9,
The volume of a sphere can be calculated using the formula V=²³, where r is the radius of the sphere.
43
Given that a sphere has a radius of 2 cm, calculate its volume correct to two decimal places.
V= Enter your next step here
cm³

Answer: There are a few different ways to approach this problem, but one common method is to use the complement rule, which states that the probability of an event happening is equal to 1 minus the probability of the event not happening. In this case, we want to find the probability of at least one psychologist being chosen, which is the same as 1 minus the probability of no psychologists being chosen.

To find the probability of no psychologists being chosen, we first need to calculate the total number of ways to choose 3 people from a group of 54, which is:

54 choose 3 = 54! / (3! * 51!) = 19,958

Then we need to find the number of ways to choose 3 psychiatrists from a group of 24, which is:

24 choose 3 = 24! / (3! * 21!) = 1,344

Now, we can use these values to calculate the probability of no psychologists being chosen:

P(no psychologists) = (24 choose 3) / (54 choose 3) = 1,344 / 19,958 = 0.067 or 6.7%

Finally, we can use the complement rule to find the probability of at least one psychologist being chosen:

P(at least one psychologist) = 1 - P(no psychologists) = 1 - 0.067 = 0.93 or 93%

So the probability that at least one psychologist is chosen from the conference is 93%

Step-by-step explanation:

if x=4, the value of  the expression x^2+2x is 24

An algebraic expression can be described as a mathematical expression comprising of variables, terms, coefficients, factors and constants.

Algebraic expressions are also known to comprise of some mathematical or arithmetic operations, such as;

From the information given, we have the expression as;

x² + 2x

For the value of x = 4, substitute the value of x as 4 in the expression, we get;

(4)² + 2(4)

find the square, we have

16 + 2(4)

expand the bracket

16 + 8

add the values

24

Thus, the value is 24

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Answer:Answer: $532.50

Step-by-step explanation:

564.45 = 1.06x

564.45/1.06 = x

532.50=x

Check: 532.50 × .06 = 31.95

532.50+31.95 = 564.45 True!

Answer: c. (5,2)

Step-by-step explanation:  We have two equations here and need to calculate the value of x and y.

The two equations are:

2x+5y = 20

3x - 4y = 7

Using the Substitution method,

2x=20-5y

x=(20-5y)/2

Now substitute the value of x in equation (2)

3 × [tex]\frac{20-5y}{2} - 4y = 7[/tex]

60-15y-8y = 14

60-23y=14

-23y = -46

y=2

Now put the value of y in any equation.

x = (20-10)/2

x=5          

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The equation of the exponential function in the table is

Exponential function is a type of function of the form: f(x) = a(b)^x. It is made up of  3 main parts

a = the starting or initial value

b = the base function

x = the exponents

Considering the given problem, as in the table

the starting = is f(0) = 0.2

Solving for the base

f(x) = a(b)^x at x = 1

0.6 = 0.2(b)^1

0.6 = 0.2b

b = 0.6 / 0.2

b = 3

hence the equation is f(x) = 0.2(3)ˣ

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Answer:

Step-by-step explanation:

The total number of drinks Roxanne buy is 124

Roxanne bought 7 packs of bottled water and 9 boxes of soda. There were 10 bottles of water in each pack and 6 cans of soda in each box.

Roxanne bought 7 pack of bottled water.

1 pack of water bottle contains 10 bottles of water,

Hence 7 pack of water bottle contains. [tex]$7 \times 10=70$[/tex] water bottles

Roxanne bought 9 boxes of soda, 1 box of soda contain 6 cans of soda, then 9 boxes of soda contains. [tex]$x=$[/tex] cans of soda,

Then the total number of drinks Roxanne buy[tex]$=70=1$[/tex]

The total number of bottles calculate by the Multiplication of number of packet of bottles and per packet bottles.

Therefore, the total number of drinks Roxanne buy = 124

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The inequality in standard form that describes this situation is  10x + 57y < 999.

This refers to the relationship between two values that are not of the same value.

Solving the inequality, we have:

Let x be the number of b=racelets that can be made and y be the number of necklaces that can be made. The inequality in standard form that describes the situation is:

x = the number of bracelets

y = the number of necklaces

Number of beads / bracelets =10

Number of necklaces = 57

10x + 57y < 999.

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The proportion of the individuals that spend more than $400 is 0.35 and  the percent of calls answered in less than 5 minutes is 5.3%

Probability 1

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

Mean = 384

Standard deviation = 48

x = 400

The z-score is calculated as

z = (x - Mean)/Standard deviation

So, we have

z = (400 - 384)/40

z = 0.4

The required probability is

P = P(z > 0.4)

So, we have

P = 0.345

Probability 2

Here, we have

Mean = 12.4

Standard deviation = 4.3

x = 5

The z-score is calculated as

z = (x - Mean)/Standard deviation

So, we have

z = (12.4 - 4.3)/5

z = 1.62

The required probability is

P = P(z > 1.62)

So, we have

P = 5.3%

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The ratio of AB to BC is 4.3 : 5 and the ratio of AD to DC is 2 : 2.3

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

A = (0, 4)

B = (-5, -3)

C = (5, -3)

D = (2.4, 0.8)

Next, we calculate the distance between the points using

Distance = √[(x2 - x1)² + (y2 - y1)²]

So, we have

AB = √[(0 + 5)² + (4 + 3)²] = 8.6

BC = √[(5 + 5)² + (-3 + 3)²] = 10

AD = √[(0 - 2.4)² + (4 - 0.8)²] = 4

DC = √[(2.4 - 5)² + (0.8 + 3)²] = 4.6

The ratios are then represented as

AB : BC = 8.6 : 10

AD : DC = 4 : 4.6

Simplify the ratios

AB : BC = 4.3 : 5

AD : DC = 2 : 2.3

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Answer:

Area of a trapezoid=1/2(a+b)h where a and b are the bases and h is the height.

Step-by-step explanation:

Answer:

18 cups but each gallon = 16 cups. so 1.125 gallons

Step-by-step explanation:

ratio = 1/3 salt :1 water = 1 salt : 3 water

so 6 salt :18 water

Answer:

See below

Step-by-step explanation:

Your question lacks context, but zero would be in the quotient if the dividend is 0 and the divisor is some natural number (all integers but 0).

To compare the two different numbers 12 and 23 using different sentences are :

a. Twelve is less than twenty three or twenty three is greater than twelve.

b. 12 < 23 or 23 > 12.

Choose two numbers:

Let the numbers be 12 and 23.

Two different sentence to compare the considered numbers we have,

First method is using words.

a. twelve is less than twenty three.

Twenty three is greater than twelve.

Second method is symbolic method :

b. 12 < 23

'<' symbol represents less than.

23 > 12

'>' symbol represents the greater than.

Therefore, using two different method to compare two numbers are :

a. Word method : Twelve is less than twenty three or twenty three is greater than twelve .

b. Symbolic method : 12 < 23 or 23 > 12.

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The expression to determine the distance between the lowest and the highest point is -

{x} = 14505 + |- 282|

Given is a diagram that shows several planes, lines, and points.

The correct statement with respect to line {h} is -

Line h has points on planes R, P, and T.

Therefore, line {h} has points on planes {R}, {P} and {T} is the correct alternative.

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The polynomial function that has the zeros 3 and 4 - 5i is P(x) = (x - 3)((x - 4)^2 + 25)

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

zeros 3 and 4 - 5i

The polynomial is represented as

P(x) = (x - zeros)

So, we have

P(x) = (x - 3)(x - (4 - 5i))(x - (4 + 5i))

Expand

So, we have

P(x) = (x - 3)((x - 4)^2 + 25)

Hence, the polynomial is P(x) = (x - 3)((x - 4)^2 + 25)

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Answer:

The first option (angle 2 and 5)

Step-by-step explanation:

Vertical angles are angles that are opposite of each other when two lines cross. Vertical angles are congruent, meaning that they have the same angle measure.

In this case, angle 2 and angle 5 are vertical angles. So, the measure of angle 2 is equal to the measure of angle 5. Angle 6 and angle 3 are also vertical angles. So, the measure of angle 6 is equal to the measure of angle 3.

The length of side x is √2 units. The solution has been obtained by using the trigonometry formulas.

What is trigonometry?

The study of the sides, angles, and connections of the right-angle triangle is the main goal of the field of mathematics known as "trigonometry." In order to find the unknown or missing angles or sides of a right triangle, one can apply the trigonometric formulas, functions, or identities. Angles can be expressed in radians or degrees in trigonometry. The most frequent trigonometric angles used in calculations are 0, 30, 45, 60, and 90 degrees.

We are given a right-angled triangle with hypotenuse 2units.

We know that sin theta = opposite side/hypotenuse

Also, sin 45° = 1/√2

So,

⇒sin 45° = x/2

⇒1/√2 = x/2

⇒2/√2 = x

⇒√2 = x

Hence, the length of side x is √2 units.

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The y-intercept of function f is 1.

f(x) = -3x -2 , -∞ < x < -2 = -x + 1, -2 ≤ x < 3  = 2x + 5, 3 ≤ x < ∞

For y-intercept, x =0, f(x) = -x + 1                   [∵ -2 < 0 < 3]

f(0) = -0 + 1 = 1

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are ubiquitous in mathematics and are essential for formulating physical relationships in the sciences. The modern definition of function was first given in 1837 by the German mathematician Peter Dirichlet.

This relationship is commonly symbolized as y = f(x)—which is said “f of x”—and y and x are related such that for every x, there is a unique value of y. That is, f(x) can not have more than one value for the same x. To use the language of set theory, a function relates an element x to an element f(x) in another set.

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The solution is Option B.

The rotation of the line JK around the point P by 180° will be J'K'

The measure of the amount a figure is rotated about the center of rotation is called the angle of rotation. The angle of rotation is usually measured in degrees. We specify the degree measure and direction of a rotation.

90° clockwise rotation: (x,y) becomes (y,-x)

90° counterclockwise rotation: (x,y) becomes (-y,x)

180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y)

270° clockwise rotation: (x,y) becomes (-y,x)

270° counterclockwise rotation: (x,y) becomes (y,-x)

Given data ,

Let the rotation angle be represented as A

Now , the value of A is 180°

Let the points be represented as J and K

Let the rotated point be represented as J'K'

And , when a point is rotated by and angle 180° , the x and y coordinates of the point will become their additive inverse

For a 180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y)

And , the figure which represents the coordinates of the point J' and K' is when K' is below and J' is above

Hence , the solution is Option B.

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Answer:

the slope of the line is -11/7 and the y-intercept is 8.

Step-by-step explanation:

First, we'll add 11x + 7y to both sides:

-11x - 7y + 11x + 7y = -56 + 11x + 7y

0 = -56 + 11x + 7y

Then, we'll add 56 to both sides:

0 + 56 = -56 + 11x + 7y + 56

56 = 11x + 7y

Finally, we'll divide both sides by 7:

56/7 = (11x + 7y)/7

8 = (11x + 7y)/7

Now we have the equation in slope-intercept form:

y = -(11/7)x + 8

So in this case, the slope of the line is -11/7 and the y-intercept is 8.

No, 35/24 will never be on the board because the arithmetic and harmonic means can only generate positive integers.

No, 35/24 will never be on the board because the arithmetic and harmonic means can only generate positive integers. To calculate the arithmetic mean of two numbers, one adds the two numbers and divides the sum by two. The harmonic mean of two numbers is calculated by taking the reciprocals of the two numbers and dividing their sum by two. In the case of 1 and 2, the arithmetic mean is 1.5 and the harmonic mean is 2/3. So, the numbers on the board will be changed to 1.5 and 2/3 every day. 35/24 is a fraction and cannot be generated from the arithmetic and harmonic means of 1 and 2. Therefore, it will never be on the board.

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A fraction in simplest form M = 3/4

Part A is 1/4 of the whole

Part B is 3/4 of the whole

Assuming there are no other parts,

the Whole = A + B is the denominator:

Whole = 3 + 9 = 12

Part A = 3 and Part B = 9 are numerators for each fraction.

The fractions are then:

3/12 and 9/12

Meaning:

Part A is 3/12 of the whole

Part B is 9/12 of the whole

Reducing the fractions, it is also true that:

Part A = 1/4 of the whole

Part B = 3/4 of the whole

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The range of the function will exist on all real numbers. Option D is correct.

what is the Range?

The range gives an idea of how spread out the values in a dataset are and it's a simple measure of dispersion.

The formula for range is:

Range = Maximum value - Minimum value

Given the function  f (x) = x^2 + 2x – 6,

The function of the table will also give a quadratic function of degree two.

The sum of the functions will also lead to a quadratic function and since for all input values of the function, there will be a corresponding output, hence the range of the function will exist on all real numbers.

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The function's description is accurate if (b) The graph of g(x) will ultimately surpass the graph of f. (x).

A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.

Graphs can be used to represent functions.

The correct statement that describes the function is: (b) The graph of g(x) will eventually exceed the graph of f(x).

From the graphs, we have the following highlights

The graph of g(x) is constantly increasing as the value of x increases

The graph of f(x) is on decreasing (not constantly) as the value of x increases

The above highlights mean that: the value of g(x) would exceed g(x), at some point.

Hence, the correct statement that describes the function is: (b) The graph of g(x) will eventually exceed the graph of f(x).

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Answer:

6 and 4

Step-by-step explanation:

the first number is x and the second is y , then triple x is 3x , so

3x + y = 22 → (1)

the second number y is equal to twice x , less 8 , that is 2x - 8 , so

y = 2x - 8 → (2)

solving the 2 equations simultaneously.

substitute y = 2x - 8 into (1)

3x + 2x - 8 = 22

5x - 8 = 22 ( add 8 to both sides )

5x = 30 ( divide both sides by 5 )

x = 6

substitute x = 6 into (2) for y

y = 2(6) - 8 = 12 - 8 = 4

first number is 6 and second number is 4

2 apples is equivalent to 6 bananas.

Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.

Given here; Scale1 as 20 bananas equal to 4 pineapples

Scale 2 as 2 pineapple equals 4 bananas and 2 apple

Let the weights of pineapple, bananas , apple as x,y,z respectively

Thus 20y=4x

      or x=5y

Again 2x=4y+2z

or      10y=4y+2z

          6y=2z

           z=3y

Thus 2 apples or 2z=6y that is 6 bananas

Hence, 2 apples is equivalent to 6 bananas.

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Answer:

30/20 = 6/4 = 2/3 (I hope this makes sense)

Step-by-step explanation:

U are dividing by LCM

The number of seconds in a year in scientific notation is 31,536,000 seconds or [tex]3.154 * 10 ^{7}[/tex]

In one hour [tex]60 \ sec * 60\ min = 3600 \ sec[/tex]

For one day we have to multiply [tex]3600 * 24 = 86400\ sec[/tex]

For one calendar year (365 days) = [tex]86400 * 365 = 31536000 \ sec[/tex]

It Can be written as : [tex]3.154 * 10 ^{7}[/tex]

∴ In a year, there are 31,536,000 seconds.

Numbers that are either too large or too little to be conveniently stated in decimal form can be expressed using scientific notation.

We must adhere to the following rule in order to calculate the power or exponent of 10:

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The following question may be like this:

Express the number of seconds in a year in scientific notation (1year= 365days)​

The number of seconds in a year is 31,536,000 seconds. Rounded to three significant figures, the number of seconds in a year can be written as 3.15 x 10^7 seconds in scientific notation.

Scientific notation is a way to represent numbers as a decimal multiplied by a power of 10. The decimal part is always between 1 and 10, and the power of 10 gives the number of zeros or decimal places in the original number. For example, the number of seconds in a year can be written as 31,536,000 seconds in scientific notation as 3.1536 x 10^7.

The number of seconds in a year is 31,536,000 (60 seconds x 60 minutes x 24 hours x 365 days).

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The theoretical yield of Fe₂(SO₄)³ if 20.00 g of FePO₄ reacts with an excess of Na₂SO₄ is 26.52g.

The amount of a product produced by a reaction is expressed in terms of the reaction's yield.

Given the chemical equation:

2FePO₄ + 3Na₂SO₄ → Fe₂(SO₄)₃ + 2Na₃PO₄

Theoretical molar ratios:

2 mol FePO₄  : 3 mol Na₂SO₄ : 1 mol Fe₂(SO₄)₃ : 2 mol Na₃PO₄

Convert 20.00 g of FePO₄  into a number of moles

number of moles = mass in grams / molar mass

molar mass of FePO₄  = 150.82 g/mol

Number of moles = 20.00 g / 150.82 g/mol = 0.1326 mol FePO₄

Proportionality

1 mol Fe₂(SO₄)₃                x

----------------------- =  ------------------------

2 mol FePO₄            0.1326 mol FePO₄

Solve for x:

x = (0.1326 / 2) x 1 mol Fe₂(SO₄)₃ = 0.0663 mol Fe₂(SO₄)₃

Convert 0.0663 mol Fe₂(SO₄)₃ into grams

mass in grams = number of moles x molar mass

molar mass Fe₂(SO₄)₃ = 399.88 g/mol

mass = 0.0663 mol x 399.88 g/mol = 26.51 g

Depending on the number of decimal digits used by one or other you might obtain 26.52 instead 26.51, that difference does not count.

Therefore, the theoretical yield of Fe₂(SO₄)³ is 26.52g.

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The equation for the plane through P₀ (-1, -7, 2) perpendicular to the following line. x = -1+t , y= -7-5t , z= -2t is x - 5y - 2z = 30

The plane is passing through point P₀(-1, -7, 2)

And the parametric equation of the line is:

x = -1+t , y= -7-5t , z= -2t

L: (-1, -7, -2) + t(1, -5, -2)

The required plane passes through P₀ and perpendicular to line L.

The direction vector of L is V = <1, -5, -2>.

The equation of a plane with normal vector <1, -5, -2> passing through a given point P(x₁, y₁, z₁) is

1(x - x₁) - 5(y - y₁) - 2(z - z₁) = 0

The equation of plane P passing through point P₀ (-1, -7, 2) is:

1(x - (-1)) - 5(y - (-7)) - 2(z - 2) = 0

(x + 1) - 5(y + 7) - 2(z - 2) = 0

x - 5y-2z + 1 - 35 + 4 = 0

x - 5y - 2z = 30 is the required equation of the plane

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The complete question is:

Find the equation for the plane through P₀ (-1, -7, 2) perpendicular to the following line. x = -1+t , y= -7-5t , z= -2t