Write the following comparison as a ratio reduced to lowest terms. 7 nickels to 47 dimes

(c) range, (d) variance, (e) standard deviation and (f) interquartile range measure variability.

Range, The range is the difference between the largest and smallest values in a dataset, indicating how spread out the data are.

Variance, The variance measures how far a set of numbers is spread out from their average. It provides a measure of how much the individual data points deviate from the mean.

Standard deviation, The standard deviation is the square root of the variance and is also a measure of how much the individual data points deviate from the mean. It is a widely used measure of variability, particularly in statistical analysis.

Interquartile range, The interquartile range (IQR) is the difference between the third and first quartiles of a dataset. It gives an idea of the spread of the middle 50% of the data and can help identify outliers.

The mean and median are measures of central tendency and do not directly measure variability.

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Answer:

XY = 18

Step-by-step explanation:

In this picture, XD = DW, and YE = EZ, so we are able to use the midline theorem. From the midline theorem, we can easily determine that (XY + WZ)/2 = DE. From this, we can plug in: (XY + [tex]\frac{4}{3}[/tex]XY) = 2 * 21. So, simplifying that equation gets: [tex]\frac{7}{3}[/tex]XY = 42. So, XY = [tex]42 * \frac{3}{7} = 18[/tex].

(if i'm going to be honest, i'm sure your geometry teacher covered this in class. just make sure to pay attention next time.)

Answer:

XY = 18 ft.

Step-by-step explanation:

To rewrite the equation in Ax + By = C form, we need to rearrange it so that the x and y terms are on the same side of the equation and the constant is on the other side and the equation become x + 3y = 9.

What is Equation?

An equation is a mathematical statement that shows the equality of two expressions or values. It typically contains one or more variables and an equal sign, which indicates that the expressions on either side of the equal sign have the same value. Equations can be used to represent various relationships between different mathematical objects and are used extensively in many fields of mathematics, science, engineering, and other disciplines. Equations can be solved to find the values of the variables that make the equation true, which is often the goal of many mathematical problems.

To rewrite the equation in Ax + By = C form, we need to rearrange it so that the x and y terms are on the same side of the equation and the constant is on the other side.

Starting with:

y = (1/3)x + 3

We can multiply both sides by 3 to eliminate the fraction:

3y = x + 9

Now we can rearrange to get the x and y terms on the left side:

-x + 3y = 9

So the equation in Ax + By = C form is:

x + 3y = 9

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Answer:

The correct answer is C, 428 feet.

To calculate the elevation of the marked point, we need to interpolate between the two contour lines. The difference in elevation between the two contour lines is 20 feet (440 - 420 = 20). And since the distance between the two contour lines is 0.5 inches, each 0.1 inch increment represents a 4-foot change in elevation (20 feet ÷ 0.5 inches = 40 feet per inch ÷ 10 = 4 feet per 0.1 inch).

Since the marked point is 0.2 inches from the 420-foot contour, the elevation of the marked point can be calculated by adding 8 feet (4 feet x 0.2 inches) to the 420-foot contour line: 420 + 8 = 428 feet.

The possible equation of the parabola is y = (x - 5)^2 - 4

from the question, we have the following parameters that can be used in our computation:

Vertex = (5, -4)

The vertex form of a parabola is given by:

y = a(x - h)^2 + k

where (h, k) is the vertex of the parabola and "a" is a constant that determines the shape of the parabola.

We are given that the vertex of the parabola is (5,-4). Substituting these values into the vertex form, we get:

y = a(x - 5)^2 - 4

Let a = 1

So, we have

y = (x - 5)^2 - 4

Hnce, the possible equation is y = (x - 5)^2 - 4

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Answer: DESMOS

Step-by-step explanation:

Your OHVA teacher reminded you in class to use DESMOS to see the graph and then sketch it on your test...

Yes, the data provided is not correct. This can be proven using the principle of inclusion-exclusion.

According to the given data, the total number of students who failed in Math is 750, the total number of students who failed in Accounts is 600, and the total number of students who failed in Costing is 600.

However, if we apply the principle of inclusion-exclusion, the total number of students who failed in at least one of the three subjects should be equal to the sum of the number of students who failed in each subject, minus the number of students who failed in two subjects, plus the number of students who failed in all three subjects.

Therefore, using this principle, we have:

750 + 600 + 600 - 450 - 400 + 75 = 975

This result shows that the number of students who failed in at least one of the three subjects is 975, which is greater than the total number of students who appeared for the examination (1000), which is not possible.

Therefore, the given data is not correct.

It would take Caro-line 3 hours to sketch 9 cartoon str-ips.

What is a ratio?

A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of the fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six.

We are given that, Caro-line can sketch 6 car-toon str-ips in two hours.

And we are asked that how much time it would require for Caro-line to sketch 9 str-ips

Now let the time required be x

Hence, the ratio becomes

6/2=9/x

x= (9*2)/6

x= 3

Hence, It would take Caroline 3 hours to sketch 9 cartoon str-ips

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if seven less than three times a number is negative one then the number is 2.

Two or more expressions with an Equal sign is called as Equation.

Let the number be x.

Seven less than three times a number is negative one.

We need to find the unknown number x from the given statement.

Less than we use when we use subtraction, times we use for multiplication.

seven less than three times a number is negative one.

3x-7=-1

Add 7 on both sides

3x=6

Divide both sides by 3

x=2

Hence, if seven less than three times a number is negative one then the number is 2.

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Answer:

x = 2.4 inch

Step-by-step explanation:

Tall retangular prism = lwh = 6 x 9 x 3 = 162 in^3

378 - 162 = 216

Long rectangular prism = lwh = (15)(6)(x) = 90x

216 = 90x

x = 2.4

Any line of the form:

y = (3/2)x + b

Is perpendicular to the given line.

A general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

Two lines are perpendicular if the product between the slopes is -1.

Here we want to find a line perpendicular to:

2x + 3y = 10

We can rewrite this as:

3y = 10 - 2x

y = (10/3) - (2/3)*x

Then the slope of the perpendicular line must be such that:

a*(-2/3) = -1

a = 3/2

Then any line of the form:

y = (3/2)*x + b

Is perpendicular to the given line.

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Answer: 6 pounds and 12 pounds.

Step-by-step explanation:

1.5(x)+2.4(18-x)=2.1(18)

1.5x+43.2-2.4x=37.8

1.5x+43.2=37.8+2.4x

0.9x=5.4

x=6 pounds of $1.50 candy

18-6=12 pounds of $2.40 candy

(check my work to see if it's correct :))

10 pounds of barley should be used by the cook to mix in with the 35 quarts of the vegetable broth.

lets say we know that there is a mix of 2 pounds of barley into 7 quarts of vegetable broth, so we can say that,

2:7 is the ratio used for the mix

similarly we can say,

let the pounds of barley into 35 quarts of vegetable broth used be x

x:35 because its given that there are 35 quarts used in the vegetable soup so we need to find the value of 'x'

then, 2/7=x/35, that is pounds/quarts

then, x= 2/7 × 5

then, x = 2×5

therefore we know that x = 10

so we can say that there are 10 pounds of barley used in the mix by the cook along with the 35 quarts of vegetable broth.

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On solving the Power equals Current times voltage as an equation we get power is P = VI

A mathematical equation is a fοrmula that joins twο statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of twο mathematical expressions is knοwn as an equation in algebra. For instance, in the equatiοn 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the twο sentences οn either side of a letter is described by a mathematical fοrmula. Often, there is only οne variable, which also serves as the symbol. fοr instance, 2x – 4 = 2.

Given to write

Power equals current times voltage

in mathematical equation, i.e.

P = V × I

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Answer:

Step-by-step explanation:

The equation that represents the town's population after 4 years can be found using the formula:

P = P0 * (1 - r)^t

Where P is the population after t years, P0 is the initial population (4.11 x 10^4), r is the annual shrink rate as a decimal (9.6% as 0.096), and t is the number of years (4).

P = 4.11 x 10^4 * (1 - 0.096)^4

P = 4.11 x 10^4 * 0.6994^4

P = 4.11 x 10^4 * 0.4139

P = 1.70 x 10^4

So the town's population after 4 years is 1.70 x 10^4.

Answer:

Let P(t) be the population of the town after t years. We know that P(0) = 4.11 x 10^4. Then, the rate of change of the population is given by -0.096P(t), so we can write the differential equation:

dP/dt = -0.096P(t)

To find the population after 4 years, we need to solve this differential equation with the initial condition P(0) = 4.11 x 10^4. We can do this by separating variables and integrating both sides:

∫(dP/P) = -0.096 ∫dt

ln|P(t)| = -0.096t + C

where C is a constant of integration that can be found using the initial condition. Solving for P(t), we get:

P(t) = Ce^(-0.096t)

where C = e^(ln|P(0)|) = e^(ln|4.11 x 10^4|) = 4.11 x 10^4

Substituting in t = 4, we get:

P(4) = 4.11 x 10^4 e^(-0.096 × 4) = 4.11 x 10^4 e^(-0.384)

So, the equation representing the town's population after 4 years is:

P(t) = 4.11 x 10^4 e^(-0.096t)

For the function y = f(x). The statements are -

A. False

B. True

C. False

D. False

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

The data points for the function y = f(x) is given.

The domain of a function is the set of "valid inputs" to the function, while the range of a function is the set of "all outputs" of the function.

The function y = f(x) represents the relation between the set of elements in the domain of f and the set of elements in the range of f, where the variable x represents an element from the domain of the function and f(x) represents an element of the range of the function.

The first row in the table lists all the inputs to the function f. The second row lists the outputs of f corresponding to the inputs in the first row.

(a) The given statement is false because the range of f is the set of all f(x) where x is in the domain of f: {-5,-3,0,2,6,7,9,10,13}

(b) The given statement is true because, according to the table, the given input x = -3 has an output of f(x)=2; that is, f(-3) = 2.

(c) The given statement is false because the domain of f is the set of all values of x for which f(x) is defined:

{1,2,30,1,2,3,0,1}

(d) The given statement is false because, according to the table, the given input x = 0 has an output of f(x)=3; that is, f(0) = 3.

Therefore, the three statements are false and one is true.

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Answer: I believe that the answer is 8x.

Step-by-step explanation:

My explanation is that since x equals a random value, we can still add 5 and 3 to get 8.

I hope this helps!

The integral f(x, y, z) dV E as an iterated integral can be expressed in six different ways, where E is the solid bounded by the given surfaces.

To express the integral as an iterated integral, we need to determine the limits of integration for each variable.

First, we can find the limits of integration for z The plane z = 0 is the xy-plane, and the plane y + 4z = 16 can be rewritten as z = (16 - y)/4. So the limits of integration for z are 0 to (16 - y)/4.

Next, we can find the limits of integration for y  The surface y = x^2 bounds the solid from below in the y direction, and the plane y + 4z = 16 bounds the solid from above in the y direction. So the limits of integration for y are x^2 to 16 - 4z.

Finally, we can find the limits of integration for x There are no explicit surfaces that bound the solid in the x direction, so we can use the limits of integration for y to determine the limits of integration for x.

With these limits of integration, we can express the integral in six different ways over dz dy dx:

∫∫∫E f(x, y, z) dV = ∫0^(16/4) ∫x^2^(16 - 4z) ∫0^g(x, y) f(x, y, z) dz dy dx

where g(x, y) = (16 - y)/4

∫∫∫E f(x, y, z) dV = ∫x^2^4 ∫0^16-4z ∫0^g(x, y) f(x, y, z) dz dx dy

where g(x, y) = (16 - y)/4

∫∫∫E f(x, y, z) dV = ∫x^2^4 ∫0^g(x, y) ∫0^(16 - 4z) f(x, y, z) dz dy dx

where g(x, y) = 16 - 4z

∫∫∫E f(x, y, z) dV = ∫0^4 ∫x^(1/2)^4 ∫0^g(x, y) f(x, y, z) dy dx dz

where g(x, y) = (16 - 4z)

∫∫∫E f(x, y, z) dV = ∫0^(16/4) ∫0^(16 - 4z) ∫y^(1/2)^4 f(x, y, z) dy dz dx

∫∫∫E f(x, y, z) dV = ∫0^4 ∫x^(1/2)^4 ∫0^(16 - 4z) f(x, y, z) dz dy dx

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Answer: [tex]x-75\geq 420[/tex]

Step-by-step explanation:

... as it say...

Answer:

x -75 ⩾ 420

Step-by-step explanation:

we take away 75 from the value of X and compare it to 420 using the greater than or equal sign.

Answer:

15 cups

Step-by-step explanation:

So we have a ratio, butter:sugar. This ratio is given as 3:5, or 3 parts to 5 parts. Basically, every 3 cups of butter you use, you use 5 cups of sugar.

In order to calculate this, we simply need to divide the amount of butter being used by 3, and then multiply that by 5. This way, we are figuring out how much a singular "part" is in this situation, and then multiplying that by 5 for the 5 parts sugar.

9/3 = 3

3*5 = 15

Therefore, you have 15 cups of sugar.

Answer: Let's call the total number of action figures you need to complete your collection "x". Based on the information given, we know that 30 action figures is 40% of x, so we can write the equation:

30 = 0.40x

To solve for x, we'll divide both sides of the equation by 0.40:

x = 30 / 0.40

x = 75

So, the total number of action figures you need to complete your collection is 75. Since you purchase 5 action figures per week, it will take you 75 / 5 = 15 weeks to complete your collection.

Step-by-step explanation:

The equation of the cubic function is 2( x-4) (x-3) x+3)

A cubic function is a polynomial function of degree 3 and is of the form f(x) = ax3 + bx2 + cx + d, where a, b, c, and d are real numbers and a ≠ 0.

The equation of a cubic function is given as;

x³-(a+b+c) x² + ( ab+bc+ca) x + abc

where a,b,c are the root of the cubic function

a = 4, b = 3 and c= -3

a+b+c = 4+3-3 = 4

ab = 4×3 = 12

bc = -3×3 = -9

ca = -3×4 = -12

ab+bc+ca = 12-9-12 = -9

abc = 4×3×-3 = -36

therefore;

x³-( 4)x² + ( -9)x -36

x³-4x²-9x -36

therefore y = a( x-4) (x-3) x+3)

at point (2,20)

substitute x by2 and y by 20

20 = a( -2) (-1) (5)

20 = a10

a = 20/10

a= 2

therefore the equation of the cubic function is

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

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Answer: A) [tex]y=\frac{3}{7}x-2[/tex]

Step-by-step explanation:

its just the answer, and if you want explanation just say...

The population at 0 hours is 1,000, at 4 hours is 1,000,024, and at 8 hours is  1,000,016.

To calculate how the number of bacteria changes over time, let's use the function provided and replace the variable t = time.

0 hours:

Population = 10^6 + (10^4)0 -(10^3)0^2

Population = 10^6 - 10^3

Population = 10^3 or 1,000

4 hours:

Population = 10^6 + (10^4)4 -(10^3)4^2

Population= 10^6 + 40,000 - 16,000

Population= 1,000,024

8 hours:

Population = 10^6 + (10^4)8 -(10^3)8^2

Population= 10^6 + 80,000 - 64,000

Population= 1,000,016

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Step-by-step explanation:

Since the original volume is 29 and they are looking for 1/7th of that, we can multiply these two numbers

[tex](29)( \frac{1}{7} ) = 4 \frac{1}{7} psi[/tex]

The option that is a factor of the function f(x) is C.

(2x - 3)

Because it becomes zero when x = 3/2.

We know that the function f(x) has zeros at x = -1/2 and x = 3/2.

And we want to see which ones of the given expressions can be a factor of the function.

If the function becomes zero at these values, then the factors need to become zero at one of these two values.

With that in mind, we can see that the correct option is C.

(2x - 3)

when x = 3/2 we get:

(2*3/2 - 3) = (3 - 3) = 0

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Answer:

Answer is in the attached photo.

Step-by-step explanation:

The solution is in the attached photo, do take note a variable is a alphabet can be assigned to any value, while a constant is a fixed number or value.

Answers:

variable = t

constant = -7

Step-by-step explanation:

So we know that a variable is a letter while a constant is a number

in here -7 is the constant (the number) and t is the variable (the letter)

Therefore, the variable is t and the constant is -7.

Answer:

Below

Step-by-step explanation:

5000   *   2.4 x 10^-6  =

12 000 x 10^-6  g

= .012 g

Answer:

1. 32 divided by 2 is 16

2.  2 x 16 = 36

Step-by-step explanation: