1
What is the length of a
segment when the
coordinates of its endpoints
are (-4, 5) and (-6, 9)?
a) 5V2 units
b) 2V5 units
c) V2 units
d) 5
e) 10 units
V5 units

The probability that a student will pass the test before the third try is 0.91 or 91%.

The probability that a student pilot passes the written test for a private pilot’s license is 0.7.

To find the probability that a student will pass the test before the third try, we can use the geometric distribution.

The Geometric Distribution is a discrete probability distribution that describes the number of failures before a success in a sequence of independent and identical Bernoulli trials. It is one of the essential examples of distributions in probability theory and statistics

Let P be the probability that a student pilot passes the written test for a private pilot’s license.

Then the probability that a student will fail the test on the first two tries is given by:

P(failure) = (1 - P)² [i.e., the probability of not passing the test]

Then the probability that the student will pass the test before the third try is the complement of the above probability, which is given by:

P(pass before 3rd try) = 1 - (1 - P)²

Let P = 0.7.

Then the probability that a student will pass the test before the third try is:

P(pass before 3rd try) = 1 - (1 - 0.7)²

P(pass before 3rd try) = 1 - 0.09 = 0.91

Therefore, the probability that a student will pass the test before the third try is 0.91 or 91%.

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The distance further from the outer edge of the path to the inner edge would be 3.28 feet.

The outer diameter of the circular path, which includes the width of the path itself, is the sum of the inner diameter and twice the width of the path:

Outer diameter = Inner diameter + 2 x Width of the path

Outer diameter = 650 feet + 2 x 2 feet

Outer diameter = 654 feet

Inner radius = Inner diameter / 2

= 650 feet / 2

= 325 feet

Outer radius = Outer diameter / 2

= 654 feet / 2

= 327 feet

Circumference of inner edge = 2 x π x Inner radius

= 2 x 3.14 x 325 feet

= 2041.4 feet

Circumference of outer edge = 2 x π x Outer radius

= 2 x 3.14 x 327 feet

= 2054.68 feet

Difference = Circumference of outer edge - Circumference of inner edge

Difference = 2054.68 feet - 2041.4 feet

Difference = 13.28 feet

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Answer:

Quotient=23 and remainder=14

Answer:

2

Step-by-step explanation:

Pick 2 coordinates on the line and do the formula for slope.

ex: (2,4) and 3,6)

4-6/2-3 = -2/-1 = 2

Answer:

The independent variable is time.

Step-by-step explanation:

(Y=mx+b format)

Maddi's rental for the car costs $13 per hour so the x variable would be the hours (x=hour). This would be a Y= mx + b equation and in this case, Y=13x + 100. Independent means (mathmatically) a variable that does not depend on any other variable for its value. The costs is always changing being dependent on the time portion. The time isn't dependent on anything. Thus, the independent variable is time.

(If you need a starting point which is b, it would be the $100 as the processing fee.)

The instantaneous rate of change of the surface area S of the balloon with respect to the radius r is 8πr.

Given a spherical balloon is being inflated, we are supposed to determine the instantaneous rate of change of the surface area s of the balloon concerning the radius r.

In order to solve the above question, we need to find the derivative of surface area w.r.t radius.

The formula for the surface area of a sphere is given as:

S = 4πr²

Now, we will differentiate the above equation with respect to r.

dS/dr = d/ds (4πr²) = 8πr

We can observe that the instantaneous rate of change of the surface area S of the balloon w.r.t the radius r will be 8πr.

Hence, the instantaneous rate of change of the surface area S of the balloon with respect to the radius r is 8πr.

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The sampling technique used to obtain the described sample is A. Systematic sampling.

In systematic sampling, the elements of the population are ordered in some way, and then a starting point is randomly selected. From that point, every nth element is selected to be part of the sample.

In the given scenario, the first 35 students leaving the library were selected. This suggests that the students were ordered in some manner, and a systematic approach was used to select every nth student. Therefore, the sampling technique used is systematic sampling.

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i. weekly receipts at a clothing boutique

ii. monthly demand for an automotive part

Time series data refers to information collected and recorded at regular intervals over a specific period. In the case of i. weekly receipts at a clothing boutique and ii. monthly demand for an automotive part, both data sets are examples of time series data.

Time series data consists of observations recorded over regular intervals, allowing for the analysis of patterns and trends over time. In i. weekly receipts at a clothing boutique, the data is collected on a weekly basis, providing insights into the boutique's revenue fluctuations over different weeks. Similarly, ii. monthly demand for an automotive part captures the demand for the part on a monthly basis, enabling analysis of monthly variations and seasonal patterns.

On the other hand, iii. quarterly sales of automobiles do not fall under time series data. While it represents sales data, the intervals between measurements are not consistent enough to qualify as time series. Quarterly intervals are less frequent and may not capture shorter-term trends or variations as effectively as weekly or monthly intervals.

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Answer:

0.563>0.536

Step-by-step explanation:

Its greater

Step-by-step explanation:

7 - 3b-2(0 + 3 - 2b)

To simplify the expression in the box, Fatua used

these steps:

Step 1:7 - 3b-2(3 - 3b)

Step 2:7 - 3-6-36-

Step 3: -13 - 66

Did Fatua calculate correctly? if nnot, in what step

did she make her FIRST mistake?

The coordinates of point D 0.25 x-axis for the points A(2, 6), B(0, 0), C(-5, 8), and D(-2, 10) are (-2, -2.5) when point D is reflected across the x-axis. This is obtained by negating the y-coordinate of point D and keeping the x-coordinate the same.

To find the coordinates of point D 0.25 x-axis, we need to reflect point D across the x-axis. This will result in the y-coordinate of point D being negated while the x-coordinate remains the same.

The coordinates of point D are (-2, 10), so when we reflect it across the x-axis, we get the new coordinates:

D 0.25 x-axis = (-2, -10/4) = (-2, -2.5)

Therefore, the coordinates of point D0.25∘rx-axis for the given points A, B, C, and D are (-2, -2.5).

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Answer:

Step-by-step explanation:

1) y  = 2x  ----------(I)

x + y = 6 -----------(II)

Plug in y =2x in equation (II)

x + 2x = 6        {Add like terms}

  3x    = 6

       x = 6/3

      x = 2

Plugin x = 2 in (I)

 y = 2*2

y = 4

Check:

     LHS = x +y

             = 2 + 4

            = 6  = RHS

2)5x + 10y = 3 ------------(I)

x = (-1/2) y     ------------(II)

Substitute x = (-1/2)y in (I)

\(5*\frac{-1}{2}y + 10y = 3\\\\\frac{-5}{2}y+ \frac{10*2}{1*2}y = 3\\\\\frac{-5}{2}y+\frac{20}{2}y=3\\\\\frac{-5+20}{2}y = 3\\\\\frac{15}{2}y=3\\\\ y = 3*\frac{2}{15}\\\\ y = \frac{2}{5}\)

Substitute y = (2/5) in equation (II)

\(x = \frac{-1}{2}*\frac{2}{5}\\\\x = \frac{-1}{5}\)

Check:

Substitute x and y value in equation (I)

\(LHS = 5*\frac{-1}{5}+10*\frac{2}{5}\\\\ = -1 + 2*2\\\\ = -1 + 4\\ = 3 = RHS\)

3) y - x = 3x + 2

        y = 3x + 2 + x

         y = 4x + 2 ---------------(I)

2x + 2y = 14 - y

2x + 2y +y = 14

2x + 3y = 14     ------------------(II)

Substitute y = 4x + 2 in equation (II)

2x + 3(4x +2) = 14

2x + 3*4x + 3*2 = 14

2x + 12x + 6 = 14

        14x + 6 = 14

              14x = 14 - 6

              14x = 8

                 x = 8/14

            x = 4/7

Substitute 'x' value in (I)

\(y = 4*\frac{4}{7} +2\\\\y = \frac{16}{7}+2\\\\y= \frac{16}{7}+\frac{2*7}{1*7}\\\\y=\frac{16}{7}+\frac{14}{7}\\\\y=\frac{30}{7}\)

Check:

\(LHS = 2x + 3y\\\\ = 2*\frac{4}{7}+3*\frac{30}{7}\\\\ = \frac{8}{7}+\frac{90}{7}\\\\=\frac{8+90}{7}\\\\=\frac{98}{7}\\\\=14 = RHS\)

Answer:

A

Step-by-step explanation:

it goes through the vertex so that means it is not moved so that rules out C and d

seeing the y value for 1 is 4 that means that it has to be A

Answer:

A

Step-by-step explanation:

by using the eqn to find for a straight line

slope = ∆y/∆x

(1,4) and (0,0) since both points are in the line

slope = 4

then,

y-y'=slope(x-x')

y-4=4(x-1)

y-4=4x-4

y=4x-4+4

y=4x

but the graph is parabolic thus

y=4x^2

this is how I did it I have no idea to do anything else so hope it works

Answer:

1. 425 kilometers

2. 780 kilometers

Step-by-step explanation:

1. 50×8.5= 450 kilometers

2. 65×12=780 kilometers

Answer:

9(a+b) x (a²+ab+b²)

Step-by-step explanation:

Answer:

adsefrthgfdsfgd

Step-by-step explanation:

Answer:

mC =mA

mC=57

FIRST OPTION IS THE ANSWER

Step-by-step explanation:

\(\sqrt{x^2-6x + 9} = \sqrt{(x - 3)^2}= x - 3\)

Answer:

x = 2.75

Step-by-step explanation:

6x - 2 (x - 5) = 22

6x -2x + 10 = 22

4x + 10 = 22

     - 10    - 10

4x = 11

11/4 = 2.75

x = 2.75

Let me know if you need any more help!

Answer:

actually what is this is you is this a geometry, trigonometry I don't know what to call

Answer:

Step-by-step explanation:

y = 3 times x

or: y divided by x = 3

Answer:

ab= 7.8

ac= 6

bc=5

Step-by-step explanation:

The length of each side of triangle ABC are,

⇒ AB = √61

⇒ BC = 5

⇒ CA = 6

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The vertices of the triangle ABC are,

⇒ A(- 2, 3), B(3, - 3) , and C(- 2, - 3)

Now, We know that;

The distance between two points (x₁ , y₁) and (x₂, y₂) is,

⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²

So, The distance between A and B is,

⇒ AB = √ (3 - (-2))² + (- 3 - 3)²

⇒ AB = √ 5² + (-6)²

⇒ AB = √ 25 + 36

⇒ AB = √ 61

And, The distance between B and C is,

⇒ BC = √ (-2 - 3)² + (- 3 - (-3))²

⇒ BC = √ 5² + (0)²

⇒ BC = √ 25

⇒ BC = 5

The distance between A and C is,

⇒ AC = √ (-2 - (-2))² + (- 3 - 3)²

⇒ AC = √ 0² + (-6)²

⇒ AC = √ 36

⇒ AC = 6

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I picked two points in the graph, (-1, 0) and (1, 1).

Find the rate by solving for the slope (rise / run).

Rise = x₂ - x₁ = 1 - (-1) = 2

Run = y₂ - y₁ = 1 - 0 = 1

Slope = 2 / 1 = 2

The rate is m = 2

include "h′(2)=" in your answer. For example, if you found h′(2)=7, you would enter 7. is -24.


Using the product rule, we know that h′(x)=f′(x)g(x)+f(x)g′(x).
Plugging in the values we know, we have f′(x)=−8x+4 and f(2)=−21.
Therefore, h′(2)=f′(2)g(2)+f(2)g′(2)=(-8(2)+4)(3)+(-21)(-4)= -24.


Thus, h′(2)=-24.



Step 1: Differentiate f(x)
f(x) = -4x^2 + 4x - 5
f'(x) = -8x + 4

Step 2: Calculate f'(2)
f'(2) = -8(2) + 4 = -16 + 4 = -12

Step 3: Use the given values
g(2) = 3 and g'(2) = -4

Step 4: Apply the product rule
h'(x) = f'(x)g(x) + f(x)g'(x)
h'(2) = f'(2)g(2) + f(2)g'(2)

Step 5: Plug in the values
h'(2) = (-12)(3) + f(2)(-4)

Step 6: Calculate f(2)
f(2) = -4(2)^2 + 4(2) - 5 = -4(4) + 8 - 5 = -16 + 8 - 5 = -13

Step 7: Substitute f(2) into the equation
h'(2) = (-12)(3) + (-13)(-4) = -36 + 52 = 16


The value of h′(2) is 16.

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Answer:

23 kids

Step-by-step explanation:

Answer:

i think it is the second one y=35x

Step-by-step explanation:

when we put for example 2  in place of x it will be

it will y=35*2

y=70 so i believe it is the second one

i am soo sorry if it was wrong

something you should keep in mind is that all three angles in a triangle always add up to 180 degrees.

so, here, since you know the two other angles, you can find the third.

180 - 106 - 42 will give you the measure of that third angle.

your answer will be 32.

hope i helped, good luck!

Answer:

32

Step-by-step explanation:

as you triangle angle add up to 180 so you add 106 by 42 which gives you 148 then

you take 180 -148 which it will give you =32

Given that sin(x) = -5/13 and the condition is to provide the answer without using sin, cos, or tan, I assume you are looking for the value of cos(x).

We can use the Pythagorean identity: sin²(x) + cos²(x) = 1

Substitute the given value of sin(x):
(-5/13)² + cos²(x) = 1

Solve for cos²(x):
cos²(x) = 1 - (-5/13)²

cos²(x) = 1 - (25/169)

Now find the common denominator (169) and subtract:
cos²(x) = (169/169) - (25/169)

cos²(x) = 144/169

Since we need the value of cos(x), we take the square root of both sides:
cos(x) = ±√(144/169)

cos(x) = ±12/13

Since the value of sin(x) is negative, we are in the third or fourth quadrant, where the cosine is also negative. Therefore, we choose the negative value for cos(x):

cos(x) = -12/13

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Answer:

The y-intercept of points A and B is -2.

Step-by-step explanation:

Point A is the y-intercept. You can tell by looking at the x and seeing that it is 0. This means the point is the y-intercept.

Hope this helps!

-Luna

Answer:

-2

Step-by-step explanation:

Linear equations are typically organized in slope-intercept form: \(y=mx+b\) where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis). To solve this question, first, find the slope, then, plug one of the given points into the equation to isolate b.

1) Find the slope (m)

\(m=\frac{y_2-y_1}{x_2-x_1}\) where the given points are \((x_1,y_1)\) and \((x_2,y_2)\)

Plug in the given points (0,-2) and (3,0)

\(m=\frac{0-(-2)}{3-0}\\m=\frac{0+2}{3}\\m=\frac{2}{3}\)

Therefore, the slope of of the line is \(\frac{2}{3}\). Plug this into  \(y=mx+b\) as m:

\(y=\frac{2}{3} x+b\)

2) Find the y-intercept (b)

\(y=\frac{2}{3} x+b\)

Plug in one of the given points: (0,-2) or (3,0)

\(0=\frac{2}{3} (3)+b\\0=2+b\\b=-2\)

Therefore, the y-intercept of the line AB is -2.

I hope this helps!