A cog wheel having 4 cogs plays into another cog wheel having 28 cogs. When the small wheel has made 28 revolutions, how many has the larger wheel made?

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Considering the definition of mass volume percent, the percent composition of lactose in skim milk is 28%.

The concentration of solutions is the amount of solute contained in a given amount of solvent or solution. In other words, the relationship between the amount of solute and the amount of solvent is called concentration.

Mass volume percent (% m/V) is a measure of concentration that indicates the number of grams of solute in each 100 mL of solution.

In other words, mass-volume percent is an intensive property that is defined as the mass of solute (in grams) that there are in 100 mL of solution and it is calculated by applying the following equation:

\(Mass volume percent=\frac{mass solute (grams)}{volume solution (mL)}x100\)

This is, mass volume percent is defined as the ratio of the mass of solute that is present in a solution, relative to the volume of the solution, as a whole.

In this case, you know:

Replacing in the definition of mass volume percent:

\(Mass volume percent=\frac{0.28 grams}{1 mL}x100\)

Solving:

mass volume percent= 28 %

Finally, the percent composition of lactose in skim milk is 28%.

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The simplified form of the given expression, 6 × 10⁻³ / 8 × 10⁻⁶, is 3/4  × 10³

From the question, we are to simplify the given expression

The given expression is

6 × 10⁻³ / 8 × 10⁻⁶

Simplifying the expression

6 × 10⁻³ / 8 × 10⁻⁶

This can be written as

6/8 × 10⁻³/10⁻⁶

Reduce the fraction

3/4  × 10⁻³/10⁻⁶

Apply the division law of indices

3/4  × 10⁻³ ⁻ ⁽⁻⁶⁾

3/4  × 10⁻³ ⁺ ⁶

3/4  × 10³

Hence, the value is 3/4  × 10³

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Answer:

0 hundreds

0 tens

7 ones

.

4 tenths

0 hundredths

8 thousandths

Standard form=7.408

Step-by-step explanation:

Lets first solve (7x1)+(4x1/10)+(8x1/1000)

7+0.4+0.008

Simplify:

7.408

Answer:

A) p = 0.230139

B) p = 0 .00001

There is not enough evidence to show that fewer DVDs a month than high school students

Step-by-step explanation:

A) The correct hypothesis are;

Null hypothesis;H0: μ = 50

Alternative hypothesis;H1: μ ≠ 50

We are given;

Sample mean; x' = 49

Standard deviation; σ = 5

Sample size;n = 36

Formula for the test statistic is given by;

z = (x' - μ)/(σ/√n)

z = (49 - 50)/(5/√36)

z = -1.2

So, from online p-value calculator from z-values as attached, using z-score of -1.2, significance level of 0.05, two tailed, we have;

p = 0.230139

B) we are given ;

x = 5.80

μ = 6.5

n = 33

Standard deviation;σ = 0.6

Significance level = 0.05

Hypotheses are;

Null hypothesis;H0: μ = 6.5

Alternative hypothesis; μ < 6.5

So, formula for the test statistic again;

z = (x' - μ)/(σ/√n)

z = (5.8 - 6.5)/(0.6/√33)

z = -6.7

from online p-value calculator z-values as attached, using z-score of -6.7, significance level of 0.05, one tailed tailed, we have;

p = 0 .00001

This is less than the significance level of 0.05, thus we will reject the null hypothesis and conclude that there is no evidence to show that fewer DVDs a month than high school students

In a case whereby Darren says that more students hands are 4 2/4 inches longer than 4 and 5 1/4 inches combined, he is wrong

\(4\frac{2}{4}\) that was given in the question can be seen as mixed fraction, we can expressed this as improper fraction so that it will be easier to handle.

\(4\frac{2}{4} = \frac{16+4}{2}\)

=\(\frac{18}{4}\)

Then \(4 + 5\frac{1}{4} = \frac{16}{4} +\frac{20+1}{4} \\\\=\frac{37}{4}\)

Then after expressing the given fractions as improper fraction we can now compare them so that e will know may be Darren is right or wrong, then here we can see that \(\frac{18}{4}\) is less than \(\frac{37}{4}\) Hence, Darren is wrong.

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Russell has to sell 270 cable packages to make the total pay of both the companies as same.

Suppose that Russell sells x cable packages such that the total pay of both the companies is the same.

Then the revenue Russell would make at the first company is $17000+20x

And, the revenue Russell would make at the second company is

$14300+30x

Since, the above two values are equal

so, 17000+20x=14300+30x

⇒17000-14300=30x-20x

⇒10x=2700

⇒x=270

The above problems are called mathematical modelling.

Mathematical modelling is the process of locating such equations to explain actual occurrences.

These formulae are referred to as mathematical models together with the definitions given to the variables.

Therefore, Russell has to sell 270 cable packages to make the total pay of both the companies as same.

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Answer:

Step-by-step explanation:

The slope of the line that contains the points (1,-9) and (-3,3) is -3 when the slope is y₂-y₁/x₂-x₁.

Given that,

We have two points they are (1,-9) and (-3,3).

We have to find the slope of the line that contains the points.

We know that,

The slope or steepness of a line is determined using the slope formula. It may be used to calculate any line's slope by comparing the change in the y-axis to the change in the x-axis. The slope of a line is the ratio of the change in the line's "y" coordinate to the change in its "x" coordinate.

Slope = y₂-y₁/x₂-x₁

So,

The points (1,-9) and (-3,3).

Slope = 3-(-9)/-3-1 = 3+9/-3-1 = 12/-4 = -3

Therefore, The slope of the line that contains the points (1,-9) and (-3,3) is -3 when the slope is y₂-y₁/x₂-x₁.

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Answer:

The balance in the account after 3 years is approximately $2313.94.

Step-by-step explanation:

The formula for calculating the balance in a continuously compounded account is:

B = Pe^(rt)

Where:

B = balance

P = principal

e = Euler's number (approximately 2.71828)

r = annual interest rate (as a decimal)

t = time in years

Using the given values, we have:

P = $2000

r = 0.051 (5.1% expressed as a decimal)

t = 3

Plugging these values into the formula, we get:

B = 2000e^(0.051*3)

B = 2000e^(0.153)

B = $2313.94 (rounded to the nearest cent)

Therefore, the balance in the account after 3 years is approximately $2313.94.

Given the perimeter, the numerical length of the rectangle is 49.5 inches.

Hence, option 3) 49.5 inches is the correct answer.

The perimeter of a rectangle is expressed mathematically as;

P = 2( l + w )

Given the data in the question;

Let "x" represent the width of the rectangle.

To determine the length of the rectangle, first plug the given values into the formula above and solve for x.

P = 2( l + w )

132 = 2( 3x + x )

Apply distributive property

132 = 2(3x) + 2(x)

132 = 6x + 2x

132 = 8x

8x = 132

x = 132/8

x = 16.5

Now, the length of the rectangle will be;

Length l = 3x

Length l = 3( 16.5 )

Length l = 49.5 inches

Given the perimeter, the numerical length of the rectangle is 49.5 inches.

Hence, option 3) 49.5 inches is the correct answer.

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An equation can be written to determine the number of students that went on this trip is: C. \(\frac{1259}{s} + 12=\frac{1259}{s+9}\)

In order to write an equation to determine the number of students that went on this trip, we would have to assign a variable and an expression to the number of students who went on the trip and the original number of students who had planned to go on the trip as follows;

Since a total of $1259 was collected from all of the students with 9 students dropping out and their portion of the money collected given back to them while the students that are all still going must contribute an additional $12, an equation to determine the number of students that went on this trip is given by;

\(\frac{1259}{s} + 12=\frac{1259}{s+9}\)

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Complete Question:

A high school class is planning a field trip to an art museum in their city. The class collected a total of $1259 from all of the students, which will go towards renting a bus, museum admission, and lunch.

However, a week before the trip 9 students had to drop out and their portion of the collected money had to be given back to them. Due to this, the students that are all still going must contribute an additional $12 each to cover all of the cost.

Now let s be the number of students who went on the trip and s + 9 be the original number of students who had planned to go on the trip

What equation can be written to determine the number of students that went on this trip?

Answer:

x =+- 6

is the answer.

Because 6² = (-6)²

Answer:

c

Step-by-step explanation:

multiply

9514 1404 393

Answer:

  a) 901,029

Step-by-step explanation:

The production volume for 1 year is ...

  1 unit/(35 s) × (3600 s)/(1 h) × (24 h)/(1 day) × (365 day)/(1 year)

  = 3600×24×365/35 unit/year = 901,029 unit/year

The given options, the only value greater than 1 is 1.003. Therefore 0.886, which is less than 1 and makes the inequality true.

The given number sentence is 5.3 × > 5.3, where we need to find the scaling factor that makes the inequality true. To do this, we can divide both sides of the inequality by 5.3. This gives us:

5.3 × x > 5.3 ÷ 5.3 × k

We need to find the value of k that makes the inequality true. Simplifying the right-hand side of the equation, we get:

5.3 ÷ 5.3 × k = k × 1 = k

Substituting this into our equation, we get:

5.3 × x > k

We know that 5.3 × 1 = 5.3, which means that k must be greater than 1 to satisfy the inequality. Among the given options, the only value greater than 1 is 1.003. However, this value would make the inequality too large, so it is not the correct answer.

The correct answer is therefore 0.886, which is less than 1 and makes the inequality true.

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the left side of this equation equal the right side through the process of completing the square that establishes the equality between the left side and the right side of the Gaussian integral equation.

using  completing the square method:

Starting with the left side of the equation:

∫\(e^(^-^x^2)\) dx

\(e^(^-^x^2) = (e^(^-x^2/2))^2\)

∫\((e^(^-^x^2/2))^2 dx\)

let  u = √(x²/2) =  x = √(2u²).

dx = √2u du.

∫ \((e^(^x^2/2))^2 dx\)

= ∫ \((e^(^-2u^2)\)) (√2u du)

The integral of \(e^(-2u^2)\)= √(π/2).

∫ \((e^(-x^2/2))^2\) dx

= ∫  (√2u du) \((e^(-2u^2))\\\)

= √(π/2) ∫ (√2u du)

We substitute back  u = √(x²/2), we obtain:

∫ \((e^(-x^2/2))^2\)dx

= √(π/2) (√(x²/2))²

= √(π/2) (x²/2)

= (√π/2) x²

A comparison  with the right side of the equation  shows that they are are equal.

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The medians are about the same.

Option C is the correct answer.

The median, in statistical terms, refers to the value in the center of a dataset that has been sorted either in ascending or descending order, and it is a commonly used measure of central tendency. This contrasts with the mean, which calculates the total value of all figures, then divides by the number of figures.

We have,

Movie theater 1.

From the box plot given,

The median is 995.

Movie theater 2.

From the box plot given,

The median is 995.

Thus,

The median in both the box plot is the same.

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Answer:

\(y = 4x\)

Step-by-step explanation:

Given

\(x = 44\)

\(y = 176\)

Required

Determine the relationship between x and y

First, we calculate the unit rate, using:

\(y = kx\)

Where k is the unit rate.

Substitute 176 for y and 44 for y

\(176 = k * 44\)

Divide both sides by 44

\(\frac{176}{44} = \frac{44*k}{44}\)

\(\frac{176}{44} = k\)

\(4 = k\)

\(k = 4\)

Substitute 4 for k in \(y = kx\)

\(y = 4x\)

Hence, the relationship between x and y is: \(y = 4x\)

Answer:

hope this hellp for for you

Step-by-step explanation:

The solution of the quadratic equation -2x² + 4x = 5 is; x = 1 ± (1/2)√-6

We are given the quadratic equation;

-2x² + 4x = 5

-2x² + 4x - 5 = 0

Quadratic formula for an equation of the form ax² + bx + c = 0 is given as; x = [-b ± √(b² - 4ac)]/(2a)

From the given quadratic equation, we can see that;

a = -2

b = 4

c = -5

Thus;

x = [-4 ± √(4² - 4*-2*-5)]/(2*-2)

x = [-4 ± √(16 - 40)]/-4

x = -4/-4 ± (1/4)√-24

x = 1 ± (2/4)√-6

x = 1 ± (1/2)√-6

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That both a and b are equally likely, is also not true since the Probability of option b is higher than that of option a.

Option b is more likely to be true. This is because the given information states that the showerhead heights were designed to be 72 inches, which is well above the mean height of 69.5 inches. Therefore, it is reasonable to assume that the majority of the players' heights are below 72 inches. Since the heights of the athletes are normally distributed, the probability of selecting a player at random with a height above 72 inches is relatively low. On the other hand, option a suggests that the mean height of a sample of 20 players is more than 72 inches, which is less likely than option b. Option c, which suggests that both a and b are equally likely, is also not true since the probability of option b is higher than that of option a.

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Answer:

only god knows

Step-by-step explanation:

because they didn't give us an answer on how many text messages anyone sent

Answer:

Null Hypothesis, H0 = The pulse rates of men have a standard deviation equal to 10 beats per minute

Alternate Hypothesis, H1 = The pulse rates of men do not have a standard deviation equal to 10 beats per minute

Step-by-step explanation:

The null hypothesis is basically the problem statement i.e

Pulse rates of men have a standard deviation equal to 10 beats per minute

Hence, H0 = The pulse rates of men have a standard deviation equal to 10 beats per minute

The alternate hypothesis will contradict or negate the null hypothesis i.e

H1 = The pulse rates of men do not have a standard deviation equal to 10 beats per minute

Answer:

6.oz and all other things are going on

Step-by-step explanation:

its been a few weeks and I've just got back to

The most reasonable temperature for a snowy day is given as follows:

C. -6°C

Considering that it snows, the temperature is either negative or very low positive, as snow only happens on temperatures close to freezing (like 2º C) or negative.

17ºC and 26ºC are far from cold enough to generate snow, hence the most reasonable temperature for a snowy day is given as follows:

C. -6°C

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2^( - 1 ) × 4^( -1 ) =

2^( -1 ) × 2^( 2 × ( - 1) ) =

2^( - 1 ) × 2^( - 2 ) =

2^( - 1 - 2 ) =

2^( - 3 ) =

1/ 2^( 3 ) =

1/8

The point at (60, 55) represents an item with an original price of $60 that is now being sold at a sale price of $55.

There are many tools we can use to find the information of the relation which was used to form the graph.

A graph contains data of which input maps to which output.

Analysis of this leads to the relations which were used to make it.

For example, if the graph of a function is rising upwards after a certain value of x, then the function must be having increasingly output for inputs greater than that value of x.

If we know that the function crosses x axis at some point, then for some polynomial functions, we have those as roots of the polynomial.

We are given that;

The point at (60, 55)

Now,

This means that customers who enter the special discount code can save $5 on this particular item.

In general, the point (x, y) on the graph represents an item with an original price of x dollars that is being sold at a sale price of y dollars. The graph is showing how the sale price of items changes as the original price increases.

Therefore, by the graph the answer will be $60 and $55.

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The equation of the parabola is y = 8\(x^2\) + 16x - 64.

The parabola has roots at (2,0) and (-4,0), which means that the quadratic equation that represents the parabola is of the form:
y = a(x - 2)(x + 4)
where "a" is some constant.
y = a(x - 2)(x + 4)

where a is some constant.

To find the value of a, we can use the fact that the parabola passes through the point (5, 216).

Substituting these values into the equation, we get:

216 = a(5 - 2)(5 + 4)

216 = a(3)(9)

216 = 27a

a = 8

So the equation of the parabola is:

y = 8(x - 2)(x + 4)

Next, we know that the parabola passes through the point (5,216), which means that we can substitute these values into the equation and solve for "a":
216 = a(5 - 2)(5 + 4)
216 = a(3)(9)
a = 8
So the equation of the parabola is:
y = 8(x - 2)(x + 4)
Simplifying, we get:
\(y = 8x^2 - 32x - 64\)
And that's it! The equation of the parabola that has roots at (2,0) and (-4,0) and passes through the point (5,216) is y = \(8x^2 - 32x - 64.\)

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Answer:

B) 48cm²

Step-by-step explanation:

find the area of the 2 rectangles

A = bh

A = 9×4

A = 36

A = bh

A = 6×2

A = 12

add them up you get 48cm²