Jutin broke a cell ample into 1010 batche, each weighing 8. 8\time 10^{-6}8. 8×10 −6 gram. How much did the original ample weigh? Ue cientific notation to expre your anwer

The formula of quadratic function at vertex form is  f(x) = a(x – h)² + k

The term vertex in math is referred as a point where two or more curved lines or edges meet.

Here as a consequence of this definition we know that the point where two lines meet to form an angle and the corners of polygons and polyhedral are vertices.

Here we need to identify the formula of quadratic function at vertex form

As we all know that If a parabola opens upward, then it has a lowest point.

Where as If a parabola opens downward, then it has a highest point.

Here this lowest or highest point is the vertex of the parabola.

Here we have take the parent function f(x) = x² has its vertex at the origin.

And now you can identify the vertex of other quadratic functions by analyzing the function in vertex form.

So, the vertex form of a quadratic function is written as

=> f(x) = a(x – h)² + k

Here a, h, and k are constants.

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The 2x²- 4, expression is equivalent to 2(x²-2) with the same variable and exponent we multiply with their constant value.

Distribution property: Multiplying numbers by the sum or difference is the same as multiplying each number in the sum or difference and then adding or subtracting. Example: 6(2+4)= 6(2) + 6(4)

Equivalent Expressions: Expressions are equivalent if they are equal to each other when contracted or expanded. Steps to write equivalent expression using distributive Property,

Step 1 : A list of all the elements with coefficient a

Step 2: List all the factors of constant b.

Step 3: Compare the factors identified in a and b and identify the factors they have in common.

Step 4: Choose one of the factors f such that f(ax/f + b/f). We have, f(x) = 2x² - 4 . Using the above steps,

=> 2x² - 4 = 2 × x × x - 2× 2

As we see, 2 is common factor in both

=> 2( x² - 2)

So, required expression is 2( x² - 2) .

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Complete question:

What is the equivalent of 2x² - 4?.

The range of a function is the set of all possible output values of the function. The range of f(x) = arcsin(x) is different than the range of g(x) = arccos(x) because the domain of each function is different.

The function f(x) = arcsin(x) is the inverse sine function, and its domain is the set of all real numbers between -1 and 1, inclusive. This is because the sine function has a range of [-1,1], and the inverse sine function takes the input value from the range of sine function and gives the corresponding angle in radians. So the range of arcsin(x) is [-π/2, π/2]

On the other hand, the function g(x) = arccos(x) is the inverse cosine function, and its domain is the set of all real numbers between -1 and 1, inclusive. This is because the cosine function also has a range of [-1,1], and the inverse cosine function takes the input value from the range of cosine function and gives the corresponding angle in radians. The range of arccos(x) is [0, π]

So, in summary, the difference in the range of f(x) = arcsin(x) and g(x) = arccos(x) is due to the difference in the domain of each function.

Answer:

Ok this is going to be a bit confusing, and I may have-actually nevermind.

Step-by-step explanation:

The range of a function is the set of all possible output values that the function can produce. The range of f(x) = arcsin(x) is different than the range of g(x) = arccos(x) because the domain of the two functions is different.

The domain of f(x) = arcsin(x) is -1 <= x <= 1. This means that x can only take on values between -1 and 1 inclusive. The range of f(x) = arcsin(x) is -(pi/2) <= f(x) <= (pi/2). This is because the arcsine function maps the interval [-1, 1] onto the interval [-(pi/2), (pi/2)].

On the other hand, the domain of g(x) = arccos(x) is also -1 <= x <= 1, but the range of g(x) = arccos(x) is 0 <= f(x) <= pi. This is because the arccosine function maps the interval [-1, 1] onto the interval [0, pi].

Both functions are defined for the same values of x, but the range of arcsin(x) is between -(pi/2) and (pi/2) while the range of arccos(x) is between 0 and pi. This means that the range of arcsin(x) is a subset of the range of arccos(x).

Another way to see this is that the arcsin(x) and arccos(x) are inverse functions, meaning that arcsin(x) = y is equivalent to arccos(sin(y)) = x and arccos(x) = y is equivalent to arcsin(cos(y)) = x.

Therefore the range of arcsin(x) will be the set of all possible y such that -1 <= sin(y) <= 1 and the range of arccos(x) will be the set of all possible y such that -1 <= cos(y) <= 1.

The required inequality is 3.5x > 63 oz, where x represents windows Savannah cleans.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

Let x be the number of windows Savannah cleans.

The amount of window cleaner Savannah uses can be represented by the equation:

3.5x = oz

To represent the inequality that Savannah uses more than 18 windows, we can write:

x > 18

This inequality states that the number of windows Savannah cleans (x) is greater than 18.

Combining both the equation and the inequality we can write

3.5x > 63 oz

It tells us that the amount of window cleaner Savannah uses (3.5x) is greater than 63 oz when she cleans more than 18 windows.

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Calculus is a branch of mathematics that deals with the study of rates of change and accumulation of quantities.

It has two main branches: differential calculus and integral calculus.

Differential calculus studies the rate of change of a function, also known as its derivative. It deals with concepts such as limits, derivatives and their properties and applications, such as optimization problems.

Integral calculus, on the other hand, deals with the accumulation of quantities, also known as integrals. It studies the concept of definite and indefinite integrals and their properties and applications, such as finding areas and volumes, solving differential equations and computing path length.

Calculus has a wide range of applications in various fields, such as physics, engineering, economics, and many more. It's also a fundamental tool for most mathematical modeling and scientific research.

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Answer:

On a logarithmic scale, numbers on the Y-axis don't move up in equal increments but instead each interval increases by a set factor – it's often 10 but could be a factor of 3 or 350 or 3,500, anything at all.

Step-by-step explanation:

Answer:

2/9

Step-by-step explanation:

First step is to understand the question. Brian can choose 3 different color shirts and 3 different color pants.

First part asks you to choose which list has all the different outcomes.

Second part asks you what the probability of choosing a white/gray shirt with black pants.

Third part asks you to plot the probability on the number line.

Brian 3 different shirt each can be matched with 1 of the three color pants.

Ex:

Now, repeat this with the gray and blue shirt and choose the list that has all this shirt and pant combo. (notice List2 is missing white shirt and navy pants combo)

After choosing List1, find and count the desired outcome asked in part2: choose a gray or white shirt and black pants.

There are 2 outcomes out of the total 9 outcomes or 2/9.

For part3, plot 2/9 on the number line.

Look at my attachment for more detail.

Hope this helped :)

One nitrogen atom and three hydrogen atoms combine to form the chemical compound known as ammonia, which has the formula NH3. Ammonia's molar mass is 17.031 g per mole or NH3.

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When drawing horizontal or vertical lines with a triangle, you need to use two triangles at the same time. You can draw lines at angles of 30, 45, 60, and 90 degrees by combining the two.

Additionally, the values of the side lengths of this triangle are always inversely proportional to one another. and x2 is the side length that is in opposition to the 90-degree angle. likewise, the side length that is in opposition to the 90-degree angle is 72. Additionally, the side length at the opposite end of the 45-degree angle is 2.

Tips for Remembering the 30-60-90 Triangle Rule Remembering the ratio 1 is all it takes to remember the 30-60-90 triangle rules: √3 : 2, and being aware that the longest side length is always in opposition to the largest angle (90 degrees) and the shortest side length is always in opposition to the shortest angle (30 degrees).

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The scale factor for the triangle is 8 : 1.

The first option is the correct option.

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).

Given:

A triangle with a perimeter of 24 meters was created from a triangle,

with a perimeter of 3 meters using a scale factor.

Then the scale factor,

= Actual triangle / scale triangle

= 24 / 3

= 8/1

= 8: 1

Therefore, 8: 1 is the scale factor.

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Answer:

8:1

Step-by-step explanation:

To evaluate the function p(x) = -x^5 + 11x^3 + 7 when x = 3, you need to substitute 3 for x in the function and then perform the arithmetic operations.

p(3) = -(3)^5 + 11(3)^3 + 7

p(3) = -243 + 363 + 7

p(3) = 137

So, p(3) = 137

The relationship between the x- and y-coordinates is described by a linear equation in two variables known as the equation of a line.

A line's slope and y-intercept are expressed in its slope intercept form as y = m x + c. Where the line meets the y-axis is known as the y-intercept.

y = 5 x is the equation for the given line.

Adding 0 to RHS and writing it in the slope-intercept form results in.

The three main types of linear equations are the slope-intercept form, standard form, and point-slope form.

A line's equation is written as ax + by + c = 0. Here, the variables x and y are the variables, while the constant term c is the coefficients. Slope-intercept form, point-slope form, two-point form, intercept form, and normal form are a few additional ways to determine and describe a line's equation.

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Full Question = What is the slope and the y-intercept of the equation y=5x?

Answer:

80 students

Step-by-step explanation:

To predict the number of students who received a flu vaccine if a school had 65 cases of the flu, we would substitute 65 for y in the equation of the trend line: y = -0.25x + 85.

y = -0.25x + 85

65 = -0.25x + 85

then we solve for x by isolating it on one side:

x = (y - 85) / -0.25

x = (65 - 85) / -0.25

x = -20 / -0.25

x = 80

So, if a school had 65 cases of the flu, it is predicted that 80 students received the flu vaccine.

Answer:

answer is (d) (5, -2)

Step-by-step explanation:

When a triangle is translated, each point is moved the same distance in the same direction. To translate a point right, we add the amount of units to the x-coordinate, and to translate it down, we subtract the amount of units from the y-coordinate.

So for point A, the original coordinates are (1,5) and it is translated right 4 and down 7. The new coordinates of point A' will be (1+4, 5-7) = (5,-2)

Hey there!

Answer:

[tex]Given[/tex] → [tex]\sqrt{18x^5*y}[/tex]

[tex]Solution[/tex] → [tex]3x^2\sqrt{2x*y}[/tex]

Hope this helps! If you mark Brainliest, TYSM! :D

Percentage of unemployment is 58.33 % in the total household of 60,000.

Although the abbreviations "pct.", "pct.", and "pct." are also used, the percent symbol, "%," is most commonly used. A percentage is a number with no dimensions and no standard measurement.

The English word "percentage" is derived from the Latin phrase "per centum," which means "by the hundred." Percentages are fractions with a numerator of 100. In other words, it is a relationship in which the total value is always assumed to be one hundred.

Percentage calculation is the process of determining a percentage of a whole in terms of 100. There are two ways to calculate a percentage:

Using the unitary approach

by adjusting fraction's denominator to 100.

It should be noted that when the denominator is not a factor of 100, the second technique of percentage calculation isn't applied. In these situations, we employ the unitary technique.

Total number of household is 60000

Total number of household which is unemployed is 35000

Percentage of unemployment = (35000/60000) * 100 = 58.33 %

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According to your solution of the given system of equations, the value of y is 7.

Simultaneous equations, a system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.

There are four methods for solving systems of equations: graphing, substitution, elimination, and matrices.

Given a system of equation y = 2x + 11 and 3x + 2y = 8

From equation 1 we will substitute the value of y in the form of x in equation 2

=> 3x + 2(2x + 11) = 8

=> 3x + 4x + 22 = 8

=> 7x = 8 - 22

=> 7x = -14

=> x = -2

Substitute this value in equation 1

=> y = 2* -2 +11

=> y = -4 + 11

=> y = 7

therefore,  the value of the y is 7 from your solution of the system of equations given.

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Based on the given exponential graph, the value of car will be decreased by half after 2 years.

The exponential function is a type of mathematical function that can be used to determine if anything is increasing or decreasing exponentially, such as population, money, or price.

Jonathan was reading a news story about the most recent bacterial growth study.

He had read that one bacteria had been used in an experiment. The bacterium doubled in size and had two by the end of the first hour. The number was four after the second hour.

he number of microorganisms was growing hourly. If this pattern holds, he wondered how many bacteria there will be in 100 hours. When he asked his teacher about the same thing, the concept of an exponential function was the response he received.

The value of y at x = 0 is 80,

So, the initial cost of car is 80 thousand dollars,

half the original value will be 40 thousand dollars,

Value with respect to 40 is 2 on the x - axis on the graph.

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Complete Question -

A reasonable prediction for the number of times a green or red bead will be drawn from the container of beads, after being replaced 60 times, would be 42.

A reasonable prediction for the number of times a green or red bead will be drawn from the container of beads, after being replaced 60 times, would be close to the proportion of green or red beads in the container. The container has 8 red beads and 6 green beads out of a total of 8 + 7 + 6 = 21 beads. The proportion of green or red beads is (8 + 6) / 21 = 14/21.

We can use this proportion to predict the number of times a green or red bead will be drawn from the container. By multiplying the proportion of green or red beads by the number of times the bead is replaced, we get (14/21) * 60 = 42.

In this scenario, we are using the concept of probability and proportion. The probability of drawing a green or red bead is 14/21, and by multiplying it by the number of trials (60), we get the expected number of times the green or red bead will be drawn. This concept is used in statistics and probability to make predictions based on the available data. It is important to note that this is only a prediction and actual results may vary.

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The turning point of the function in this problem is given as follows:

(-5,2).

The function for this problem is defined as follows:

[tex]f(x) = 2\sqrt[3]{x + 5} + 1[/tex]

The parent function is the cube root function, which has a turning point at (0,0).

The transformations are given as follows:

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Answer:

7r is the correct answer

Step-by-step explanation:

7 x 8 = 56

The area of hexagon is 20 square units.

polygon, in geometry, any closed curve consisting of a set of line segments connected such that no two segments cross

Hexagon is a six-sided polygon or 6-gon creating the outline of a cube.

Each square in the grid below has area 1 unit.

The total number of grids are 8×8=64 grids.

1 grid of area 1 unit.

As 20 grids are used to form the hexagon.

So the area of hexagon is 20 square units.

Hence,  the area of hexagon is 20 square units.

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Answer: 20

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

The dependent changes because of the independent. So basically it depends on the  independent variable

Answer:

The first one

Step-by-step explanation:

s is the independent variable and f is the dependent variable.

the number of host families depends on the number of students.

side of image = 3.5 inch and 5 Inch

Area = 3.5 × 5 = 17.5 inch²

Now length is Enlarge by x

new length and Breadth are (3.5+x) and (5+x)

Area of new Image =(x+3.5)(x+5)

Area of new Image = x² + 5x + 3.5x + 17.5

Area of new Image = x² + 8.5x + 17.5

i hope it's helpful

Answer:3x^2+2x

Step-by-step explanation

The amount of money that each team raised are;

Amount raised by Back Street location = $200

Amount raised by Main Street location = $250

Amount raised by Washington Street = $150

We are told that the main street location raised $50 more than the Back Street location. Thus;

m.s = b.s + 50    ------(eq 1)

The Washington Street location raised $50 more than half the amount raised at the Back Street location. Thus;

w.s = ¹/₂b.s + 50    -------(eq 2)

Total raised = $600. Thus;

m.s + b.s + ws = 600    -------(eq 3)

-----------------------------

Plug in b.s + 50 for m.s and ¹/₂b.s + 50 for w.s in eq 3 to get;

(b.s + 50) + (¹/₂b.s + 50) + b.s = 600

Solve for b.s;

b.s + ¹/₂b.s + b.s + 50 + 50 = 600

(5/2)b.s + 100 = 600

(5/2)b.s = 500

b.s = $200 (amount raised by Back Street location)

m.s = b.s + 50

= 200 + 50

= $250 (amount raised by Main Street location)

w.s = (1/2)b.s + 50

w.s = 100 + 50

w.s = $150 (amount raised by Washington Street)

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Answer: IQR=32

Step-by-step explanation:IQR=Q3-Q1

The value of 'x' = 12°

A circle is a closed polygon and a two-dimensional object where every point in the plane is equally spaced from a central point. Examples are rings, discs, wheels, bangles, coins, etc.

In a circle angle at the center will always equal 360°. There is a number of circular items that we can observe in the real world.

Here we have

(x²)°, 10x°, and (5x+36)° angles made by 3 sectors in a circle

As we know the sum of the angles at the center of a circle = 360°

=> x² + 10x + 5x+36  = 360  

=> x² + 15x  +36 = 360  

=>  x² + 15x - 324 = 0

Now factorize the above equation for the 'x' value

=> x² + 27x - 12x - 324 = 0  

=> x(x + 27) - 12(x + 27) = 0

=> (x + 27) (x - 12) = 0  

=> (x + 27) = 0     or     (x - 12) = 0             144 + 96

=> x = -27                      x = 12

Here 'x' cannot be negative  

Therefore,

The value of 'x' = 12°

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The mass of one molecule of methane is 2.658 × [tex] {10}^{-23} [/tex] and number of molecules of methane is 3.76.

Mass of one molecule of methane = mass of one carbon atom + 4×mass of one hydrogen atom

Mass of methane = 1.99 × [tex] {10}^{-23} [/tex] + 4 × 1.67 × [tex] {10}^{-24} [/tex]

Performing multiplication first

Mass of methane = 1.99 × [tex] {10}^{-23} [/tex] + 4 × 6 68 × [tex] {10}^{-24} [/tex]

Equating the exponents

Mass of methane = 1.99 × [tex] {10}^{-23} [/tex] + 0.668 × [tex] {10}^{-23} [/tex]

Performing addition

Mass of methane = 2.658 × [tex] {10}^{-23} [/tex]

Now, 2.658 × [tex] {10}^{-23} [/tex] is the weight of molecules number = 1

1 gram will have number of molecules = 1/ 2.658 × [tex] {10}^{-23} [/tex]

Number of molecules = 3.76

Thus, mass is 2.658 × [tex] {10}^{-23} [/tex] and 3.76 molecules are there.

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