Two piecewise functions are shown below. What is the value of 3h(2) + 4g(1)?

Answer:

C

Step-by-step explanation:

Answer:

- 7√10

Step-by-step explanation:

Step 1 : Take √10 common

2√10 - 5√10 - 4√10

= √10 ( 2 - 5 - 4 )

Step 2 : Subtract the numbers separately.

2 - 5 - 4

= 2 - 9

= - 7

Step 3 : Multiply √10 and - 7

√10 * - 7 = - 7√10

To find the MEAN of Natural numbers, such as  1, 2, 3, 4, 5, 6, 7, 8, 9, and 10, a + b + c3 is the sum of the three numbers a, b, and c. Therefore, 5.5 is the MEAN of the first 10 natural numbers.

Firstly The Given set of numbers Represents Natural numbers,

A natural number is an integer greater than 0. Natural numbers begin at 1 and increment to infinity: 1, 2, 3, 4, 5, etc.

Therefore, the first ten natural numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

And the mean of three numbers a, b, c is a + b + c3

Then the mean of 10 numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 is:-

⇒1+2+3+4+5+6+7+8+9+1010

Adding and dividing we get the value of the above term as,

⇒1+2+3+4+5+6+7+8+9+1010=5510=5.5

Hence, the mean of the first 10 natural numbers is 5.5.

Note: To solve this problem, you must understand that the integers greater than zero are natural numbers and that the mean of the three numbers a, b, and c equals a + b + c3. Knowing how to calculate the average number of elements and being familiar with natural numbers can help you arrive at the correct conclusion.

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Answer:

hhhhhhhhhhhhhhhh hhhhhhhhhhh

Step-by-step explanation:

hhhhhhhhh hhhhhhhhh hhhhhhh hhhhhh

The maximal number of consecutive integers by using the expression [tex]2*sqrt(n*|a|).[/tex]

Let f(x) = ax^n + bx^{n-1} + ... + z be a polynomial with integer coefficients and degree n>1. According to the theorem of Tchebychev, the maximal number of consecutive integers belonging to the sequence f(1),f(2),f(3),... is bounded by the expression 2*sqrt(n*|a|), where a is the coefficient of the highest degree term of f(x).

For example, let f(x) = 3x^3 + 4x^2 - 5. The coefficient of the highest degree term is 3, and the degree of the polynomial is 3. Therefore, the maximal number of consecutive integers belonging to the sequence f(1),f(2),f(3),... is 2*sqrt(3*|3|) = 6.

To calculate this maximal number, we can follow these steps:

Identify the degree of the polynomial, n.

Identify the coefficient of the highest degree term, a.

Calculate the maximal number of consecutive integers by using the expression 2*sqrt(n*|a|).

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Answer: Marissa divided the marked section of the wall into 3 equal parts. If she painted one of these parts blue, then the part that she painted blue is 1 out of the 3 equal parts. So, the fraction of the wall that is blue is 1/3.

Another way of understanding this is that if the wall is divided into 3 equal parts and Marissa painted 1 part, then the fraction of the wall that is painted is 1/3.

So the fraction of the whole wall that is blue is 1/3.

Step-by-step explanation:

$855.78

Interest, in this context, is the amount of money a saving account can earn over time.

Compound Interest Formula

There are 2 types of interest: simple and compound. For this question, we are going to use the compound interest formula. This formula is [tex]A = P(1+\frac{r}{n})^{nt}[/tex]. As stated in the question, A is the total balance, P is the principal, r is the interest rate, n is how often the interest is compounded, and t is time.

Variables

The values of these variables for this question are as follows:

The principal is the initial amount, and the question states that the account starts at 300 dollars.

The question says the interest rate is 14%, so we can convert this to the decimal 0.14.

If something is compounded annually, it is compounded once a year, so n must be 1.

If we want to find the balance after 8 years, we should set t equal to 8.

Solving for A

To find A, all we have to do is plug the variables into the formula.

This can be rewritten as:

Solve this to find that A ≈ 855.78. After 8 years, the balance will be $855.78.

The equation 5x + 5 = 5x - 5 has no solution because the left side of the equation (10) cannot equal the right side of the equation (-5).

No solution equation:

5x + 5 = 5x - 5

To solve this equation, we must first isolate the variable. To do this, we can subtract 5x from both sides of the equation.

5x + 5 = 5x - 5

Subtract 5x from both sides:

5 + 5 = - 5

Simplify:

10 = -5

At this point, we can see that this equation has no solution because the left side of the equation (10) cannot equal the right side of the equation (-5).

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Answer:

B

Step-by-step explanation:

14.50 / 1.75 = 8.3

26.25 / 2.5 = 10.5

3/8 * 2 = 0.75 .... 5.5 * 2 = 11 (no need to continue)

The radius of a sphere whose surface area is  324*pi cm² is:

R = 9 cm.

We know that the surface of a sphere of radius R is given by:

S = 4*pi*R^2

Where pi = 3.14

Here we know that a sphere has a surface of 324*pi cm², then we can write the equation:

S =  324*pi cm² = 4*pi*R^2

We can divide both sides by pi, so we get:

324 cm^2 = 4*R^2

Now we can solve that equation for R, we will get:

R^2=  (324 cm^2)/4 = 81cm^2

R = √(81 cm^2)

R = 9cm

The radius of the sphere is 9cm.

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The value of  expression - a² - 2bc - |c| if a = -2, b = 3, and c = -3, is 11.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.

Given:

- a² - 2bc - |c|, a = -2, b = 3, and c = -3,

Plug the values of a, b, and c as shown below,

- a² - 2bc - |c|  = -(-2)² - 2 × (3) × (-3) - |-3|

- a² - 2bc - |c|  = - 4 - 6 × (-3) - 3

- a² - 2bc - |c|  = -4 + 18 - 3

- a² - 2bc - |c|  = 18 - 7

- a² - 2bc - |c|  = 11

Thus, the value of the expression is 11.

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Null hypothesis (H0): The proportion of newsletter readers who own a Rolls Royce is greater than or equal to 0.68.

Alternative hypothesis (H1): The proportion of newsletter readers who own a Rolls Royce is less than 0.68.

In statistics, hypothesis testing is the process by which an analyst tests an assumption about a population's parameter. Using sample data, hypothesis testing is performed to examine the plausibility of a theory.

In this scenario, we can set up the null and alternative hypotheses as follows:

Null hypothesis (H0): The proportion of newsletter readers who own a Rolls Royce is greater than or equal to 0.68.

Alternative hypothesis (H1): The proportion of newsletter readers who own a Rolls Royce is less than 0.68.

In order to determine if there is sufficient evidence to support the publisher's claim, we would need to conduct a statistical test to determine if the proportion of newsletter readers who own a Rolls-Royce is significantly less than 0.68. The significance level of 0.02 is used to determine the level of evidence required to reject the null hypothesis.

If we run a test, if the p-value is below 0.02, we can reject the Null hypothesis and conclude that the evidence is sufficient to show that the proportion of newsletter readers who own a Rolls Royce is less than 0.68, and thus the publisher's claim is substantiated.

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No, It is not possible to have a complex number in the form of a + bi when b = 0.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Complex number.

It is in the form of a + ib.

Where a and b are real numbers.

Now,

If b = 0 then we can not have a complex number.

Example:

a + bi

a = 1 and b = 0

1 + 0i = 1 which is not a complex number.

In order to have a complex number a can be any real number and 0 but b  can not be a zero.

Thus,

It is not possible to have a complex number in the form of a + bi when

b = 0.

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The price of the sales tax on the elephant could be 0.75$

What is percentage ?

percentage can be defined as the product of ratio of given value and total value and hundred.

Given

he sells a stuffed elephant for $14.95,

the sales tax is 5% of the sale price .

So,

as the tax is 5% of the given value.

so we are here multiplying the given value to the 5/100

we get,

The amount of the tax could be

 = 14.95*5/100

 = 0.7475

≈ 0.75 (rounded)

Hence the  price of the sales tax on the elephant could be 0.75$

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The probability of each of your three friends having an ace is 32%.

The probability of each of your three friends having an ace is calculated using the Binomial Probability Formula. The formula is P(x) = nCr * p^x * (1-p)^(n-x). Here, n = 13 (number of cards dealt to each person) , r = 1 (number of aces you want to calculate the probability of), p = 4/52 (probability of getting an ace from a deck of 52 cards) and x = 1 (number of aces each of your three friends have).

Therefore, the probability of each of your three friends having an ace is P(x) = 13C1 * (4/52)^1 * (48/52)^(13-1) = 0.32.

This means that the probability of each of your three friends having an ace is 32%.

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Statement 1 is correct and Statement 2 is not correct.

As A, B and C represent distinct non-zero digits

For least value of x

Let A=1, B=2, C=3

The possible numbers that can be formed using 1,2,3 are 6 {using permutations}

123, 132, 213, 312, 231, 321

x is the sum of all possible 3-digit numbers formed by A, B and C without repetition so

x= 123+ 132+ 213+ 312+ 231+ 321

x=1332

So statement 1 is correct

statement 2 cannot be correct as least value of x is  4-digit so  greatest value of x cannot be a three digit number.

The 4-digit least value of x is 1332 so Statement 1 is correct and Statement cannot be correct.

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Step-by-step explanation:

y varies inversely as x=

y= k/xz

-5= k(-5)/6

k= 6

y=6/xz

y=6/5×-8

y= -3/20

The upper and lower bounds of the parameter h is found to be 0 and 1 respectively.

What is upper and lower bound of a function?

A number U serves as an upper bound for a function f, meaning that for any x, f(x) ≤ U. A number L serves as a function's lower bound, ensuring that for all x, f(x) ≥ L.

Given,

 [tex]f(h) = \frac{48-h}{48}[/tex]

where    f(h) = Percentage of battery left

              h = Hours of cell phone use

Lower Bound of parameter h,

h = 0 ( When percentage is 100%)

f(h) = [tex]\frac{48 - 0}{48}[/tex] = 1

Upper bound of parameter h,

h = 48 (When percentage is 0%)

f(h) = [tex]\frac{48-48}{48}[/tex] = 0

Therefore the upper bound of h is 0 and lower bound of h is 1.

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The locations of A' and B' are A' (0, 6) and B' (6, 0); lines f and f' are parallel.

To explain this using a formula, we can use the dilation formula. This formula states that for any point (x,y) on the original line (f), when dilated with a scale factor of k and the center of dilation is the origin (0,0), the coordinates of the point on the new line (f') would be (kx, ky).

For point A, which has coordinates (2,0) on line f, when dilated with a scale factor of 3 and the center of dilation being the origin, the coordinates of point A' on line f' would be (3 * 2, 3 * 0) = (6, 0).

Similarly, for point B, which has coordinates (0,2) on line f, when dilated with a scale factor of 3 and the center of dilation being the origin, the coordinates of point B' on line f' would be (3 * 0, 3 * 2) = (0, 6).

Since the two lines have the same slope, line f and line f' are parallel.

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Answer: HL

Step-by-step explanation:

HL because the hypotenuse leg theorem shows how a given set of right triangles are congruent if the corresponding lengths of their hypotenuse and one leg are equal.

The algebraic expression to show Jill's age will be;

Jill = 1/3 x b

Algebraic expressions are the mathematical statements that are derived when operations such as addition, subtraction, multiplication, division, etc. are operated upon on variables and constants.

There are different parts of an algebraic expression and they are; Variables - a symbol that doesn't have a fixed value is called a variable. It can take any value assigned to it.

Constants - a symbol that has a fixed numerical value is called a constant. All numbers are constants.

Terms - A term is a variable alone (or) a constant alone (or) it can be a combination of variables and constants and the operation of multiplication or division with it.

Coefficients - the numbers that are multiplying the variables are called coefficients.

Beth's age = b

Jill's age = 1/3 of Beth's age

Jill's age = 1/3 x b

Jill's age = 1/3b

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Answer:

y = [tex]\frac{2}{3}[/tex] x + 2

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 2 ) and (x₂, y₂ ) = (3, 4 )

m = [tex]\frac{4-2}{3-0}[/tex] = [tex]\frac{2}{3}[/tex]

the line crosses the y- axis at (0, 2 ) ⇒ c = 2

y = [tex]\frac{2}{3}[/tex] x + 2 ← equation of line

The diameter of the circle is 30 feet

To compute the diameter of the circle, we can use the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the hypotenuse is the diameter of the circle, and the other two sides are the radius and the distance between the chord and the center of the circle.

So, we can write the equation:

diameter^2 = radius^2 + (distance between chord and center)^2

We know the radius is half the diameter, so we can substitute that in:

diameter^2 = (diameter/2)^2 + (15)^2

And we can solve for the diameter:

diameter^2 = diameter^2/4 + 225

diameter^2 = diameter^2/4 + 225

4diameter^2 = diameter^2 + 900

3diameter^2 = 900

diameter^2 = 900/3

diameter = sqrt(900/3)

So the diameter of the circle is 30 feet.

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AAA triangles are impossible to solve further since there is nothing to show us the size.

The AAA triangle is a triangle in which all three angles are given, and the triangle is said to be similar to another triangle if any two of its three angles are equal to any two of its three angles.

Knowing only angle-angle-angle (AAA) is insufficient because it can result in triangles that are similar but not congruent.

There are four shortcuts that can be used to check whether two triangles are congruent.

You don't need to be familiar with all of the six corresponding parts, which include three angles and three sides.

When a triangle's three angles are known but not its sides, the answer is "AAA."

Since there is no information to indicate size, AAA triangles are impossible to solve further. We know their shape but not their size.

Hence, the AAA triangles are not solvable or difficult to find angles.

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A line segment is merely a portion of a line, one with definite ends and a finite length.

A line segment is merely a portion of a line, one with definite ends and a finite length. An object with only one dimension, a line has length but no width. A line is made up of several points that are endlessly stretched in the opposing directions. In a two-dimensional plane, it is specified by two points. Collinear points are described as two points that are on the same line.

An endlessly long, two-directional line is referred to as a line. It just has one, and that is length. Collinear points are those that are situated along the same path. Two points make up a line, which is written as follows with an arrowhead: AB.

O is between M and P, and N is the midpoint of MO. IF NO=3 and MP = 10, find OP.

Given the following details as:

N is between M and O.

O is between N and P .

NO=6 and NP = 8.

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Kaiser roll packet cost $1 more than the price of a pepperoni roll at Luis's store.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Given is that the graph shows the prices, in dollars, of different numbers of pepperoni rolls at Luis's store. The table shows the prices, in dollars, of different numbers of Kaiser roll packets at the same store.

The price of a Kaiser roll packet = {C1} = (48 - 24)/(8 - 4) = 24/4 = 6

The price of a Kaiser roll  = {C2} = (40 - 20)/(8 - 4) = 20/4 = 5

$6 - $5 = 1

Therefore, Kaiser roll packet cost $1 more than the price of a pepperoni roll at Luis's store.

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The number of seeds that Frank will plant, expressed in algebraic form, exists 3n + 9.

An expression that includes variables, constants, and algebraic operations is known as an algebraic expression in mathematics (addition, subtraction, etc.).

Given that n and (2n + 9) are the seeds that Frank will plant in various gardens, the total number of seeds that Frank will plant can be represented algebraically by combining the two formulas.

Like terms with the same variables are added together.

Let the equation be n + 2n + 9

simplifying the above equation, we get

3n + 9

Therefore, the number of seeds that Frank will plant, expressed in algebraic form, exists 3n + 9.

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The number of seeds that Frank will plant, expressed in algebraic form, exists 3n + 9.

An expression that includes variables, constants, and algebraic operations is known as an algebraic expression in mathematics (addition, subtraction, etc.).

Given that n and (2n + 9) are the seeds that Frank will plant in various gardens, the total number of seeds that Frank will plant can be represented algebraically by combining the two formulas.

Like terms with the same variables are added together.

Let the equation be n + 2n + 9

simplifying the above equation, we get

3n + 9

Therefore, the number of seeds that Frank will plant, expressed in algebraic form, exists 3n + 9.

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If Conan borrows $3,000 at a yearly simple interest rate of 1.6% for 2 years then he has to pay 3009.6 back.

percentage, a relative value indicating hundredth parts of any quantity.

Given that Conan borrows $3,000 at a yearly simple interest rate of 1.6% for 2 years.

A=P(1+rt)

Where, A is final amount, P is principal amount, r is rate of interest, t is time period.

P=3000, r=0.16%=0.16/100=0.0016, t=2

A=3000(1+(0.0016)2)

=3000(1+0.0032)

=3000(1.0032)

=3009.6

Hence, Canon needs to pay back 3009.6

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There is no shape with exact 3 sides and 3 right angles.

The shape with three sides is a triangle. A triangle is a polygon with three edges and three vertices. It is a basic shape in geometry and can be classified into several types based on the length of its sides and the measure of its angles. Triangles can be classified as acute, right, or obtuse, depending on the measure of their angles.

A right triangle is a triangle with one right angle (90 degrees ). But there can not be a triangle with 2 or more right angle.

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