Question 2 of 10
What is the point-slope form of a line with slope -4 that contains the point
(-2, 3)?

Considering the sample mean, the best estimate for the mean monthly electric bill for all residents of the local apartment complex is of $86.

The point estimate for the population parameter is found according to the parameter for a sample from the population. For example:

In this problem, the mean bill for 132 residents is of $86, hence the best estimate for the mean monthly electric bill for all residents of the local apartment complex is of $86.

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Answer:

Step-by-step explanation:

Answer:

2h 1' 1"

Step-by-step explanation:

1h = 1 hora

1' = 1 minute

1" = 1 secind

The sum of the three days is:

  58'  45"

+ 40'  40"

  20'  36"

= 118'  121"

118' 121" = 118' + 121"

1' = 60"

121" = 120" + 1"  = (120/60) + 1 = 2' + 1"

Then:

118' + 121" = 118' + 2' ´+ 1" = 120' + 1"

1 h = 60'

(120/60) + 1 = 2h + 1'

then:

118' + 121" = 2h + 1' + 1"

= 2h 1' 1"

Answer:

6 hours

Step-by-step explanation:

Let the smaller pipe fill the pool in x hours and the bigger pipe y hours.

x-y=4

1/x+1/y=4/15

x=10, y=6

so 6 hours

Step-by-step explanation:

l = large pipe

s = small pipe

s needs x hours alone to fill the pool.

l needs x-4 hours alone to fill the pool.

s does 1/x of the work in 1 hour.

l does 1/(x-4) of the work in 1 hour.

3 hours 45 minutes = 3.75 hours

3.75 × 1/x + 3.75 × 1/(x-4) = 1 (= the whole work)

3.75 + 3.75 × x/(x-4) = x

3.75×(x-4) + 3.75×x = x(x-4) = x² - 4x

3.75x - 15 + 3.75x = x² - 4x

7.5x - 15 = x² - 4x

-15 = x² - 11.5x

0 = x² - 11.5x + 15

the general solution to such a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 1

b = -11.5

c = 15

x = (11.5 ± sqrt(132.25 - 4×1×15))/(2×1) =

= (11.5 ± sqrt(72.25))/2 = (11.5 ± 8.5)/2

x1 = (11.5 + 8.5)/2 = 20/2 = 10

x2 = (11.5 - 8.5)/2 = 3/2 = 1.5

x = 1.5 would turn l = 1/(x-4) negative, which does not make sense.

so, x = 10 is our solution.

that means

s does 1/10 of the work in 1 hour.

so, the small pipe alone fills the pool in 10 hours.

l does 1/(10-4) = 1/6 of the work in 1 hour.

so, the large pipe alone fills the pool in 6 hours.

The  rule that describes the composition of transformations that maps ΔJKL to ΔJ"K"L" is Rotation  0° to  90°  and reflection about the x-axis.

A transformation is a rule that is used to manipulate the position of a point of geometric figure.

Analyzing the figure, rotation of ΔJKL through the angle 90 degrees in a counter-clockwise direction gives us  ΔJ'K'L' .

ΔJ"K"L" is been gotten also using ΔJ'K'L'  through the refraction of ΔJ'K'L' across the x-axis.

In this case,   rule that describes the composition of transformations that maps ΔJKL to ΔJ"K"L" is Rotation  0° to  90°  and reflection about the x-axis.

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Answer: C). 90 degree rotation about point 0 composition translation of negative 2 units x, 0 units y

Step-by-step explanation:

Answer:

Step-by-step explanation:

The area of a parallelogram is h*b where h is the height/altitude and b is the base.

The base is 27 millimeters and the altitude is 18 millimeters, so we multiply those together.

27*18= 486.

The area of the parallelogram is 486mm²

Hope this helps!

Answer:

-86,-85,-84,-83 and so on...

Step-by-step explanation:

Use the Number Line

Answer:

-88,-89,-90,-91,-92

Step-by-step explanation:

Answer:

0.350  (3 d.p.)

Step-by-step explanation:

[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]

Let P(A) = probability that the student is a freshman

Let P(B) = probability that the student owns a credit card

Use the given table to calculate the probability that the student is a freshman:

[tex]\implies \sf P(A)=\dfrac{60}{100}=0.6[/tex]

And the probability that the student is a freshman and owns a credit card:

[tex]\implies \sf P(A \cap B)=\dfrac{21}{100}=0.21[/tex]

To find the probability that the student owns a credit card given that the they are a freshman, use the conditional probability formula:

Conditional Probability Formula

The probability of B given A is:

[tex]\sf P(B|A)=\dfrac{P(A \cap B)}{P(A)}[/tex]

Substitute the found values into the formula:

[tex]\implies \sf P(B|A)=\dfrac{0.21}{0.6}=0.35[/tex]

Therefore, the probability that the student owns a credit card given that they are a freshman is 0.35

Answer:

4x+2y=4

3x-y=-7

first one by 3

second by 4

12x+6y=12

12x-4y=-28

subtract

10y=40

y=4

plug in

3x-4=-7

add 4

3x=-3

x=-1

(-1,4)

c

Hope This Helps!!!

Answer: third option

Step-by-step explanation:

There are 2 ways to go about systems of equations normally, and that's elimination and substitution. For this particular problem, I would recommend elimination.

we see the first equation 4x+2y=4

we want to be able to simplify it as much as possible (so it's easier to solve)

so we divide all the terms by 2, giving 2x+y=2.

the second equation can't be simplified, so we set up the elimination method.

   2x+y=2

  -3x-y=-7

multiplying both equations by 2 and 3, we subtract them and get that y equals 4, which is clearly the answer.

Answer:

f(-14) = -6

f(-4) = 6

f(12) = 6

f(0) = -3

negative

Step-by-step explanation:

f(-14) = -6

This is because when x is -14, y is -6, as seen in the graph

f(-4) = 6

This is because when x is -4, y is 6, as seen in the graph

f(12) = 6

This is because when x is 12, y is 6, as seen in the graph

f(0) = -3

This is because when x is 0, y is -3, as seen in the graph

is f(4) positive or negative?
negative

This is because when x is 4, y is -6, as seen in the graph

Answer:

C. no, because the arcs do not have the same measure.

Step-by-step explanation:

for 2 structures to be congruent all the angles need to be the same (and then all the lines must have the same scaling factor between both structures - but that is not relevant here anymore, since the angles are already off).

The length of the altitude to the hypotenuse of the right triangle is 3 / 5

A right triangle has one of it's angle as 90 degrees. Therefore,

area of right triangle = 1 / 2 bh

where

Hence,

6 = 1 / 2 × 4 × h

6 = 4h / 2

cross multiply

12 = 4h

divide both sides by 4

h = 12 / 4

h = 3 units

Hypotenuse² = 4² + 3²

c² = 16 + 9

c = √25

c = 5

Therefore, the length of the altitude to the hypotenuse of the right triangle is 3 / 5

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Answer:

3

Step-by-step explanation:

first find g(-2) by plugging in -2 as x in the g(x) equation

g(-2) = 3(-2)+5

g(-2) = -6+5

g(-2) = -1

then plug that value (-1) as x in the f(x) equation

f(-1) = 4-(-1)^2

f(-1) = 4-1

f(-1) = 3

Step-by-step explanation:

The derivative of log is

[tex] \frac{d}{dx} ( log_{a}(x) ) = \frac{1}{x \: ln(a) } [/tex]

You can easily derive this using the Change of base rule, and natural log rules

[tex] log_{a}(x) = \frac{ log_{e}(x) }{ log_{e}(a) } = \frac{ ln(x) }{ ln(a) } [/tex]

Next, we differentiate with respect to x.

[tex] \frac{d}{dx} \frac{ ln(x) }{ ln(a) } = \frac{1}{ ln(a) } \times \frac{d}{dx} ln(x) [/tex]

[tex] = \frac{1}{x ln(a) } [/tex]

So back to the topic at hand,.

a=7, so we get

[tex] \frac{1}{x ln(7) } [/tex]

We plug in 0, we would get undefined

Answer:

help to others the exact amount u have

Step-by-step explanation:

If you roll the die once, the probability of getting a 3 is 1/6

If you roll the die twice and get a three both times, the probability of that happening is 1/6 * 1/6 or 1/36

and so on...

The probability of rolling a 3 is 1/6.

Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.

The value of probability will be always in the range from 0 to 1.

Given that,

A number cube is rolled several times.

There are a total of 6 numbers in a number cube.

Total outcomes = 6

We have to find the probability of rolling a 3.

Probability = 1/6

Hence the required probability is 1/6.

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Answer: Segment AD

Reason:

Any diameter goes through the center of a circle, with both endpoints on the circle edge.

Another diameter is segment FC.

Answer:

CF and AD

Step-by-step explanation:

Hello!

Given the definitions, we are simply looking for any line that goes through the center of the circle, and touches twice on the circumference of the circle.

There are only two lines that seem to go through the circle, and have endpoints on the circle:

Answer:

Law of sines

Step-by-step explanation:

The law of sines is a formula used to find either an angle or side in a non-right triangle.

You have to have at least three parts to use it.

For example, if you have angle A and its side (a) along with angle B, you can use it to find side b.

1) If the limit [tex]L[/tex] is

[tex]L = \displaystyle \lim_{\Delta x\to0} \frac{\sin\left(\frac\pi3 + \Delta x\right) - \sin\left(\frac\pi3\right)}{\Delta x}[/tex]

then using the hint as well as [tex]\sin\left(\frac\pi3\right)=\frac{\sqrt3}2[/tex] and [tex]\cos\left(\frac\pi3\right)=\frac12[/tex] we have

[tex]\displaystyle L = \lim_{\Delta x\to0} \frac{\sin\left(\frac\pi3\right)\cos(\Delta x) + \cos\left(\frac\pi3\right)\sin(\Delta x) - \sin\left(\frac\pi3\right)}{\Delta x}[/tex]

[tex]\displaystyle L = \sin\left(\frac\pi3\right) \lim_{\Delta x\to0} \frac{\cos(\Delta x) - 1}{\Delta x} + \cos\left(\frac\pi3\right) \lim_{\Delta x} \frac{\sin(\Delta x)}{\Delta x}[/tex]

[tex]L = \dfrac{\sqrt3}2 \times 0 + \dfrac12\times1 = \boxed{\dfrac12}[/tex]

which follows from the well-known limits,

[tex]\displaystyle \lim_{x\to0} \frac{1-\cos(x)}x = 0 \text{ and } \lim_{x\to0} \frac{\sin(x)}x=1[/tex]

Alternatively, if you already know about derivatives, we can identify the limit as the derivative of [tex]\sin(x)[/tex] at [tex]x=\frac\pi3[/tex], which is [tex]\cos\left(\frac\pi3\right)=\frac12[/tex].

2) It looks like you may be using double square brackets deliberately to denote the greatest integer or floor function which rounds the input down to the nearest integer. That is, [tex][\![x]\!][/tex] is the greatest integer that is less than or equal to [tex]x[/tex]. The existence of [tex]L[/tex] depends on the equality of the one-sided limits.

Suppose [tex]3\le x<4[/tex]. Then [tex]2[tex]\displaystyle \lim_{x\to4^-} [\![x - 1]\!] = 2[/tex]

Now suppose [tex]4\le x<5[/tex], so that [tex]3\le x-1 < 4 \implies [\![x-1]\!]=3[/tex] and

[tex]\displaystyle \lim_{x\to4^+} [\![x-1]\!] = 3[/tex]

The one-sided limits don't match so the limit doesn't exist.

The area of the shaded face of the cylinder with the given radius is approximately 1520cm².

This question is incomplete, the missing diagram is uploaded along the answer below.

From the diagram, the shaded region is a circle with radius 22 meters.

Area of a circle is expressed as;

A = π × r²

r is radius and π is constant pi ( π = 3.14 )

We substitute our values into the equation above.

A = π × r²

A = 3.14 × (22m)²

A = 3.14 × 484m²

A = 1519.76 ≈ 1520cm²

Therefore, the area of the shaded face of the cylinder with the given radius is approximately 1520cm².

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Step-by-step explanation:

The figure below shows a portion of the graph of the function [tex]j\left(x\right) \ = \ 4^{x-2}[/tex], hence the average rate of change (slope of the blue line) between the [tex]x[/tex] and [tex]x+h[/tex] is

                     [tex]\text{Average rate of change} \ = \ \displaystyle\frac{\Delta y}{\Delta x} \\ \\ \rule{3.7cm}{0cm} = \dsiplaystyle\frac{f\left(x+h\right) \ - \ f\left(x\right)}{\left(x \ + \ h \right) \ - \ x} \\ \\ \\ \rule{3.7cm}{0cm} = \displaystyle\frac{f\left(x + h\right) \ - \ f\left(x\right)}{h} \\ \\ \\ \rule{3.7cm}{0cm} = \displaystyle\frac{4^{x+h-2} \ - \ 4^{x-2}}{h} \\ \\ \\ \rule{3.7cm}{0cm} = \displaystyle\frac{4^{x-2+h} \ - \ 4^{x-2}}{h}[/tex]

                                                            [tex]\\ \\ \\ \rule{3.7cm}{0cm} = \displaystyle\frac{\left(4^{x-2}\right)\left(4^{h}\right) \ - \ 4^{x-2}}{h} \\ \\ \\ \rule{3.7cm}{0cm} = \displaystyle\frac{\left(4^{x-2}\right)\left(4^{h} \ - \ 1 \right)}{h}[/tex]

Answer:

23 degrees

Step-by-step explanation:

We can use basic trigonometric equations to solve for the angle x because we are given a right triangle.

I will use the sin x = opposite / hypotenuse

sin x = 5 / 13

x = sin^-1 (5 / 13)

x = 22.61986 degrees

The question requires us to round to the nearest degree which is 23.

Other alternative methods you can use include the tangent and cosine functions or the law of cosines.

Answer:

x = 23°

Step-by-step explanation:

I will use

[tex]tanx=opposite/adjacent[/tex]

[tex]tanx=\frac{5}{12}[/tex]

[tex]x=tan^{-1} (\frac{5}{12} )=tan^{-1} (0.417)=22.62^{o}[/tex]

rounded to the nearest degree : 23°

Hope this helps

Step-by-step explanation:

This triangle is acute! ✅

It is also scalene.

see the picture below

It really depends what situation you are trying to set goals at,

Trying to understand math concept or any really concept, I would set little goals such as " Study for 15 mins a day" or something and the big goal would be "UNDERSTAND THE CONCEPT"

for goals, I would set small goals that work towards your main goal.

Answer:

Marriage and Family Harmony. ...

Proper Mindset and Balance. ...

Commitment to Improved Physical Health. ...

Career Passion and Personal Satisfaction. ...

Develop Empathy and Gentleness. ...

Financial Stability. ...

Service and Social Responsibility.

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Answer:  [tex]\textsf{285 total calories}[/tex]

-------------------------------------------------------------------------------------------------------------

Given: [tex]\textsf{1 egg = 95 calories}[/tex]

Find: [tex]\textsf{Calories in 3 eggs}[/tex]

Solution: In order to determine the total amount of calories in 3 eggs we must multiply the amount of calories in one egg by 3.  So we do 95 * 3 which gives us 285 total calories.

The perimeter of the hollow shape is 16d + 4(a + b + c)

The question is incomplete, and the missing parameters cannot be found.

So, I will give a general explanation on how to determine perimeter.

The given information are:

The perimeter of a right triangle that has sides a, b and c is:

P = a + b + c

Since there are 4 triangles, the perimeter of the 4 triangles is:

P = 4(a + b + c)

The perimeter of a square that has side length d is:

P = 4d

Since there are 4 squares, the perimeter of the 4 triangles is:

P = 4 * 4d

P = 16d

Add the perimeters of the squares and the triangles

P = 16d + 4(a + b + c)

Hence, the perimeter of the hollow shape is 16d + 4(a + b + c), where a, b, c and d are the unknown variables

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Answer:

  (a) No; rainfall amounts are positive

Step-by-step explanation:

Rainfall amounts are measured using a gauge that reports the amount as zero when the gauge is empty. Any rainfall adds to the amount in the gauge, so is reported as a positive number. There is no way to remove more rainfall than is in the gauge, so there is no way to have a negative rainfall amount

A prediction of a negative rainfall amount makes no sense, because you can't have a negative amount of rainfall.

Answer:

x=1/3

Step-by-step explanation:

-4(3x-2)=6x+2

or,-12x+8=6x+2

or,-12x-6x=2-8

or,-18x=-6

or,x=-6/-18

or,x=1/3

According to scientific notation the decimal point is shifted to the right (option D).

Scientific notation is a term to refer to the way of writing numbers based on powers of 10. Generally this tool is used for very large or small values.

According to the above, the number 2,420 x 10⁵ expressed in decimal would look like this:

According to the above, it can be inferred that the point is placed in the final right part of the number, that is, it moves to the right.

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The weight of relish prepared after the evaporation of water is 2,226.02 pounds

Total = 1000 + 500 + 900 + 75 + 5

= 2,480 pounds

pickles are 92% water

= 92/100 × 1000

= 920 pounds

onions are 85% water

= 85/100 × 500

= 425 pounds

salt brine is 88% water

= 88/100 × 75 pounds

= 66 pounds

Total water in the mixture = 920 pounds + 425 pounds + 66 pounds

= 1,411 pounds

Amount of water evaporated = 18/100 × 1,411 pounds

= 253.98 pounds

Weight of the relish prepared = 2,480 pounds - 253.98 pounds

= 2,226.02 pounds

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