To win at LOTTO in one​ state, one must correctly select 7 numbers from a collection of 50 numbers​ (1 through 46​). The order in which the selection is made does not matter. How many different selections are​ possible?

The equation for the temperature  with respect to x minutes is

y(x)=  580 - 56x

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

The temperature at any  instant of time in minutes( x)  is given by

y(x)=  initial temperature  - (decrement rate * number of minutes)

=>  y(x)=  580 - 56x

The equation for the temperature  with respect to x minutes is

y(x)=  580 - 56x

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The conversion of 28 Fahrenheit to Celsius is -2.22.

To convert 28 degrees Fahrenheit (28°F) to Celsius (°C), you can use the formula:

°C = (°F - 32) x 5/9

Substituting 28 for °F in the formula, we get:

°C = (28 - 32) x 5/9

Simplifying the expression inside the parentheses and performing the arithmetic operations, we get:

°C = (-4) x 5/9

°C = -2.22

Therefore, 28°F is equal to -2.22°C (rounded to two decimal places).

Celsius and Fahrenheit are two scales used to measure temperature.

Celsius, also known as the centigrade scale, is a temperature scale where the freezing point of water is 0 degrees Celsius and the boiling point of water is 100 degrees Celsius at standard atmospheric pressure.

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Correct Question :

What is the conversion of 28 Fahrenheit to Celsius?

The volume of the empty portion of Container B is approximately 47.1 cubic feet, to the nearest tenth of a cubic foot.

The formula V = r2h, where r is the cylinder's radius and h is its height, can be used to determine a cylinder's volume.

Water in Container A has a volume of:

V A is equal to (3 ft)2(5 ft) 141.37 ft3.

This amount of water will be moved to Container B, which has a 15-foot height and a 2-foot radius. Container B contains a total of:

V B = (1.5 x 2 x 15) x 188.5 ft 3

The volume of the empty space in Container B after the water has been pumped from Container A to Container B can be estimated by deducting the volume of the water from the overall volume of Container B:

47.1 ft3 = V empty = V B - V A

As a result, to the nearest tenth of a cubic foot, the volume of Container B's empty space is roughly 47.1 cubic feet.

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Answer:

The solutions to the equation f(x) = g(x) to the nearest hundredth are x ≈ 1.76 and x ≈ 7.85.

Step-by-step explanation:

f(x) = 0.15x³ - 2x² + 7x - 3.3

g(x) = 1.5|x - 7.3|

To solve the equation, we can set the two functions equal to each other and then solve for x:

0.15x³ - 2x² + 7x - 3.3 = 1.5|x - 7.3|

We can split this equation into two cases, depending on the sign of x - 7.3:

Case 1: x - 7.3 ≥ 0

In this case, we have:

0.15x³ - 2x² + 7x - 3.3 = 1.5(x - 7.3)

0.15x³ - 2x² + 7x - 3.3 = 1.5x - 10.95

0.15x³ - 2x² + 5.5x + 7.65 = 0

We can solve this cubic equation by using numerical methods, such as the Newton-Raphson method or the bisection method. One solution to this equation is x ≈ 1.76.

Case 2: x - 7.3 < 0

In this case, we have:

0.15x³ - 2x² + 7x - 3.3 = -1.5(x - 7.3)

0.15x³ - 2x² + 7x - 3.3 = -1.5x + 10.95

0.15x³ - 2x² + 8.5x - 14.25 = 0

Again, we can solve this cubic equation by using numerical methods. One solution to this equation is x ≈ 7.85. Therefore, the solutions to the equation f(x) = g(x) to the nearest hundredth are x ≈ 1.76 and x ≈ 7.85.

Answer:

x = -4.05, x = 2.15, and x = 4.96.

Step-by-step explanation:

To find the solutions to the equation f(x) = g(x), we need to substitute the expressions for f(x) and g(x) and solve for x.

0.15x³ - 2x² + 7x - 3.3 = 1.5x - 7.3

0.15x³ - 2x² + 5.5x + 3 = 0

We can solve this equation using numerical methods, such as graphing or using a calculator, to find the solutions to two decimal places. One possible method is to use a graphing calculator and graph the function y = 0.15x³ - 2x² + 5.5x + 3, and then use the intersect function to find the x-values where the function intersects the line y = 1.5x - 7.3.

Using this method, we find that there are three solutions to the equation, to the nearest hundredth: x = -4.05, x = 2.15, and x = 4.96.

Therefore, the solutions to the equation f(x) = g(x) to the nearest hundredth are x = -4.05, x = 2.15, and x = 4.96.

The number of adults and the number of children who used the swimming pool is 102 and 304 respectively.

Linear equations involve one or more expressions including variables and constants and the highest exponent of the variable is 1.

System of linear equations involve two or more linear equations which on solving gives the intersecting point of all the solutions.

Let x be the number of adults and y be the number of children who swam on that day.

Total of 406 people swam in the swimming pool that day.

Number of adults + number of children = 406

x + y = 406

Assuming the receipts for admission totaled $609.5.

Cost per child is $1.25 and cost per adult is $2.25.

Cost for x adults and y children is $609.5.

2.25x + 1.25y = 609.5

We have to solve,

x + y = 406

2.25x + 1.25y = 609.5

Multiplying the first equation with 2.25,

2.25x + 2.25y = 913.5

Subtracting 2.25x + 1.25y = 609.5 from 2.25x + 2.25y = 913.5,

y = 304

x = 406 - 304 = 102

Hence the number of adults are 102 and the number of children are 304.

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The factored form of the polynomial 7x³ + 14x² + 3x + 6​ is ( x + 2 )( 7x² + 3 ).

Given the polynomial in the question;

7x³ + 14x² + 3x + 6​

To completely factor, we factor out the greatest common factor from each group.

First, group the first two terms and the last two terms.

( 7x³ + 14x² ) + ( 3x + 6 ​)

Now, factor out the greatest common factor from each group.

( 7x³ + 14x² ) + ( 3x + 6 ​)

7x²( x + 2 ) + ( 3x + 6 )​

7x²( x + 2 ) + 3(x + 2 )

Hence, we have;

( x + 2 )( 7x² + 3 )

Therefore, the factored form is ( x + 2 )( 7x² + 3 ).

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The solution to the given system of linear equations is: x =3, y= -4

Here we have 2 linear equations

(1) y = -7/3x + 3

(2) y = 5/3x - 9

Firstly we need to convert these equations into their simplest forms:

(1) 7/3x - y = 3

(2) -5/3x - y = -9

to calculate the value of x, we need to subtract both equations:

7/3x + 5/3x = 3 +9

12/3x = 12

4x = 12

x = 12/4

x = 3

Now, to solve for y, we need to put the value of x in the first equation

y = -7/3 ( 3) +3

y= -7 + 3

y = -4

Therefore, the solution to the system of linear equations is:

(x,y) = ( 3, -4)

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Step-by-step explanation:

Examples of like terms in math are x, 4x, -2x, and 7x. These are like terms because they all contain the same variable, x. The terms 8y2, y2, and -2y2 are like terms as well. These all contain the same variable, y, raised to the second power.

Answer:

80 degrees

Step-by-step explanation:

The sum of the interior angles of any quadrilateral is 360 degrees. Adding up the known measures gives you 95 + 123 + 62 = 280. Then you can subtract that from 360. 360 - 280 = 80. So x has to be 80 degrees.

Answer:

1) What are your options?

2) 847,200

3) 6.7 × 10^5

Step-by-step explanation: You always move the decimal until you get to the first digit after zeroes and then x 10 and the power is how many times it took to place the decimal in front of the number.

Over the interval [-3, 1], the local minimum is 0,  Over the interval [-1, 0], the local maximum is 4.39,  Over the interval [0, 3], the local minimum is -32.

By plot the function on a graphing tool and visually identify the local minimum and maximum values over the specified intervals .A function that is continuous for an interval [a,b], a is not equal to b, then there is a local maximum and minimum if:

Local maximum: f(d) > f(x), ∀ x ≠ d, a ≤ d ≤ b

Local minimum: f(c)< f(x), ∀ x ≠ to c, a≤c≤b

we can proceed to solve each question:

Over the interval [-3, 1], the local minimum is 0,

since f(-2) < f(x), ∀ x ≠ -2,-3 ≤ x ≤ -1 .

Over the interval [-1, 0], the local maximum is 4.39,

since f(-0.8) > f(x), ∀ x ≠ -0.8, -1 ≤ x ≤ -1.

Over the interval [0, 3], the local minimum is -32,

since f(-2) < f(x), ∀ x ≠ -2.0 ≤ x ≤3.

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Answer:

0

4.39

-32

Step-by-step explanation:

on edge

We can see here that determining which polygons are being described below, we have:

1. A parallelogram with congruent sides - rhombus

2. A polygon with equal sides and equal angles - equilateral polygon.

3. A quadrilateral with 1 pair of acute angles and 1 pair of obtuse angles - kite.

4. Can be classified as a parallelogram and a rhombus - rhombus.

A quadrilateral is a geometric shape that has four sides, four vertices (corners), and four angles. The sum of the angles in a quadrilateral is always 360 degrees. Some common examples of quadrilaterals include rectangles, squares, trapezoids, parallelograms, rhombuses, and kites.

5. Can be classified as a quadrilateral and a parallelogram - parallelogram.

6. Has 4 sides, 2 pairs of parallel sides, and 2 sets of congruent sides - rectangle.

7. Has only one set of parallel sides - trapezoid

8. A polygon with 3 equal sides and 3 acute angles - equilateral triangle.

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The value of x is 20 using the extension of Triangle Proportionality Theorem.

Transversal lines are lines that passes intersects the two lines on a plane in two different points.

Here given three parallel lines and two transversal lines cutting these parallel lines.

By the extension of Triangle Proportionality Theorem, we have "When two or more lines which are parallel to each other are cut by two transversals, then the parallel lines divide the transversals proportionally."

Applying the theorem here,

4x / 5x = (6x - 8) / (8x - 20)

4 / 5 = (6x - 8) / (8x - 20)

Cross multiplying,

4 (8x - 20) = 5 (6x - 8)

Using the distributive property,

32x - 80 = 30x - 40

2x = 40

x = 20

Hence the value of x is 20.

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The number of terms in the expression, 6 + 2 x - 4 y + 5 z is 4 terms.

In the expression 6 + 2x - 4y + 5z, the number of terms is four, not the number of signs. The terms in this expression are:

Each term is separated by an operator (either addition or subtraction), which is represented by a sign. Therefore, the expression contains three addition signs and one subtraction sign.

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The full question is:

How many terms are in the following expression 6 + 2 x - 4 y + 5 z

The home buyer saves $26,289 by choosing Loan A. The closest answer choice is $26,351.02.

From the question, we are to determine the amount the home buyer saves in total by choosing loan A

To calculate the savings, we need to find the total amount paid for both loans and then subtract the total paid for Loan A from the total paid for Loan B.

For Loan A:

M = $3,509.71

Total amount paid = 15 years x 12 months/year x $3,509.71/month = $631,748.20

For Loan B:

M = $3,659.86

Total amount paid = 15 years x 12 months/year x $3,659.86/month = $658,037.20

The difference between the two is:

$658,037.20 - $631,748.20 = $26,289.00

Hence, the amount the home buyer saves is $26,289

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Answer:

B. 11,427.00

Step-by-step explanation:

got it right on test

The solution to the system of linear equations y = 2x and y = x - 2 is (2, 0).

Answer:

16

Step-by-step explanation:

12-(-4)

12+4

16

This is the answer you looking for.

well, we know the points are all colinear, so the slope from the 1st to the 2nd, will be the same as from the 2nd to the 3rd, same exact slope, hell let's check what's up

[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{8}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{8}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{3}-\underset{x_1}{2}}} \implies \cfrac{ 3 }{ 1 } \implies 3[/tex]

ahaaa! that means that the slope of (3 , 8) and (-1 , y) is 3, hmmmm

[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{-1}~,~\stackrel{y_2}{y}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{y}-\stackrel{y1}{8}}}{\underset{\textit{\large run}} {\underset{x_2}{-1}-\underset{x_1}{3}}} ~~ = ~~\stackrel{\stackrel{\textit{\small slope}}{\downarrow }}{ 3 }\implies \cfrac{y-8}{-4}=3 \\\\\\ y-8=-12\implies \boxed{y=-4}[/tex]

Answer: 96

Step-by-step explanation:

Answer:

You are correct! The actual distance, in miles, between Zionsville and Lafayette is 96 miles. This is calculated by multiplying 8 inches (the distance on the map) by 12 miles (the scale of the map), which results in 96 miles.

The correct statements are (a) and (d). which are the graph is reflected over the x - axis and the the graph is shifted down 1 unit.

a. The graph is reflected over the x-axis.

This statement is true. The negative sign in front of the sine function reflects the graph of the parent function over the x-axis.

b. The frequency decreases by a factor of 1/4.

This statement is false. The coefficient in front of the x in the sine function determines the frequency of the wave. Since there is no coefficient in front of x in this case, the frequency of the wave remains the same.

c. The phase shift is 1/4 unit to the right.

This statement is false. The phase shift determines how the graph is horizontally shifted left or right. However, there is no horizontal shift in this case, so the phase shift is 0.

d. The graph is shifted down 1 unit.

This statement is true. The negative sign in front of the sine function also shifts the graph down by 1 unit.

e. The graph is reflected over the y-axis.

This statement is false. A reflection over the y-axis would require a negative sign in front of x, not in front of the sine function.

f. The frequency increases by a factor of 4.

This statement is false. As mentioned in (b), there is no change in frequency in this case.

Therefore, the correct statements are (a) and (d).

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Answer:

see photo

Step-by-step explanation:

Plato/Edmentum

The correct answer is D. Both A and B are correct, to make predictions about values of y for given x value and to determine the strength of linear association between variables.

The regression line is a statistical tool that allows us to model the relationship between two variables, usually called X (the independent variable) and Y (the dependent variable), assuming a linear relationship between them. Once the regression line has been fitted to the data, it can be used for two main purposes:

A. To make predictions about the values of Y for a given X-value: Once the regression line has been fitted, we can use it to predict the value of Y for any given X-value. This is done by plugging in the X-value into the equation of the regression line, which will give us an estimated value of Y.

B. To determine the strength of a linear association between two variables: The regression line is also a measure of the strength of the linear relationship between X and Y. Specifically, the slope of the regression line (which represents the change in Y for a unit change in X) is a measure of how much Y changes for a given change in X. The closer the slope is to zero, the weaker the linear relationship between X and Y; the farther the slope is from zero, the stronger the linear relationship between X and Y.

Therefore, both A and B are correct uses of the regression line.

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The measurement of the LM will be 42.0

The hypotenuse's square is equal to the sum of the squares of the other two sides if a triangle has a straight angle (90 degrees), according to the Pythagoras theorem. Keep in mind that BC² = AB² + AC² in the triangle ABC signifies this. Base AB, height AC, and hypotenuse BC are all used in this equation. The longest side of a right-angled triangle is its hypotenuse, it should be emphasized.

Here given in the question that one side of the wall 5 feet

So as it is a rectangular bedroom it can be split into 2 right-angled triangles.

So the hypotenuse of the triangle is 13 feet

Now using the Pythagoras theorem we can find out the length of the other wall

b² = h² -p²

given KM = 52, NL = 33

So the triangle MLN

LM = √(33²+26²) = 42.0

Hence The measurement of the LM will be 42.0

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The solution of the given equation is 1/4

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

Given equation can be rewritten as:

(1/8 -x)^(1/3) = -1/2

raising the power 3 on both the sides, we get

(1/8 -x) = (-1/2)³

(1/8 -x) = -1/8

=> x= 1/8 + 1/8 = 2/8 = 1/4

The solution of the given equation is 1/4

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The inverse of the function [tex]y=e^{x-4}[/tex] is obtained as y = log (x) + 4.

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 function is given as - [tex]y=e^{x-4}[/tex]

A function g is the inverse of the function f if for y = f(x) and x = g(y).

[tex]y=e^{x-4}[/tex]

Replace x with y.

[tex]x=e^{y-4}[/tex]

Now solve for y -

y = log (x) + 4

Therefore, the inverse is y = log (x) + 4.

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Find the inverse of [tex]y=e^{x-4}[/tex].

Sections taken through the narrow width of an entire building are known as transverse sections.

A building is an enclosed structure with a roof and walls standing more or less permanently in one place, such as a house or factory.

Given is a structural analysis blank statement as -

"Sections taken through the narrow width of an entire building are known as __________ sections.

Sections taken through the narrow width of an entire building are known as transverse sections. Those through the long dimension are known as longitudinal sections.

Therefore, Sections taken through the narrow width of an entire building are known as transverse sections.

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Sure! A table of values for f(x) = log base 8 of x is shown below:

x) f(x)

1) 0

2) 1/3

3) 0.54

4) 0.67

5)0.79

6)0.89

7) 0.97

8) 1

9) 1.10

10) 1.18

A logarithmic function is a type of mathematical function that involves the use of logarithms. Logarithms are a way of expressing numbers in terms of exponents, and logarithmic functions are functions that involve the logarithm of one or more variables.

The general form of a logarithmic function is:

f(x) = log_b(x)

where b is the base of the logarithm, and x is the argument of the logarithm.

Logarithmic functions have several important properties. One of the main properties is that they can be used to convert between exponential and logarithmic forms of equations. For example, the equation[tex]2^3[/tex] = 8 can be written in a logarithmic form as log_2(8) = 3.

Logarithmic functions are also used in many applications in science, engineering, and finance. In science, logarithmic functions are used to describe the behavior of phenomena that exhibit exponential growth or decay, such as radioactive decay or population growth. In finance, logarithmic functions are used to calculate compound interest and to model the growth of investments over time.

The graph of a logarithmic function is a curve that approaches but never touches the x-axis as the x approaches zero. The shape of the curve depends on the base of the logarithm, and it becomes steeper as the base gets larger. The inverse function of a logarithmic function is an exponential function.

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The angle measures of the triangle are  45°,45°, and 90°.

What is the angle measure?

When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.

Here, we have

Given, the triangle is a right-angle triangle.

And the sides are 7√3, 14√3, 21.

Sides are a multiple of 7.

So, divide each side by 7.

We get the sides  √3, 2√3, 3.

In a 45°−45°−90° triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is √3 times the length of the shorter leg.

Hence, the angle measures of the triangle are 45°, 45° and 90°

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The 1.2 meter is 3.93701 feet.

The 1 meter is  3.28084 feet.

1.2 meter = 1.2*3.28084=3.93701

Since 1983, the meter has been internationally defined as the length of the path traveled by light in a vacuum in 1/299,792,

58 seconds. This definition can be applied easily and precisely with modern techniques, and the speed of light is considered a universal constant, making it an ideal  basis for a standard of length.

foot, plural of feet, measured by a number of  ancient, medieval and modern linear measurements (usually 25–3

cm) based on the length of a human foot, used exclusively in English-speaking countries, where it usually consists of 12 inches. , or a third of a yard.

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The area of the shaded part in the circle will be 10840.99 ft².

The circumference = 2 * pi * r = 221.056

Use this fact to find r

2*pi*r =  221.056

Divide by pi

2*r =  221.056 / 3.141

2*r =  70.378      

Divide by 2

r = 35.19

Now that you have the radius of the inner circle, use it to find the area.

Area = pi * r^2

Area = 3888.37

Now we need the radius of the outer circle

r = 35.19 + 33.3

r = 68.49

Find the area of the other circle

Area = pi * 68.49^2

Area = 14729.36

Finally the area of the shaded region is the area of the large circle - the area of the small circle

Area of the shaded area = 14729.36- 3888.37

Area of the shaded area = 10840.99 to the nearest hundredth.

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