4/7(b-c)=a solve for c

Answer:

0.0182 = 1.82% probability that the proportion of vegetarians in a sample of 403 Americans would differ from the population proportion by more than 3%.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1-p)}{n}}\)

A statistician calculates that 7% of Americans are vegetarians.

This means that \(p = 0.07\)

Sample of 403 Americans

This means that \(n = 403\)

Mean and standard deviation:

\(\mu = p = 0.07\)

\(s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.07*0.93}{403}} = 0.0127\)

What is the probability that the proportion of vegetarians in a sample of 403 Americans would differ from the population proportion by more than 3%?

Proportion below 7 - 3 = 4% or above 7 + 3 = 10%. Since the normal distribution is symmetric, these probabilities are equal, which means that we find one of them, and multiply by 2.

Probability the proportion is below 4%

p-value of Z when X = 0.04.

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{0.04 - 0.07}{0.0127}\)

\(Z = -2.36\)

\(Z = -2.36\) has a p-value of 0.0091

2*0.0091 = 0.0182

0.0182 = 1.82% probability that the proportion of vegetarians in a sample of 403 Americans would differ from the population proportion by more than 3%.

The value of length BD is 3.0 units

Pythagoras theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

since AC is a radius that joins a tangent, the angle between them is 90°. Therefore ∆ABC is a right triangle and Pythagoras theorem can be applied.

therefore c² = a²+b²

c² = 4.5²+6²

c²= 20.25+36

c²= 56.25

c = √7.5

AC = CD(radii of a circle)

therefore BD = BC -CD

= 7.5-4.5

= 3.0units

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Simplifying

10x + -8 = ax + b

Reorder the terms:

-8 + 10x = ax + b

Solving

-8 + 10x = ax + b

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1ax' to each side of the equation.

-8 + -1ax + 10x = ax + -1ax + b

Combine like terms: ax + -1ax = 0

-8 + -1ax + 10x = 0 + b

-8 + -1ax + 10x = b

Add '8' to each side of the equation.

-8 + -1ax + 8 + 10x = 8 + b

Reorder the terms:

-8 + 8 + -1ax + 10x = 8 + b

Combine like terms: -8 + 8 = 0

0 + -1ax + 10x = 8 + b

-1ax + 10x = 8 + b

Reorder the terms:

-8 + -1ax + -1b + 10x = 8 + b + -8 + -1b

Reorder the terms:

-8 + -1ax + -1b + 10x = 8 + -8 + b + -1b

Combine like terms: 8 + -8 = 0

-8 + -1ax + -1b + 10x = 0 + b + -1b

-8 + -1ax + -1b + 10x = b + -1b

Combine like terms: b + -1b = 0

-8 + -1ax + -1b + 10x = 0

The solution to this equation could not be determined.

Answer:

a = 10 and b = 8

Step-by-step explanation:

comparing the two equations

The inequality for the given statement is 0<n≤8 and the solution set the inequality -8 ≤ w < 2 are w=-8, w=-5 and w=0.

The given inequality is -8 ≤ w < 2.

The solution set of inequality is the set of all solutions. Typically an inequality has infinitely many solutions and the solution set is easily described using interval notation.

a) The solution set the inequality -8 ≤ w < 2 is {-8, -7, -6, -5, -4, -3, -2, -1, 0, 1}

So, the solution sets from the options are w=-8, w=-5 and w=0.

b) The given equation is "a number n is greater than 0, and less than or equal to 8"

The inequality for the given statement is 0<n≤8.

Therefore, the inequality for the given statement is 0<n≤8 and the solution set the inequality -8 ≤ w < 2 are w=-8, w=-5 and w=0.

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The rate of change of the Distance between the planes is zero. This means that the distance between the planes remains constant throughout their respective flights.

The rate of change of the distance between the planes, we need to determine how the distance between them changes over time.

the distance between the two planes is represented by the variable D, and time is represented by the variable t.

At noon, the southbound plane starts flying and continues for 4 hours until 4 pm. During this time, the plane covers a distance of 900 km/h * 4 hours = 3600 km due south.

Meanwhile, the eastbound plane is also traveling towards the airport. It starts from a distance of 2000 km away from the airport at 4 pm.

To find the distance between the planes at any given time, we can use the Pythagorean theorem, as the planes are moving at right angles to each other. The distance D between the planes can be calculated as:

D^2 = (2000 km)^2 + (3600 km)^2

Simplifying the equation:

D^2 = 4000000 km^2 + 12960000 km^2

D^2 = 16960000 km^2

Taking the square root of both sides:

D = sqrt(16960000) km

D = 4120 km

Now, we can find the rate of change of the distance between the planes by calculating the derivative of the distance equation with respect to time

dD/dt = 0

Since the distance between the planes is constant, the rate of change is zero.

Therefore, the rate of change of the distance between the planes is zero. This means that the distance between the planes remains constant throughout their respective flights.

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Answer:

a = 8 m

Step-by-step explanation:

Since, given is an isosceles right triangle.

So, by Pythagoras theorem:

\( {a}^{2} + {a}^{2} = {(8 \sqrt{2} )}^{2} \\ \\ 2 {a}^{2} = 128 \\ \\ {a}^{2} = \frac{128}{2} \\ \\ {a}^{2} = 64 \\ \\ a = \sqrt{64} \\ \\ a = 8 \: m\)

Answer:

square root of 25

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

the square root of 25 is 5, and thats the only rational number there

I hope I was helpful! :D

Answer:

Zero solutions.

Step-by-step explanation:

4x - 8 - 4x = 9

-8 = 9

No solutions.

Answer:

Zero

Step-by-step explanation:

because:

4x - 8 -4x = 9

combine like terms:

4x - 4x = 0x

then look at the equation:

-8 = 9

this is not true. therefore, it has no solutions.

Hope this helped!!

Answer:

1) 3x+18=45       x=9

2)8-5x=-7          x=3

3)3+2x=15         x=6

4) 12million - 2 million  = 10 million

Step-by-step explanation:

Answer:

420 = 4.2 x 100 = 4.2 × 102

Step-by-step explanation:

The remainder is 0, so k=-6 is a zero

Answer: 17 1/3

Step-by-step explanation: hope this helps!

The sequence is a arithmetic sequence if difference between two consecutive terms always remain same. In arithmetic sequence next term can be obtaiend by addition or subtraction of a constant value.

In sequence 4,1, -2, -5,... next term is obtained by substraction of number 3. So this sequence is an arithmetic sequence.

Answer: 4, 1, -2, -5, ...

Answer:

0.56

Step-by-step explanation:

9514 1404 393

Answer:

  2800 tiles

Step-by-step explanation:

Each tile has an area of (0.05 m)² = 0.0025 m². Then the number of tiles required to cover 7 square meters is ...

  (7 m²)/(0.0025 m²/tile) = 2800 tiles

It will take 2800 tiles to cover the entryway.

Answer:

Step-by-step explanation:

Total money spent = 71

Parking fee = 15

71 - 15 = 56

Each ride costs = 4

Total rides = 56 ÷ 4 = 14 rides

The dimensions of the room are approximately 7 meters by 10.5 meters.

In Mathematics, dimensions are referred to as measures of size such as length, width, and height of an object or a shape. A rectangle has length and width as its dimensions that define the area of a rectangle.

Let's start by using algebra to represent the information given in the problem. Let x be the width of the rectangular room, then the length is 1.5 times the width or 1.5x.

The perimeter of a rectangle is the sum of the lengths of all its sides, which can be expressed as:

\(\text{Perimeter} = 2(\text{length} + \text{width})\)

Substituting the values we have for length and width, we get:

\(\rightarrow35 = 2(1.5\text{x} + \text{x})\)

Simplifying the equation, we get:

\(\rightarrow35 = 2(2.5\text{x})\)

\(\rightarrow35 = 5\text{x}\)

\(\rightarrow\text{x}=\dfrac{35}{5}\)

\(\rightarrow\bold{x\thickapprox7}\)

So the width of the room is 7 meters.

To find the length, we can substitute x into the expression we have for the length:

\(\rightarrow\text{Length} = 1.5\text{x}\)

\(\rightarrow\text{Length} = 1.5(7)\)

\(\rightarrow\bold{Length=10.5}\)

So the length of the room is 10.5 meters.

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The correct answer is d i.e. The variation of the data points.

What is mean absolute deviation?

Mean absolute deviation (MAD) is a measure that describes the average distance between each data point in a set and the mean of that set. It is a way of measuring how spread out the data points are from the average or central value.

The correct answer is d. The mean absolute deviation tells you about the variation of the data points in a set. Specifically, it measures how much the data points deviate, on average, from the mean value of the set.

A higher mean absolute deviation indicates that the data points are more spread out from the mean, while a lower mean absolute deviation indicates that the data points are closer to the mean. The mean absolute deviation is useful for comparing the amount of variation between two or more sets of data, and can provide insight into the consistency or stability of the data.

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Answer:

2 coefficients

Step-by-step explanation:

2n,3p Are your Coefficients because they have variables

Step-by-step explanation:

-2 and  3 are coefficients while n and p are the variables

Answer:

y=-4x+3

Step-by-step explanation:

Point slope form equation is

\(y-y_1=x(x-x_1)\)

where \((x_1,y_1)\) is the point through which the line passes and m is the slope in this case we have the point (1,-1) and slope that is m= -4

so,

\(y-y_1=m(x-x_1)\) becomes

\(y-(-1)=(-4)(x-1)\)

\(y+1=-4(x-1)\)

\(y+1=-4x+4\\y=-4x+4-1\\y=-4x+3\)

Answer:

\(h(t)=-25\cos(\pi t)+29\)

Step-by-step explanation:

First thing to understand is that we will be producing a sine or cosine function to solve this one. I'll use a cosine function for the sake of the problem, since it's most easily represented by a cosine wave flipped over. If you're interested in seeing a visualization of how a circle's height converts to one of these waves, you may find the Better Explained article Intuitive Understanding of Sine Waves helpful.

Now let's get started on the problem. Cosine functions generally take the form

\(y=a\cos(b(x-c))+d\)

Where:

\(|a|\) is the amplitude

\(\frac{2\pi}{b}\) is the period, or the time it takes to go one full rotation around the circle (ferris wheel)

\(c\) is the horizontal displacement

\(d\) is the vertical shift

Step one, find the period of the function. To do this, we know that it takes six minutes to do three revolutions on the ferris wheel, so it takes 2 minutes to do one full revolution. Now, let's find \(b\) to put into our function:

\(\frac{2\pi}{b}=2\)

\(2\pi=2b\)

\(\pi=b\)

I skipped some of the basic algebra to shorten the solution, but we have found our b. Next, we'll get the amplitude of the wave by using the maximum and minimum height of the wheel. Remember, it's 4 meters at its lowest point, meaning its highest point is 54 meters in the air rather than 50. Using the formula for amplitude:

\(\frac{\max-\min}{2}\)

\(\frac{54-4}{2}\)

\(\frac{50}{2}=25=a\)

Our vertical transformation is given by \(\min+a\) or \(\max-a\), which is the height of the center of the ferris wheel, \(4+25=29=d\)

Because cosine starts at the minimum, \(c=0\).

The last thing to point out is that a cosine wave starts at its maximum. For that reason, we need to flip the entire function by making the amplitude negative in our final equation. Therefore our equation ends up being:

\(h(t)=-25\cos(\pi t)+29\)

The total volume is the one in option C, 708 cubic centimeters.

We know that this prism can be divided into two prisms, and remember that the volume of a prism is equal to the product between its dimensions.

Then the volume of the first prism is:

V = 8cm*6cm*13cm = 624 cm³

And the volume of the second prism is:

v' = 3cm*4cm*7cm = 84 cm³

Adding that we will get:

total volume =  624 cm³+  84 cm³ = 708 cm³

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Answer:

The solutions for 1 + 3 + 5 +...+ (2n - 1), for the first 10 natural numbers are given in the explanation section below.

Step-by-step explanation:

To calculate 1 + 3 + 5 +...+ (2n - 1) for several natural numbers n, we will use several natural numbers to represent n.

For n= 1,

2n - 1 = 2(1) - 1 = 2 - 1 = 1

Hence, 1 = 1

For n = 2,

2n - 1 = 2(2) - 1 = 4 - 1 = 3

Hence, 1 + 3 = 4

For n = 3,

2n - 1 = 2(3) - 1 = 6 - 1 = 5

Hence, 1 + 3 + 5 = 9

For n = 4,

2n - 1 = 2(4) - 1 = 8 - 1 = 7

Hence, 1 + 3 + 5 + 7 = 16

For n = 5,

2n - 1 = 2(5) - 1 = 10 - 1 = 9

Hence, 1 + 3 + 5 + 7 + 9 = 25

For n = 6,

2n - 1 = 2(6) - 1 = 12 - 1 = 11

Hence, 1 + 3 + 5 + 7 + 9 + 11 = 36

For n = 7,

2n - 1 = 2(7) - 1 = 14 - 1 = 13

Hence, 1 + 3 + 5 + 7 + 9 + 11 + 13 = 49

For n = 8,  

2n - 1 = 2(8) - 1 = 16 - 1 = 15

Hence, 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 = 64

For n = 9,

2n - 1 = 2(9) - 1 = 18 - 1 = 17

Hence, 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 = 81

For n = 10,

2n - 1 = 2(10) - 1 = 20 - 1 = 19

Hence, 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 = 100

Answer:

y=9/8x+-3/2

Step-by-step explanation:

Step 1: Add -9x to both sides.

9x−8y+−9x=12+−9x

−8y=−9x+12

Step 2: Divide both sides by -8.

-8y/-8=-9x+12/-8

y=9/8x+ -3/2

Answer:

Step-by-step explanation:

For Diane's account:

Year 1: Interest = $70,000 x 0.03 = $2,100

Year 2: Interest = ($70,000 + $2,100) x 0.03 = $2,163

Year 3: Interest = ($70,000 + $2,100 + $2,163) x 0.03 = $2,227.89

For Henry's account:

Year 1: Interest = $70,000 x 0.03 = $2,100

Year 2: Interest = $70,000 x 0.03 = $2,100

Year 3: Interest = $70,000 x 0.03 = $2,100

For the first year, both Diane and Henry earn the same interest of $2,100. However, for the second and third years, Diane earns more interest than Henry. Therefore, Diane earns more interest for each year after the first year

Answer:

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Step-by-step explanation:

Answer: -628

Step-by-step explanation:

F(140) = 212 - 6(140)

F(140) = 212 - 840

F(140) = -628

Answer:

42 m^2

Step-by-step explanation:

Answer:

39 meters squared

Step-by-step explanation:

i dont care if i got it wrong because i am a geniuds yhsnkd thanks

Answer:

TWO CRACKERS

Step-by-step explanation:

I'm assuming they want to find x. Here we see that these two are similar triangles, so the sides are reflective. 5x/5 should be equal to 4/x, so 5x/5 = 4/x. If we use cross multiplying we get 5x^2 = 20. divide both sides by 5 and we get x^2 = 4 or x = 2.

Hope this helped

Answer:

A. -6 is the correct answer.

Answer:

So the remainder when 3 is synthetically divided into the polynomial -2x² + 7x - 9 is -6. The correct answer is therefore A.