What is the name of the segment inside the large triangle?
perpendicular bisector
altitude
median
angle bisector

Answer: A good equation would be 1.20/12 and then 0.80/12.

Step-by-step explanation: after getting the answers from both equations you can determine how much to spend on each tea to evenly spend your money on both

Answer:

y = 0.5x + 4

Step-by-step explanation:

1. Move terms to one side of the equation

0.5y - 2= 0.25x +0

     +2               +2  

__________________

0.5y = 0.25x + 2

2. Divide the coefficient of y (0.5) to both sides of the equation

[tex]\frac{0.5y}{0.5} = \frac{0.25x}{0.5} + \frac{2}{0.5}[/tex]

3. Solve and simifpy

[tex]y = 0.5x +4[/tex]

The experimenters would then plot the number of viruses per milliliter of culture on a graph over time.

This graph will show the rate of infection for each virus and the total amount of virus present in the culture at any given time. This data can then be used to compare the infectivity of the two viruses and any differences in their replication rates.

The experimenters infected cells with either virus A or virus B and then sampled the mixture at five-minute intervals. After removing the intact cells, the number of viruses per milliliter of culture was determined and plotted on a graph over time. This data can then be used to compare the infectivity of the two viruses and any differences in their replication rates.

The experimenters would then plot the number of viruses per milliliter of culture on a graph over time.

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Answer:

[tex]6 {x}^{2} + 10x[/tex]

Answer:

Step-by-step explanation:

There are 529 students standing in the assembly hall, and since there are as many students in a row as there are rows in the hall, there must be an equal number of students in each row. Therefore, each row must have 529/rows = 529/rows students in it.

Answer:

x = 5

y = -4

Step-by-step explanation:

3x+4y = -1

-2x-5y = 10

We time the first equation by 2 and the second equation by 3

6x + 8y = -2

-6x -15y = 30

-7y = 28

y = -4

Now put -4 back in for y and solve for x

3x+4(-4) = -1

3x - 16 = -1

3x = 15

x = 5

Let's check

3(5) + 4(-4) = -1

15 - 16 = -1

-1 = -1

So, x = 5 & y = -4 is the correct answer.

False. The margin of error of a confidence interval is a measure of the amount of random sampling error in a survey's results.

Error in math is defined as an incorrect result or procedure in mathematical calculations or reasoning. It can be caused by a miscalculation, a wrong formula or equation, or a misinterpreted concept or instruction. It can also be caused by a misreading or misunderstanding of data, a misapplication of a theorem or rule, or a mistake in logic. Error in math can lead to incorrect or misleading results, and can have serious implications for applications relying on mathematics, such as engineering and financial analysis.

It reflects the amount by which an estimate from a sample might differ from the true population value. The margin of error does not reflect errors from using volunteer sampling methods. Volunteer sampling is a type of non-probability sampling in which individuals volunteer to participate in the survey. The margin of error is not affected by the type of sampling method used; it is affected by the sample size, confidence level, and variability of the population.

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Answer:

x^2 +9

Step-by-step explanation:

expand and simplify

(2x-3)^2-3x(x-4)

First expand the squared term

4x^2 -6x -6x+9 -3x(x-4)

Distribute the -3x

4x^2 -6x -6x+9 -3x^2 +12x

Combine like terms

4x^2 -3x^2-6x -6x +12x+9

x^2 +9

Answer:

[tex]{x}^{2} - 12x + 21[/tex]

Step-by-step explanation:

We know that,

[tex] {(a - b)}^{2} = {a}^{2} - 2ab + {b}^{2} [/tex]

Accordingly, let us solve the sum.

[tex] {(2x - 3)}^{2} - 3x(x - 4)[/tex]

Expand and solve the brackets.

[tex]4 {x}^{2} - 12x + 9 - 3 {x}^{2} + 12[/tex]

Combine like terms.

[tex] {x}^{2} - 12x + 21[/tex]

The largest 3 digit number that is divisible by 9 and 7 is 945.

A factor is a number that divides another number, leaving no remainder. In other words, if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product because they are divisible by the product. There are two methods of finding factors: multiplication and division.

If a number is divisible by 7 and 9 it shows that 7 and 9 are factors of the number. Since the number is a three digit number, the product of 7and 9 which is 63 will also be a factor.

the highest three digit multiple of 63 is 945.

This means that 945 can be divided by 7 and 9. i.e 945/7 = 135 and 945/9 = 105

Therefore the largest three digit number that can be divisible by both 9 and 7 is 945

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Two fractions are equivalent if they represent the same decimal number. For example, the three previous fractions represent the same decimal: 0.5. 1/2 is 1 between 2, which is 0.5

The converse is:

If a number is a whole number, then it is a natural number.

The following information should be considered:

Considering the conditional:

In the case when the number is a natural number, then it is a whole number.

>If a number is not a whole number, then it is not a rational number. The converse is false. ( converse must be true)

>If a number is a rational number, then it is a whole number. The converse is false. (converse must be true)

>If a number is not a rational number, then it is a whole number. The converse is false. (hypothesis should've been "then it is not a whole number")

In the Law of Detachment, if both conditional and hypothesis are true, then the conclusion is true.

All whole numbers are rational numbers.

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One of the right triangles that are given which can be used to approximate PQ of the given triangle above is triangle labelled 3 and it's value = 9.5.

A right triangle is defined as the triangle that is has one of its angle equal to 90 degrees.

Therefore, the value of the side of the triangle PQ can be obtained using the Pythagorean formula;

c² = a² + b²

c² = PR = 7²

a² = 6.4²

b² = PQ = ?

b² = c² - a²

b² = 49+40.96

b² = 89.96

b= √ 89.96

b = 9.5.

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The vertex form is

y = (x - 1)^2 - 4.

Generally, The equation of a parabola, which is a kind of quadratic function, may be written in a particular format known as the vertex form. The equation of the parabola may be written out in vertex form as follows:

y = a(x - h)^2 + k

If the vertex of the parabola is located at (h, k), and the leading coefficient is denoted by a. If an is positive, the parabola will have its lowest point at the vertex, and if an is negative, the vertex will have its highest point.

The vertex form is important because it makes it simple to determine where the vertex of a parabola is located, and it may also be used to establish the direction in which the parabola is pointing.

The vertex form of the equation y = x^2 - 2x - 3 is

y = (x - 1)^2 - 4.

The vertex of this parabola is at the point (1, -4).

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For a set of 16 positive integers to have a mean, median, and mode all equal to 16, the numbers in the set must all be equal to 16. Therefore, the largest possible value of one of the numbers in the set is 16.

The mean, median and mode of a set of numbers are all measures of the "typical" or "central" value of the set.

The mean is the sum of all the numbers divided by the number of elements in the set, the median is the middle value when a set of numbers is arranged in order of magnitude, and the mode is the number that appears most frequently in the set.

In this case, if all the 16 integers in the set are equal to 16, then the mean, median, and mode will all be 16 as well. Since the question states that the median, mode, and mean are all equal to 16, the only way for this to be true is if all the 16 integers in the set are equal to 16. So the largest possible value of one of the numbers in the set would be 16.

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The mean as this data set has no outliers causing the mean to be skewed. option ( D )

The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set.

The median is the middle value when a data set is ordered from least to greatest.

The mode is the number that occurs most often in a data set.

Mean - Add all numbers and divide by the total number of numbers

-> 5.5

Median - When all the numbers are put in order least to greatest, the middle value (if there are two numbers, find the average of the two numbers)

-> 5.5

Mode - Number that shows up most often

-> None

I would use the mean or median to describe the typical central value because they are the same value.

Therefore, The mean as this data set has no outliers causing the mean to be skewed. option ( D )

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Answer:

Step-by-step explanation:

x: Andre's Age

(x+3): Andre's Brother's Age

(x−2): Andre's Sister's Age

3(x+3): Andre's Mom's Age

87: The Sum of All Four Ages

Answer:

B

Step-by-step explanation:

There are a total of 16 fingerboards. 4 of these are white. The probability that he will select a white fingerboard is 1/4. B represent 1/4.

The the probability of finding a white finger board is 0.25.

Probability is the measure of how likely are the chance for any event to happen.

Given is that David has a Collection of nine gray fingerboards 4 white fingerboards and 3 yellow fingerboards.

We can write the probability of finding a white finger board as -

P{white} = 4/16

P{white} = 1/4

P{white} = 0.25

Therefore, the the probability of finding a white finger board is 0.25.

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The equation helps determine the distance x on each side of the mirror O is X + 36 + x = 18 (Option 3)

This equation helps determine the distance x on each side of the mirror. The mirror is 36 inches wide, so the distance on each side of the mirror should be equal. The wall is 18 feet wide, so we add the distance on each side and the width of the mirror to find the total width of the wall.

X + 36 inches (width of the mirror) + x = 18 feet (width of the wall)

So the equation is X + 36 inches + x = 18 feet

We can convert the inches to feet by dividing it by 12, so the equation becomes X + 36/12 + x = 18

X + 3 + x = 18

This is the equation that helps determine the distance x on each side of the mirror.

Therefore, The equation helps determine the distance x on each side of the mirror O is X + 36 + x = 18 (Option 3)

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The 2x2x2 cube has 6 fully white faces.

A cube is a solid shape with six square faces. Each square face has the same side length and thus all the faces have the same size. A cube has 12 edges and 8 vertices. Each vertex refers to a corner where three edges of a cube meet.

from given conditions, a 2x2x2 cube is made of 8 small cubes of which 4 are blue and 4 are white. the surface of the cube is formed from 6 2x2 squares.

and have to arranged in such a a way that the surface has as many fully white faces (faces white no black color anywhere) as possible.

So, A 2x2x2 cube has a total of 6 faces, and since the goal is to have as many fully white faces as possible, there must be at least 1 fully white face on each of the 6 sides. hence, the 2x2x2 cube has 6 fully white faces.

Therefore, the 2x2x2 cube has 6 fully white faces.

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Thursday and Friday show a negative balance, then the answer is option c: II and II.

Overdrafts are charged when your balance is negative because it means the bank made a loan (an unexpected one) to you.

An overdraft occurs when a bank account holder withdraws more money than they have in their account. Banks typically allow account holders to spend more money than they have in their accounts, but they charge a fee or interest for doing so.

Overdraft protection is a service offered by many banks that automatically covers a certain amount of overdrafts, usually up to a certain limit, by transferring funds from a savings account or a line of credit. Banks will also charge a fee for this service.

Initial balance: $274

Day                Debit ($)     Credit ($)          Balance($)

Monday          194.62        35.45              274.00 - 194.62 + 35.45 = 114.83

Tuesday             ---             11.20              114.83 - 0 + 11.2 = 126.03

Wednesday      145.86        24.75             126.03 - 145.86 + 24.75 = 4.92

Thursday           53.35          33.80             4.92 - 53.35 + 33.8 = - 14.63

Friday                31.60          45.77            -14.63 - 31.60 + 45.77 = -0.46

Saturday           12.90          61.63            -0.46 - 12.90 + 61.63 =48.27

Thursday and Friday show a negative balance, then the answer is option c: II and II.

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The graph of the function h(x) = 7sin(x) is given by the image presented at the end of the answer.

The sine function is given as follows:

y = Asin(Bx) + C.

For which the parameters are given as follows:

From this problem, the amplitude is given as follows:

A = 7.

Hence:

As there is no phase shift, the minimum and maximum values have the x-coordinate given as follows:

As the function has no phase shift, the period is given as follows:

2π.

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Answer: The length of the radius is 13/2 m.

Step-by-step explanation:

The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle and π is pi (approximately 3.14159).

Given that C = 13πm. To find the length of the radius, we can divide both sides of the equation by 2π:

C = 2πr

13πm = 2πr

r = 13πm/2π

r=13/2 m.

The length of the radius of the circle is 6.5 m

If the circumference of the circle is C and the radius is r

Therefore, C= 2πr

According to the sum, the circumference of the circle is 13π m

Substituting that value in the equation,

13π= 2πr

=> r= 13π/ 2π

=> r= 6.5 m

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The value of R for the given expression will be 0.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is 750=1000 x (1-(1/(1.01¹³⁹)))+(R/(1.01¹⁴⁰). The expression for the R will be solved as below,

750=1000 x (1-(1/(1.01¹³⁹)))+(R/(1.01¹⁴⁰)

1000(1 - 1 / 4 + R / 4 ) = 750

1000(4 -1 + R ) / 4 = 750

1000 ( 3 + R ) = 3000

3 + R = 3

R = 3 - 3

R - 0

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The area, in square inches, of a right triangle with a 24-inch leg and a 25-inch hypotenuse is 84 cm.

The area of a right triangle of base b and height h can be calculated using the formula 1/2 × b × h and its perimeter is obtained by just adding all the sides.

Length of one side of the right triangle (p) = 24-inch

Length of the hypotenuse of the right triangle (h) = 25-inch

Therefore, we can calculate the third side (b) of the triangle by applying the Pythagorean theorem

p² + b² = h²

24² + b² = 25²

b² = 625 - 576

b² = 49

b = 7 inch

Now, the area of the right triangle will be

= 1/2 × b × h

= 1/2 × 7 × 24

= 84 inch²

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The sample size that would be required for the width of 99% is 2653.

The number of subjects involved in a sample size is referred to as the sample size in market research. A set of people chosen from the general community who are thought to be a representative sample size for that particular study is referred to as the sample size.

The following details are given:

Margin of error, E = 0.025; Significance Level, = 0.01

The proportion p is estimated to be p = 0.53.

The significance level with a critical value of 0.01 is 2.58.

The smallest sample size needed to estimate the population proportion p within the necessary margin of error is determined using the formula shown below:

n >= p*(1-p)*(zc/E)2 n = 0.53 *(1 - 0.53*)2 n = 2652.97 *(1-p)*(2.58/0.025)2

As a result, we determine that n = 2653 is the minimal sample size needed to satisfy the criteria that

n >= 2652.97 and that it must be an integer value.

Sample size is 2653.

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On solving the provided question, we can say that the relationship between the domain and range of f(x) = [tex]y = 9x + 1 = 10 + (x-1)(9)[/tex]

Domain of a function is the set of possible values that it can accept. X-values of a function like f are represented by these integers (x). A function's domain is the set of possible values on which it can be used. Set the value that the function returns after the insertion of the x value. Y = f is the definition of a function with x as the independent variable and y as the dependent variable (x). A value of x is said to be in a function's domain if it can be successfully utilised to produce a single value of y by using the value of x.

[tex]f(x) = y = 9x + 1 = 10 + (x-1)(9)\\f(1) = 9+1 = 10\\f(2) = 9(2)+1 = 19\\f(3) = 9(3)+1 = 28\\f(4) = 9(4)+1 = 37[/tex]

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The exact value of the trigonometric expression sin(x - y) is given as follows:

[tex]sin{(x - y)} = \frac{\sqrt{84} - 2\sqrt{7}}{12}[/tex]

The trigonometric expression in the context of this problem is defined as follows:

sin(x - y).

The identity used to obtain the sine of the subtraction of two angles is given as follows:

[tex]sin{(x - y)} = \sin{x}\cos{y} - \cos{x}\sin{y}[/tex]

Considering the sine of x, the cosine of x is obtained as follows:

[tex]\sin^2{x} + \cos^2{x} = 1[/tex]

[tex]\left(\frac{\sqrt{28}}{6}\right)^2 + \cos^2{x} = 1[/tex]

[tex]\frac{28}{36} + \cos^2{x} = 1[/tex]

[tex]\cos^{2}{x} = \frac{7}{9}[/tex]

[tex]\cos{x} = \frac{\sqrt{7}}{3}[/tex]

The angle y, with a tangent of [tex]\frac{1}{\sqrt{3}}[/tex], is the angle of 30º, hence the sine and cosine are given as follows:

Hence the trigonometric expression is given as follows:

[tex]\sin{(x - y)} = \sin{x}\cos{y} - \cos{x}\sin{y}[/tex]

[tex]\sin{(x - y)} = \left(\frac{\sqrt{28}}{6}\right) \times \frac{\sqrt{3}}{2} - \frac{\sqrt{7}}{3} \times \frac{1}{2}[/tex]

[tex]\sin{(x - y)} = \frac{\sqrt{84}}{12} - \frac{2\sqrt{7}}{12}[/tex]

[tex]sin{(x - y)} = \frac{\sqrt{84} - 2\sqrt{7}}{12}[/tex]

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Answer: 20 + x = y.

Step-by-step explanation:

When you deposit, you are adding onto something. Because there is no real value for x, the expression would be 20 + x = y. Also, it would be = y because it says clearly the total amount would be equal to y. and also since why has no value in this context, it would still be y.

The coin will be worth $299.23 in 11 years when increasing at the rate of 11% Option A is the correct answer.

A steady rate of expansion that is proportionate to the quantity's current size is referred to as exponential growth. In other words, a quantity expands more quickly the larger it is. The exponential function, which has the formula y = ab raised to x, can be used to mathematically represent exponential growth. Here, "a" stands for the beginning quantity or value, "b" is the growth factor or base, and "x" stands for the duration or number of growth periods. Population expansion, compound interest, and the spread of infectious illnesses are a few examples of real-world processes that show exponential growth.

The exponential growth is given by the formula:

[tex]A = P(1 + r/n)^{(nt)}[/tex]

For the given situation we have:  (P) = $115, the interest rate (r) = 11% or 0.11, and the number of years (t) = 11.

Thus,

[tex]A = $115(1 + 0.11/1)^{(1*11)}\\A = $115(1.11)^{11}[/tex]

A = $299.23

Hence, the coin will be worth $299.23 in 11 years. Option A is the correct answer.

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The probability that the hand contains 4 jacks is solved to be

0.003697

Probability is solved using the formula

= required outcome / possible outcome

The required outcome

= number of ways of picking 4 jacks * number of ways of 10 cards from 48

= ⁴C₄ * ⁴⁸C₁₀

= 1 * 6540715896

= 6540715896

The possible outcome

= number of ways of picking 14 card from possible 52 cards

= ⁵²C₁₄

= 1.768966345 * 10¹²

The probability

= required outcome / possible outcome

=  6540715896 / 1.768966345 * 10¹²

= 11 / 2975

= 0.00369747

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