What is the equation in slope-intercept form of the line that passes through the points (-4,8) and (12,4)?

Answer:

I'm not exactly sure, but I'm positive that it's 60 degrees.

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

90 = 30 + (4x)

60 = 4x

x = 60/4 = 15

30° and (4x)° must add up to 90° because they are complementary angles

The 10,100 cards will be necessary to build a 100-story card tower.

To build a 100-story card tower, we can use the triangular number formula to calculate the total number of cards needed. The formula is:

Triangular number = (n * (n + 1)) / 2

In this case, n represents the number of stories in the tower (100). Plug in the value for n:

Triangular number = (100 * (100 + 1)) / 2
Triangular number = (100 * 101) / 2
Triangular number = 10,100 / 2
Triangular number = 5,050

Additionally, each story requires two cards, so we multiply the triangular number by 2 to get the total number of cards:

Total cards = 5,050 * 2
Total cards = 10,100

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The equation the completes the proof in step 6 is m<w + m<x = m<x + m<z

In step 4 of the proof, we have the following equation

m<w + m<x = m<y + m<z

In step 5, we have

m<x = m<y

When m<x = m<y is substituted to the equation in step 4, we have:

m<w + m<x = m<x + m<z

Hence, the equation the completes the proof in step 6 is m<w + m<x = m<x + m<z

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9514 1404 393

Answer:

  11 years, 7 months

Step-by-step explanation:

When the investment reaches its desired value, it will be 3 times the original amount. So, we are looking for the number of half-month periods (n) of compounding such that ...

  (1 +0.095/24)^n = 3

Taking logarithms, we have ...

  n·log(1.003958333...) = log(3)

  n = log(3)/log(1.009358333...) ≈ 278.09

This is 278.09/24 ≈ 11.59 years.

It will take about 11 years and 7 months for the investment to reach the desired value.

__

Additional comment

The amount will be about tzs 2,758 short after 11 years 7 months. It will exceed the desired amount after 2 more days' interest is added.

We know that,

each digit in a number has a place value. The place a number occupies in a number tells us its importance. The product of a number and the digit value it occupies gives the digit value.

What are some example location values?

Product Importance Image Results

A digit value can be defined as a value represented by a digit within a number given its position within the number. For example, the sevens digit value of 3,743 is 7000 or 700. However, the 7th digit value of 7,432 is 7,000 or 7,000.

tens

According to the question,

We find the value of tens

1. 4 tens ×8 =320

2.5×6 tens=30 tens =300

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Answer:

A) NO and NM

Step-by-step explanation:

Answer:

The 95% confidence interval for the proportion of all US adults who would say they subscribe to a video-streaming service is (0.5362, 0.6048).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which

z is the zscore that has a pvalue of \(1 - \frac{\alpha}{2}\).

Of the 801 participants in the survey, 457 indicated they subscribed to at least one video-streaming service.

This means that \(n = 801, \pi = \frac{457}{801} = 0.5705\)

95% confidence level

So \(\alpha = 0.05\), z is the value of Z that has a pvalue of \(1 - \frac{0.05}{2} = 0.975\), so \(Z = 1.96\).

The lower limit of this interval is:

\(\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5705 - 1.96\sqrt{\frac{0.5705*0.4295}{801}} = 0.5362\)

The upper limit of this interval is:

\(\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5705 + 1.96\sqrt{\frac{0.5705*0.4295}{801}} = 0.6048\)

The 95% confidence interval for the proportion of all US adults who would say they subscribe to a video-streaming service is (0.5362, 0.6048).

Answer:

357.1573 (If you don't round)

Step-by-step explanation:

To find area of a rectangle is to multiply length by width, which in this situation would be 15 by 16.6, which is equal to 249. Next, we need to add this to the area of the semicircle. The area of a semicircle is equal to 1/2 * pi * radius^2 (Because a semicircle is half a circle and a circle's area is pi * radius^2). The radius is equal to half the diameter, which in this case is 16.6. 16.6/2 = 8.3, so the radius is 8.3. If we plug this into the equation, we get that 108.1573 is the area of the circle (If you use 3.14 as pi). 108.1573 + 249 is equal to 357.1573.

A la sala de cine ingresaron 180 niños y 165 adultos.

De acuerdo con el enunciado, la sala de cine tiene capacidad para 345 espectadores y cobra 3 dólares por cada niño y 5 dólares por cada adulto. Asimismo, esta sala tiene un recaudo diario de 1365 dólares. La situación puede ser sintetizada en la siguiente ecuación algebraica:

3 · x + 5 · (345 - x) = 1365

Donde x es el número de niños que asistieron a la sala de cine.

Ahora despejamos la variable correspondiente mediante propiedades algebraicas:

3 · x + 1725 - 5 · x = 1365

1725 - 2 · x = 1365

2 · x = 1725 - 1365

2 · x = 360

x = 180

Ahora, el número de adultos es:

y = 345 - 180

y = 165

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If an auto body shop repaired 22 cars and trucks and there were 8 fewer cars than trucks, 15 trucks were repaired.

Let's assume the number of trucks repaired is "x". We know that the total number of cars and trucks repaired is 22. Since there were 8 fewer cars than trucks, the number of cars repaired must be x-8. Therefore, we can set up the following equation:

x + (x-8) = 22

Simplifying, we get:

2x - 8 = 22

Adding 8 to both sides:

2x = 30

Dividing by 2:

x = 15

We can check this by plugging x back into the equation and verifying that the number of cars repaired is 7, which is 8 fewer than 15.

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Answer:

D, 9:1

Step-by-step explanation:

There is 36 peach juice for 4 lemon-lime, simplified is 9:1. Hope this helps!

Answer:

9:1

Step-by-step explanation:

If you read the graph, the line that runs down the page shows 9 and 1, therefore 9:1. It's hard to explain radio so let me know if you want more detail.

Neither statement "E and F are always independent" nor "E and F are always dependent" is correct for mutually exclusive events E and F with positive probabilities p(e)>0 and p(f)>0.

Events that are mutually exclusive cannot occur at the same time. For example, if we have two events E and F such that E represents "rolling a 1 on a fair die" and F represents "rolling a 2 on a fair die", These events cannot occur simultaneously since a 1 and a 2 cannot be rolled.

In probability theory, two events E and F are considered independent if the occurrence of one event has no effect on the probability of the other event occurring. For example, if we have two events E and F such that E represents "rolling a 1 on a fair die" and F represents "rolling a 6 on a fair die", these events are independent because the occurrence of one event (rolling a 1) does not affect the probability of the other event (rolling a 6) occurring.

In the case where events E and F are mutually exclusive, their occurrence does affect each other, as the occurrence of one event makes it impossible for the other event to occur. Therefore, the statement "E and F are always independent" is not correct. Similarly, the statement "E and F are always dependent" is also not correct because dependence is a different concept from mutual exclusiveness.

Therefore, "Neither of the above statements is correct" is the appropriate response.

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The complete question is:

Which of the following statements is correct if e and f are mutually exclusive and p(e)>0 and p(f)>0?

a) E and F are always independent

b) E and F are always dependent

c) Neither of the above statement is correct

Answer:55 nail boxes

Step-by-step explanation: first we have to find out the total amount of nails in all the boxes so for this we do 38*8=304

when he gave all the nails to all his students he has 26 extra nails left. so we add this amount to the original which gives us 330 total nails.

to find out the number of nails in eadh box we divide 330/6=55

Answer:

22.

\(rcos \theta = rsin \theta\)

23.

\((rcos \theta) ^{2} + (rsin \theta) ^{2} = 25\)

Step-by-step explanation:

To change the equation to polar form replace x with \( rcos\theta\)

and y with \( rsin\theta\)

Answer:

Y=KX so its 10=K2

Step-by-step explanation:

Plug in the Number OR K=y/x

Answer:

i think it's 40 I don't know.

Step-by-step explanation:

(:

Answer:

÷3==533740£; ok8iejeoeoeo

Answer:

2

Step-by-step explanation:

the line meets the y axis at (0,2)

Answer:

you need this ?

the y is

y=-x+2

All the values of x, y and z are,

z = 12.99

y = 7.01

x = 28.3 degree

We have to given that;

In a triangle,

Two angles are, 61.7 degree and 90 degree

And, One side is, 14.76.

Now, We can formulate;

sin 61.7° = Perpendicular / Hypotenuse

sin 61.7° = z / 14.76

0.88 = z / 14.76

z = 0.88 x 14.76

z = 12.99

And, By Pythagoras theorem we get;

14.76² = z² + y²

14.76² = 12.99² + y²

217.85 = 168.74 + y²

y² = 217.85 - 168.74

y² = 49.1

y = 7.01

And, By sum of all the angles in triangle, we get;

x + 61.7 + 90 = 180

x + 151.7 = 180

x = 180 - 151.7

x = 28.3 degree

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Answer:  \(-\frac{\sqrt{2a}}{8a}\)

=======================================================

Explanation:

The (x-a) in the denominator causes a problem if we tried to simply directly substitute in x = a. This is because we get a division by zero error.

The trick often used for problems like this is to rationalize the numerator as shown in the steps below.

\(\displaystyle \lim_{x\to a} \frac{\sqrt{3a-x}-\sqrt{x+a}}{4(x-a)}\\\\\\\lim_{x\to a} \frac{(\sqrt{3a-x}-\sqrt{x+a})(\sqrt{3a-x}+\sqrt{x+a})}{4(x-a)(\sqrt{3a-x}+\sqrt{x+a})}\\\\\\\lim_{x\to a} \frac{(\sqrt{3a-x})^2-(\sqrt{x+a})^2}{4(x-a)(\sqrt{3a-x}+\sqrt{x+a})}\\\\\\\lim_{x\to a} \frac{3a-x-(x+a)}{4(x-a)(\sqrt{3a-x}+\sqrt{x+a})}\\\\\\\lim_{x\to a} \frac{3a-x-x-a}{4(x-a)(\sqrt{3a-x}+\sqrt{x+a})}\\\\\\\)

\(\displaystyle \lim_{x\to a} \frac{2a-2x}{4(x-a)(\sqrt{3a-x}+\sqrt{x+a})}\\\\\\\lim_{x\to a} \frac{-2(-a+x)}{4(x-a)(\sqrt{3a-x}+\sqrt{x+a})}\\\\\\\lim_{x\to a} \frac{-2(x-a)}{4(x-a)(\sqrt{3a-x}+\sqrt{x+a})}\\\\\\\lim_{x\to a} \frac{-2}{4(\sqrt{3a-x}+\sqrt{x+a})}\\\\\\\)

At this point, the (x-a) in the denominator has been canceled out. We can now plug in x = a to see what happens

\(\displaystyle L = \lim_{x\to a} \frac{-2}{4(\sqrt{3a-x}+\sqrt{x+a})}\\\\\\L = \frac{-2}{4(\sqrt{3a-a}+\sqrt{a+a})}\\\\\\L = \frac{-2}{4(\sqrt{2a}+\sqrt{2a})}\\\\\\L = \frac{-2}{4(2\sqrt{2a})}\\\\\\L = \frac{-2}{8\sqrt{2a}}\\\\\\L = \frac{-1}{4\sqrt{2a}}\\\\\\L = \frac{-1*\sqrt{2a}}{4\sqrt{2a}*\sqrt{2a}}\\\\\\L = \frac{-\sqrt{2a}}{4\sqrt{2a*2a}}\\\\\\L = \frac{-\sqrt{2a}}{4\sqrt{(2a)^2}}\\\\\\L = \frac{-\sqrt{2a}}{4*2a}\\\\\\L = -\frac{\sqrt{2a}}{8a}\\\\\\\)

There's not much else to say from here since we don't know the value of 'a'. So we can stop here.

Therefore,

\(\displaystyle \lim_{x\to a} \frac{\sqrt{3a-x}-\sqrt{x+a}}{4(x-a)} = -\frac{\sqrt{2a}}{8a}\\\\\\\)

Answer:

4x² + 22x - 12

Step-by-step explanation:

A = bh/2

A = (4x - 2)(2x + 12)/2

A = (8x² + 48x - 4x - 24)/2

A = (8x² + 44x - 24)/2

A = 4x² + 22x - 12

Answer:

There are 16 square blocks.

Step-by-step explanation:

The area is 16 square blocks.

Hope this helps!

A sine function is as shown below

A cosine function is as shown below

The combination of both sine and cosine function is as shown below

It can be observed from the above combination that:

Cosine is better when the maximum is on the y- axis and sine is better if the midline is at the center.

Answer: 5

Step-by-step explanation:

8/10 = 4/N

0.8 = 4/N

0.8N  = 4

N = 4/0.8 = 5

An equation which is true include the following: A. 4 × n × n × n × n = 4n⁴.

In Mathematics, an exponent is a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.

This ultimately implies that, an exponent is represented by the following mathematical expression;

bⁿ

Where:

By applying the multiplication law of exponents for powers to each of the expressions, we have the following:

4 × n × n × n × n = 4n⁴

4 × n⁴ = 4n⁴

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Answer:

Step-by-step explanation:

1. The measurement is actual and should be considered as such. Estimate is approximate most of the time.

2. The error is:

3. Percent error:

A fraction can easily be written as a percent when the denominator is 100 , the correct option is (a) .

in the question a fraction is given ,

we need to find , what should be the denominator to express the fraction in percent .

the definition of percent states that one part of every hundred is called as percent ,

So , by the definition of percent we can conclude that A fraction can easily be written as a percent when the denominator is 100 .

For Example : 5% can be written as 5/100 , where the denominator is 100 .

Therefore , A fraction can easily be written as a percent when the denominator is 100 .

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The amount of time he spent on bicycle is 4.5 hours.

Given Jim began a 145 mile bicycle trip.

The whole trip took 7 hours.

Jim walks at a rate of 4 miles per hour  and rides at 30 miles per hour.

speed = distance / time

time = distance / speed

ride:

d = distance ridden

t = d/30 (given from the problem)

walk:

t = (145 - d)/4 (given from problem)

total trip time:

7 = d/30 + (145 - d)/4.

7 = 4d/120 + 30(145 - d)/120

7×120 = 4d + 30(145 - d)

840= 4d +4350-30d

840 ₋ 4350 = ₋30d ₊ 4d

₋3510 = ₋26d

d = 3510/26

d = 135

d=135 then from here using the formula t = d / s we can solve

t=135/30 = 4.5 hours

hence the amount of time Jim spent on the bicycle is 4.5 hours.

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Since  the resulting function has a leading degree of 1, hence the set or ordered pairs (1,6), (2,9), (3,12), (4,15) satisfies a linear function

The standard equation of a linear function is y = mx + b

where:

m is the slopee

b is the y-intercept

Using the coordinate point (1, 6) and (2, 9)

Find the slope

Slope = 9-6/2-1
Slope = 3/1

Slope = 3

For the y-intercept

Recall that y = mx + b

9 = 3(2) + b

b = 3

Determine the equation

y = 3x + 3

Since the resulting function has a leading degree of 1, hence the set or ordered pairs (1,6), (2,9), (3,12), (4,15) satisfies a linear function.

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