This graph shows the heights of the rose plants in Mrs. Melton's garden.

Answer:

Below

Step-by-step explanation:

6^5 = x^2    

7776 = x^2      sqrt both sides

x = ± 88.18

Let's represent the number with the variable "x". According to the given property, we can write the following equation:

3(x + 4) < 7x

Now, let's solve this inequality to find the range of numbers that satisfy the property.

3x + 12 < 7x

Subtract 3x from both sides:

12 < 4x

Divide both sides by 4 (since the coefficient of x is 4):

3 < x

So, the range of numbers that satisfy the given property is x > 3.

Therefore, any number greater than 3 will satisfy the condition. For example, 4, 5, 6, 7, 8, etc.Step-by-step explanation:

The total value of the loan with quarterly compounded interest is approximately $45,288.38, while the total value of the loan with monthly compounded interest is approximately $45,634.84. The difference in total interest accrued is approximately $346.46.

Part A: To determine the total value of the loan with quarterly compounded interest, we can use the formula for compound interest:

A = P(1 + r/n)^(nt),

where:

A is the total value of the loan,

P is the principal amount (initial loan amount),

r is the interest rate (in decimal form),

n is the number of times interest is compounded per year,

and t is the number of years.

Given:

P = $20,000,

r = 9% or 0.09,

n = 4 (quarterly compounding),

t = 10 years.

Substituting the values into the formula, we have:

A = 20000(1 + 0.09/4)^(4*10).

Calculating this value, we find:

A ≈ $45,288.38.

Therefore, the total value of the loan with quarterly compounded interest is approximately $45,288.38.

Part B: To determine the total value of the loan with monthly compounded interest, we follow the same formula but with a different value for n:

n = 12 (monthly compounding).

Substituting the values into the formula, we have:

A = 20000(1 + 0.09/12)^(12*10).

Calculating this value, we find:

A ≈ $45,634.84.

Therefore, the total value of the loan with monthly compounded interest is approximately $45,634.84.

Part C: The difference between the total interest accrued on each loan can be calculated by subtracting the principal amount from the total value of each loan.

For the loan with quarterly compounding:

Total interest = Total value - Principal

Total interest = $45,288.38 - $20,000

Total interest ≈ $25,288.38.

For the loan with monthly compounding:

Total interest = Total value - Principal

Total interest = $45,634.84 - $20,000

Total interest ≈ $25,634.84.

The difference between the total interest accrued on each loan is approximately $346.46.

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Answer:

81.64

that's the answer

The largest number of people for whom she can buy tickets, is 4 people.

:: Available money = $6000

:: Cost per person = $1300

So,

No. of maximum tickets = 6000/1300 = 4.6

That is,

Only 4.6 persons can have the tickets, and since, number of persons can only be a positive integer, so we have to only take the integer part of the number and eliminate the decimal part.

Therefore, the largest number of people for whom she can buy tickets, is 4 people.

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Answer: 21

Step-by-step explanation:

We know 9x - 56 is equal to 6x + 7

So:

9x - 56 = 6x + 7

Add 56 to each side

9x = 6x + 63

Subtract 6x from each side

3x = 63

Now divide each side by 3

x = 21

The length AC in the kite is 8.7 cm.

A kite is a quadrilateral that has two pairs of consecutive equal sides and

perpendicular diagonals. Therefore, let's find the length AC in the kite.

Hence, using Pythagoras's theorem, let's find CE.

Therefore,

7² - 4² = CE²

CE = √49 - 16

CE = √33

CE = √33

Let's find AE as follows:

5²- 4² = AE²

AE = √25 - 16

AE = √9

AE = 3 units

Therefore,

AC = √33 + 3

AC = 5.74456264654 + 3

AC = 8.74456264654

AC = 8.7 units

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Answer:

yes

Step-by-step explanation:

the value of theta in the given complex expression is equal to 16°.

Given, a number. \(rcis\theta, is\) expressed by.

cis75° + cis83° + cis91°+.... + cis147°.

we have to find the value of angle in degrees.

The function cisA is a shorthand way of writing the equivalent expression cisA=cosA+i sinA

By definition: CisA=CosA+iSinA

This form simplifies complex arithmetic and allows for the study of complex analysis, as well as reduces the workload in writing the expressions.

now, we have to find the sum of the given expressions.

\(cis75+cis83+cis91+...+cis147 as, cis\theta=e^{i\theta}\)

\(e^{75i}+e^{83i}+e^{91}+....+e^{147i}\\\\e^{\frac{75\pi}{180} }+e^{\frac{83\pi}{180} }+.....+e^{\frac{147\pi}{180} }\)

on using geometric sum of the series we get,

\(Sum=\frac{e^{\frac{75i\pi}{180}}(1-e^{\frac{72i\pi}{180} ) }}{(1-e^{\frac{8i\pi}{180} })}\\ \\\theta=16\)

the value of theta of the angle be 16 degree.

the complete question is.

The number cis 75 + cis 83 + cis91 +...+ cis 147 is expressed in the form r cis(theta), where 0 <= theta < 360.

Find theta in degrees.

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Answer:

It is 603 units greater

Step-by-step explanation:

Given

See attachment for table

Average rate of change over (a,b) is calculated as:

\(Rate = \frac{f(b) - f(a)}{b-a}\)

For interval [7,9], we have:

\([a,b] = [7,9]\)

So, we have:

\(Rate = \frac{f(9) - f(7)}{9-7}\)

\(Rate = \frac{f(9) - f(7)}{2}\)

From the table:

\(f(9) = 3878\)

\(f(7) = 1852\)

So:

\(Rate = \frac{f(9) - f(7)}{2}\)

\(Rate = \frac{3878 - 1852}{2}\)

\(Rate = \frac{2026}{2}\)

\(Rate = 1013\\\)

For interval [4,6], we have:

\([a,b] = [4,6]\)

So, we have:

\(Rate = \frac{f(6) - f(4)}{6-4}\)

\(Rate = \frac{f(6) - f(4)}{2}\)

From the table:

\(f(6) = 1178\)

\(f(4) = 358\)

So:

\(Rate = \frac{f(6) - f(4)}{2}\)

\(Rate = \frac{1178 - 358}{2}\)

\(Rate = \frac{820}{2}\)

\(Rate = 410\)

Calculate the difference (d) to get how much greater their rate of change is:

\(d = 1013 - 410\)

\(d = 603\)

Answer:

603

Step-by-step explanation:

i took it

Answer:

Step-by-step explanation:

Each intercept is found by setting the other variable to zero and solving for the variable value of interest.

  2x +3y = 54

x-intercept:

  2x = 54

  x = 27

y-intercept:

  3y = 54

  y = 18

__

By definition, the intercept values are the values that satisfy the equation when the other variable is zero.

x-intercept: To score 54 points, the team would have to make 27 2-point baskets if no 3-point baskets were made.

y-intercept: To score 54 points, the team would have to make 18 3-point baskets if no 2-point baskets were made.

Answer:

Total periodic pension costs (TPPC) is equal to the contributions plus change in the pension liability during the year. Each period, the periodic pension cost is recognized in profit or loss (P&L) and/or in other comprehensive income (OCI).

The statement “For a set of decimals, the longest numeral will belong to the largest number” is false because it doesn't determine the value of a number.

In Mathematics and statistics, a numerical data can be defined as a data set that is primarily expressed in numbers only. This ultimately implies that, a numerical data refers to a data set consisting of numbers rather than words.

In Mathematics and statistics, a numeral simply refer to the symbol and numerical figure that is used for representing or denoting a numerical data (number).

For instance, by using the numerical data (numbers) 8 and 9;

8 is represented as VIII in Roman numerals while 9 is represented as IX in Roman numerals. However, the numeral VIII for 8 is longer than the numeral IX for 9, but IX for the number 9 is greater than VIII for the number 8.

In conclusion, we can logically deduce that the given statement is false.

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Complete Question:

Is the statement “For a set of decimals, the longest numeral will belong to the largest number” true or false?

The point of intersection of the medians of a triangle is called a Centriod.

A median is the line segment from the vertex of a triangle that bisects the opposite side.

Hence, option A is the answer.

Answer:

A)  Mr. Simpson's class; it has a larger median value 14.5 pencils.

Step-by-step explanation:

A box plot is a visual display of the five-number summary:

From inspection of the box plots (attached), the measures of central tendency (median) and dispersion (range and IQR) are:

Mr Johnson's class:

Mr Simpson's class:

In a box plot, the median is a measure of central tendency and tells us the location of the middle value in the dataset. It divides the data into two equal halves, with 50% of the values falling below the median and 50% above it.

The median number of pencils lost in Mr Simpson's class is greater than the median number of pencils lost in Mr Johnson's class. Therefore, Mr. Simpson's class has a larger median value.

The spread of data in a dataset can be measured using both the range and the interquartile range (IQR).

As Mr Simpson's class has a greater IQR and range than Mr Johnson's class, the data in Mr Simpson's class is more spread out than in Mr Johnson's class.

In summary, as Mr Simpson's class has a larger median 14.5 and a wider spread of data, then Mr Simpson's class lost the most pencils overall.

Step-by-step explanation:

1.

Plane with two axes as a frame of reference. - Coordinate plane

2.

The vertical number line in a coordinate plane - Y-axis

3.

The horizontal number line in a coordinate plane - X-axis

4.

A pair of numbers that are used to correspond to a point on a graph where the first number is the x-coordinate and the second number is the y-coordinate. - Ordered Pairs

5.

Where the x and y axis meet. The point (0, 0). - Origin

6.

One of the four regions into which the x and y axis separate the coordinate plane.- Quadrant

7.

An equation with two variables that makes up a straight line on a coordinate plane. - Linear Equation

8.

The vertical change in a line from one point (x1,y1) to a second point (x2, y2). - Rise

9.

The horizontal change in a line from one point (x1,y1) to a second point (x2,y2). - run

10.

The ratio of a line's rise over its run. - Slope

11.

The point where a graph crosses the x axis. - X Intercept

12.

The point where a graph crosses the y axis. - Y Intercept

13.

A linear equation in the form y = mx + b, where m is the slope and b is the y-intercept. - Slope-intercept form

14.

Lines that have the same slope and never intersect. - Parallel Lines

15.

Two lines that intersect at a 90° angle. Slopes of these lines are opposite reciprocals. - Perpendicular Lines

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Answer:

Step-by-step explanation:

Given function: f(x)=|3x-6|

To find: Vertex of the function

When we solve the given equation, 3x-6, by equating it to 0, we get

3x=6

x=2 ......(1)

Now, we will use the obtained value of x to find the value of y

To find the vertex at x=2, we will have to find the value of the y coordinate

let's assume the equation to be: 3x-6+y ......(2)

Let's solve equation (2) by equating it to 0

3x-6+y=0

Substituting equation (1), we get

3(2)-6+y=0

6-6+y=0

y=0

Therefore, we get the value of x as 2 and y as 0.

Therefore the vertex of f(x)=|3x-6| is (2,0).

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The missing term in the second pair is YUL.

To determine the relationship between the first two terms, let's analyze the given pattern: AZP : ZAR.

If we look closely, we can observe that each letter in the first term is shifted one position forward in the alphabet to form the corresponding letter in the second term.

So, applying the same pattern to the second pair (TXK), we need to shift each letter one position forward in the alphabet:

T + 1 = U

X + 1 = Y

K + 1 = L

Therefore, the missing term in the second pair is YUL.

The analogy between the pairs is that each letter in the first term is shifted one position forward in the alphabet to form the corresponding letter in the second term.

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Answer:

im taking a nap

Step-by-step explanation:

Answer:

535,095 different samples of size six that contain exactly 2 defective parts.

0.0337 = 3.37% probability that a sample contains exactly 2 defective parts.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

As the order of the parts is not important, the combinations formula is used to solve this question.

Combinations formula:

\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

How many different samples are there of size six that contain exactly 2 defective parts?

2 defective from a set of 3, and 4 non-defective from a set of 47. So

\(D = C_{3,2}*C_{47,4} = \frac{3!}{2!1!}*\frac{47!}{4!43!} = 535095\)

535,095 different samples of size six that contain exactly 2 defective parts.

What is the probability that a sample contains exactly 2 defective parts?

The total number of samples is:

\(T = C_{50,6} = \frac{50!}{6!44!} = 15890700\)

Then...

\(p = \frac{D}{T} = \frac{535095}{15890700} = 0.0337\)

0.0337 = 3.37% probability that a sample contains exactly 2 defective parts.

Answer:

11+13

Step-by-step explanation:

because of math boom

a. reflexive, symmetric, and transitive only
b. congruence and midpoint.

A segment proof is a type of proof that shows the steps used to establish the congruence or equality of two line segments. The goal of a segment proof is to provide a clear and logical argument that demonstrates why the two segments are equal or congruent.
Segment proofs typically involve using a combination of definitions, postulates, and theorems to justify each step of the argument. For example, to prove that two line segments are congruent, one might use the segment addition postulate, the definition of congruence, and the reflexive, symmetric, and transitive properties of congruence.

The appropriate matching is:

1. Segment proofs include the following definitions as justifications/reasons: ⇔ reflexive, symmetric, and transitive only

2. Segment proofs include the following as congruence of segments: ⇔ congruence and midpoint.

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Answer:

Function, function

Step-by-step explanation:

Each input corresponds to one output. Thus, by the definition of a function, both graphs represent functions

Answer:

8 nickels, 5 dimes and 7 quarters

Step-by-step explanation:

Each nickel is $0.05, each dime is $0.10 and each quarter is $0.25.

So, if we have n nickes, d dimes and q quarters, we can write the system of equations:

\(n + d + q = 20\ (eq1)\)

\(0.05n + 0.1d + 0.25q = 2.65\ (eq2)\)

\(7n + 5d + 20q = 221\ (eq3)\)

If we multiply (eq2) by 140 and (eq1) by 7, we have:

\(7n + 14d + 35q = 371\ (eq4)\)

\(7n + 7d + 7q = 140\ (eq5)\)

Now, making (eq4) - (eq3) and (eq5) - (eq3), we have:

\(9d + 15q = 150\ (eq6)\)

\(2d - 13q = -81\ (eq7)\)

Multiplying (eq7) by 4.5, we have:

\(9d - 58.5q = -364.5\ (eq8)\)

Subtracting (eq6) by (eq8), we have:

\(73.5q = 514.5\)

\(q = 7\)

Finding 'd' using (eq6), we have:

\(9d + 15*7 = 150\)

\(9d = 150 - 105\)

\(d = 5\)

Finding 'n' using (eq1), we have:

\(n + 5 + 7 = 20\)

\(n = 8\)

So we have 8 nickels, 5 dimes and 7 quarters.

Question 1:

(a) The equation representing Elaine's total parking cost is:

C = x * t

(b) So the cost of parking for a full 24 hours would be 24 times the cost per hour.

Question 2:

The given system of equations is inconsistent and has no solution.

(a) To represent Elaine's total parking cost, C, in dollars for t hours, we need to know the cost per hour. Let's assume the cost per hour is $x.

(b) If Elaine wants to park her car for a full 24 hours, we can substitute t = 24 into the equation from part (a):

C = x * 24

Question 2:

To solve the linear system:

-x - 6y = 5

x + y = 10

We can use the elimination method.

Multiply the second equation by -1 to create opposites of the x terms:

-x - 6y = 5

-x - y = -10

Add the two equations together to eliminate the x term:

(-x - 6y) + (-x - y) = 5 + (-10)

-2x - 7y = -5

Now we have a new equation:

-2x - 7y = -5

To check the answer, we can substitute the values of x and y back into the original equations:

From the second equation:

x + y = 10

Substituting y = 3 into the equation:

x + 3 = 10

x = 10 - 3

x = 7

Checking the first equation:

-x - 6y = 5

Substituting x = 7 and y = 3:

-(7) - 6(3) = 5

-7 - 18 = 5

-25 = 5

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The value of sin 3° will be;

⇒ sin 3° = 1/8 (√(3 - √5) (√3 + 1) - √ (5 + √5) (√3- 1)

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The values are,

sin 18° = √(3 - √5) / 2√2

cos 18° = √ (5 + √5) / 2√2

Now,

Find the value of sin 3° as;

⇒ sin 3° = sin (18 - 15)°

   = sin 18° cos 15° - cos 18° sin 15°

   = √(3 - √5) / 2√2 × (√3 + 1) / 2√2  - √(5 + √5) / 2√2 × (√3-1)/2√2

   = 1/8 (√(3 - √5) (√3 + 1) - √ (5 + √5) (√3- 1)

Thus, The value of sin 3° will be;

⇒ sin 3° = 1/8 (√(3 - √5) (√3 + 1) - √ (5 + √5) (√3- 1)

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Answer:

11 units

Step-by-step explanation:

-3-1 = -4 = 4

8-1=7

4+7 = 11