 / √49) = -2 / (7 / 7) = -2

Therefore, the test statistic for the provided information is -2. This value represents the standardized difference between the sample mean and the hypothesized population mean, accounting for the sample size and standard deviation. It indicates that the sample mean is 2 standard deviations below the hypothesized population mean of 52.

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Using inequalities we know that x=68 and x=66 respectively.

A mathematical phrase in which the sides are not equal is referred to as being unequal.

In essence, a comparison of any two values reveals whether one is less than, larger than, or equal to the value on the opposite side of the equation.

So, solve the inequalities as follows:

x+3>70

x>70-3

x>67

Then, it will be x = 68.

Then,

x+3<70

x<70-3

x<67

Then, it will be s = 66.

Therefore, using inequalities we know that x=68 and x=66 respectively.

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The area of the 1/4 inch diameter circle, expressed to the nearest thousandth square inch, is 0.049 square inches.

The formula to find the area of a circle is A = π\(r^2\).

Where,

r is the radius of the circle.

Since the diameter of the circle is given as 1/4 inch, the radius is 1/8 inch (radius = diameter/2).
Substituting the value of r in the formula, we get A = π(1/8) = π/64 square inches.
Now, to express the answer to the nearest thousandth square inch, we need to calculate the value of π/64 and round it to the nearest thousandth. Using a calculator, we get π/64 = 0.04908738521...
The area of a circle with a 1/4 inch diameter, we'll use the formula A = π\(r^2\), where A is the area, and r is the radius.

First, we need to find the radius.

Since the diameter is 1/4 inch, the radius (r) is half of that: 1/8 inch.

Now, we'll calculate the area: A = π\(\frac {1}{8} ^{2}\) = π(1/64) ≈ 0.0123 square inches. So, the area of the circle is approximately 0.0123 square inches to the nearest thousandth.
Rounding this value to the nearest thousandth gives us 0.049 square inches.

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Answer:whole

Step-by-step explanation:

a whole number and a fraction make a mixed number.

explanation:

\(midpoint = ( \frac{x1 + x2}{2} , \frac{y1 + y2}{2} )\)

Hello there, hope you are having a nice day.

We are given the slope of the line and a point on the line, so we can write the equation in point-slope form:

y-7=-3(x-(-1)

y-7=-3(x+1)

y-7=-3x-3

Now, we move -7 to the right side, using the opposite operation:

y=-3x-3+7

y=-3x+4

This is the equation of our line. Hope it helps.

Ask me if you have any queries.

~An emotional teen who helps others with joy

Good luck.

Answer:

Zero is not a natural number

Step-by-step explanation:

Hope this helps!

the Greatest Common Divisor is 252 and it can be expressed as the linear combination -2 * 6,066 + 3 * 2,286.

The greatest common divisor (GCD) is the biggest positive integer that divides two or more integers without leaving a remainder. It's also referred to as the greatest common factor (GCF) or the highest common factor (HCF). The Euclidean procedure, which continually divides the greater of the two integers by the smaller until a remainder of zero is obtained, is one way to calculate the GCD. The GCD is a crucial idea in mathematics, notably in number theory, and it has several applications in other disciplines, such as computer science and encryption. Finding the greatest common divisor of the coefficients of a linear equation in two variables is another popular geometry task.

How to solve?

The Greatest Common Divisor of 6,066 and 2,286 can be expressed as 252 = 6,066 * (-2) + 2,286 * 3. So, the GCD is 252 and it can be expressed as the linear combination -2 * 6,066 + 3 * 2,286.

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Answer:

3645

Step-by-step explanation:

65610/18=3645

Answer:

-5/24 miles

Step-by-step explanation:

The submarine descends at a rate of -5/6 miles every 4 minutes.

To find the depth of the submarine relative to sea level after the first minute, we have to multiply the rate of descent by he time spent (1 minute). That is:

\(\frac{\frac{-5}{6} }{4} * 1\)

=> D = -5 / (6 * 4) = -5/24 miles

Therefore, the submarine's depth is -5/24 miles.

Answer:

-1 1/5

Step-by-step explanation:

I took the test and this was the correct answer :D