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The percentage of compounds formed from this plant extract fell within two standard deviations of the mean, equal to 95.45%.

We tested an extract of a plant native to Taiwan as a possible treatment for leukemia. The amounts of collagen were found to be normally distributed with a mean = 62

standard deviation = 6.9 g/ml.

This is true for any normal distribution, regardless of the actual values of the mean and standard deviation.

The standard normal distribution is a normal distribution with mean zero and standard deviation 1. The standard normal distribution is centered around zero and the degree to which measurements deviate from the mean is represented by the standard deviation.

Therefore, the required percentage is approx. 95.45% are within 2 standard deviations of the mean 62.

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Complete question:

The extract of a plant native to Taiwan has been tested as a possible treatment for Leukemia. One of the chemical compounds produced from the plant was analyzed for a particular collagen. The collagen amount was found to be normally distributed with a mean of 62 and standard deviation of 6.9 grams per mililiter.What percentage of compounds formed from the extract of this plant fall within 2 standard deviations of the mean?

Answer:

Step-by-step explanation:

In mathematics and statistics, a bar graph is commonly employed. Bar graphs, generally referred to as bar charts, are graphic illustrations of grouped data. A bar graph is a graph that displays all of the data in the form of rectangular bars with heights proportionate to the values they represent. The graph’s bars can be depicted vertically or horizontally. The bars provide a visual representation of quantities in various categories.

Graphical Representation is a way of analyzing numerical data. It exhibits the relation between data, ideas, information, and concepts in a diagram. It is easy to understand and it is one of the most important learning strategies. It always depends on the type of information in a particular domain. There are different types of graphical representation. Some of them are as follows:

Line Graphs – A line graph or linear graph is used to display continuous data and it is useful for predicting future events over time.

Bar Graphs – Bar Graph is used to display the category of data and it compares the data using solid bars to represent the quantities.

Histograms – The graph that uses bars to represent the frequency of numerical data that are organized into intervals. Since all the intervals are equal and continuous, all the bars have the same width.

Line Plot – It shows the frequency of data on a given number line. ‘ x ‘ is placed above a number line each time when that data occurs again.

Frequency Table – The table shows the number of pieces of data that falls within the given interval.

Circle Graph – Also known as the pie chart that shows the relationships of the parts of the whole. The circle is considered 100% and the categories occupied are represented with that specific percentage like 15%, 56%, etc.

Stem and Leaf Plot – In the stem and leaf plot, the data are organized from the least value to the greatest value. The digits of the least place values from the leaves and the next place value digit from the stems.

Box and Whisker Plot – The plot diagram summarises the data by dividing it into four parts. The box and whisker show the range (spread) and the middle ( median) of the data.

Answer:

(C) −5x^3 + x + 3.

Step-by-step explanation:

To divide 15x^5 - 3x^3 - 9x^2 by -3x^2, we can follow these steps:

Divide the coefficient of the first term by the coefficient of the divisor: (-15x^5) / (-3x^2) = 5x^3.

Multiply the divisor by the quotient obtained in step 1: -3x^2 * 5x^3 = -15x^5.

Subtract the product obtained in step 2 from the dividend: 15x^5 - (-15x^5) = 30x^5.

Repeat steps 1 to 3 for the next term: (-3x^3) / (-3x^2) = x, -3x^2 * x = -3x^3, -3x^3 - (-3x^3) = 0.

Repeat steps 1 to 3 for the last term: (-9x^2) / (-3x^2) = 3, -3x^2 * 3 = -9x^2, -9x^2 - (-9x^2) = 0.

Therefore, the result of the division is:

5x^3 + 0x + 3

Simplifying the expression, we get:

5x^3 + 3

Therefore, the correct answer is (C) −5x^3 + x + 3.

Answer:

C:−5x3 + X + 3

Step-by-step explanation:

I took the test and got it right

Answer:

y = 2/3x +6  for x< -3.

y = 2/3x +1     for x> 3.

Step-by-step explanation:

Explanations are given in attachment!

Ally will have 91.148 meters of tape in all if Ally needs 90 meters of tape for a project.

What is Algebraic expression ?

An algebraic expression is a mathematical phrase that can include numbers, variables, and operators (such as addition, subtraction, multiplication, and division), as well as grouping symbols like parentheses.

Ally needs a total of 90 meters of tape for her project. She bought three rolls of tape, one with 50 meters, another with 22.86 meters, and the last one with 18.288 meters. To find the total amount of tape she has, she needs to add the length of all three rolls together.

Adding the length of the first two rolls, we get:

50 meters + 22.86 meters = 72.86 meters

Then adding the length of the third roll to the sum above, we get:

72.86 meters + 18.288 meters = 91.148 meters

Therefore, Ally will have 91.148 meters of tape in all.

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The ordered pairs in the quadrants are option A and option D:

A. A= (2, 1)

D. C = (-1, -2)

The quadrant is the area that is bounded by the point where the X and Y axes connect. The cartesian plane's two axes, the X and Y axes, intersect at a 90° angle, forming four zones surrounding the intersection that are known as quadrants.

The points are given as:

A = (2, 1)

B = (1, 2)

C = (-1, -2)

D = (-1, -2)

Now, point A is in 1st quadrant so both the points will be positive.

So, A = (2, 1) is an ordered pair.

Now, B is in 2nd quadrant, so x coordinate will be negative and y coordinate will be positive.

B = (1,2) is hence not an ordered pair.

Now, C is in 3rd quadrant, so both the points will be negative.

C = (-1, -2) is an ordered pair.

Similarly, D is in 4th quadrant and x coordinate will be positive and y coordinate will be negative.

D = (-1, -2) is not an ordered pair.

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Answer:

The answer to your problem is, The difference of the values of the first and third quartiles of the data set is 12 - 6 = 6

Step-by-step explanation:

Numbers in order:

4,5,6,6,7,8,9,9,10,10,12,12,14,15

List into two equal parts:

4,5,6,6,7,8,9 and 9,10,10,12,12,14,15

Find middle numbers:

4,5,6,6,7,8,9 and 9,10,10,12,12,14,15

Lower quartile: 6

Upper quartile: 12

Thus the answer to your problem is, The difference of the values of the first and third quartiles of the data set is 12 - 6 = 6

Step-by-step explanation:

(x+90°)=7x (vert opp angles)

x-7x=-90°

-6x/-6=-90°/-6

x=15

Answer:

n+9 = 14

Step-by-step explanation:

Let's Sean friends in grade 7 be n.

Then In grade 8, 9 persons are there.

Equation: n+9 = 14.

n = 14-9 = 5.

It should be noted that the quotient of the division is 9r^2 + 2r - 5 and the remainder is -5

In this case, to solve this polynomial division, we can use either long division or synthetic division. Here, we'll use long division:

   9r^2 + 2r - 5

        ___________________________

r - 7  | 9r^3 - 73r^2 + 64r + 37

        - 9r^3 + 63r^2

        --------------------

                 - 10r^2 + 64r

                 + 10r^2 - 70r

                 ----------------

                          -6r + 37

                          -6r + 42

                          --------

                                -5

Therefore, the quotient is 9r² + 2r - 5 and the remainder is -5. Therefore: (9r³-73r² +64r +37)÷(r-7) = 9r^2 + 2r - 5 + (-5)/(r-7).

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The element defined by the given information p = 17 n° = 20 e- = 17 is Chlorine (Cl).

An atom consists of protons, neutrons, and electrons. The atomic number of an element corresponds to the number of protons present in the nucleus of an atom. Hence, the atomic number (p) of the given element is 17. A neutral atom contains an equal number of protons and electrons.

Therefore, the number of electrons (e-) of the given element is 17 as well. The number of neutrons (n°) can be calculated as the difference between the atomic mass number (A) and the atomic number (p).

In the case of the given element, the atomic number is 17, and the atomic mass number is 37 (as chlorine has two stable isotopes of mass numbers 35 and 37). Hence, n° = 37 - 17 = 20. Therefore, the element defined by the given information p = 17 n° = 20 e- = 17 is Chlorine (Cl).

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Answer: 5654.9

Step-by-step explanation:

V=pi*r^2*h

r=10

h=18

V=pi*10^2*18

V=pi*100*18

V=pi*1800

V=5654.866776

tenths place:

V=5654.9

The coordinates of the child after 75 seconds on a carousel that revolves once every minute counter-clockwise, assuming the child entered at point (1,0), are (-0.766, -0.643).

Since the carousel revolves once around in one minute, its angular velocity is 2π/60 radians per second or π/30 radians per second.

Let's find the angle that the child has covered in 75 seconds.

angle = (angular velocity) x (time) = (π/30) x 75 = 2.5π

After 2.5π radians, the child has completed 2.5 full revolutions and is back at the starting point. Therefore, the coordinates of the child at point (1, 0) are (-0.766, -0.643).

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Answer:

The value of b will be completed when b = 24

Step-by-step explanation:

f(x) can also be determined as y.

(-6, 2)

y = 2x²+bx+74

Plug it in.

2 = 2(-6) ² + b (-6) + 74

2 = 2(36) - 6b + 74

2 = 72 - 6b + 74

2 + 6b = 72 + 74

6b = 70 + 74

6b = 144

b = 24

The correct options for the average speed of both runners are:

B: Candace ran 4 meters per second

F: Candice ran at a faster rate

The formula for slope between two coordinates is:

Slope = (y2 - y1)/(x2 - x1)

For Antonio, we take two coordinates from the table to find the average speed.

The coordinates are: (8, 29) and (12, 41)

Thus:

Average speed = (41 - 29)/(12 - 4)

= 12/8 = 1.5 m/s

For candice, we take two coordinates which are:

(10, 42) and (15, 62)

Thus:

Average Speed = (62 - 42)/(15 - 10)

= 20/5

= 4 m/s

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Answer:

It really just deleted my answer..

Solve.

4p^2 - 50 = 350

O {-100, 100}

O {-400, 100}

O {-10, 100}

Step-by-step explanation:

You're welcome.

The value of x in the similar triangle is 9 units.

The midsegment of a triangle is a line connecting the midpoints between two sides of a triangle. Therefore, the midsegment theorem states that a line segment connecting the midpoints of any two sides of a triangle is parallel to the third side of a triangle and is half of it.

Hence,

9 / 72  = 3x - 20 / 56

cross multiply

9 × 56 = 72(3x - 20)

504 = 216x  - 1440

504 + 1440 = 216x

1944 = 216x

divide both sides by 216

x = 1944 / 216

x = 9

Therefore,

x = 9

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Answer: (-3u + -3) -5

Step-by-step explanation:
Use distributive property

Answer:

4 m

Step-by-step explanation:

The formula to find the area of the triangle is:

[tex]\sf Area = \frac{1}{2} *base*height[/tex]

Given that,

Area = 32m²

Base = 16m

Height =?

Let us use the given formula to find the height of the triangle.

[tex]\sf Area = \frac{1}{2} *base*height\\\\\sf 32m^2 = \frac{1}{2} *16*h\\\\32= \frac{16h}{2} \\\\32=8h\\\\\frac{32}{8} =\frac{8h}{8} \\\\4m = height[/tex]

The value of x in the parallelogram is 10.

A parallelogram is a quadrilateral with opposite sides equal to each other and opposite sides parallel to each other.

The sum of angles in a parallelogram is 360 degrees. The parallelogram JKPQ has the following angles.

Therefore,

m∠J = 2x + 10

m∠P = 3x - 20

Hence, the opposite angles of a parallelogram are congruent.

Therefore,

m∠J  = m∠P

2x + 10 = 3x - 20

2x - 3x = -20 - 10

-3x = -30

divide both sides by -3

x = -30 / -3

x = 10

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By answering the presented question, we may conclude that Therefore, the 25th term of the arithmetic sequence is 53.

In mathematics, a sequence is an ordered list of items. Elements can be numbers, functions, or other mathematical objects. A series is commonly expressed by putting the phrases in parentheses and separating them with commas. A natural number series, for example, can be denoted as: (1, 2, 3, 4, 5, ...) Similarly, the even number series is labelled as follows: (2, 4, 6, 8, 10, ...) A series can be finite or infinite depending on whether it has a finite or infinite number of words.

To find the 25th term,

an = a1 + (n - 1)d

In this case, a1 = 5 and d = 2. Plugging these values into the formula, we get:

a25 = 5 + (25 - 1)2

a25 = 5 + 48

a25 = 53

Therefore, the 25th term of the arithmetic sequence is 53.

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To solve this problem, we can set up a system of equations to represent the given information. Let R be the number of red tiles and B be the number of blue tiles. We are trying to find the value of R, the number of red tiles.

The first piece of information we are given is that the ratio of red to blue tiles is 3:5. This can be written as:

[tex]\dfrac{\text{R}}{\text{B}} =\dfrac{3}{5}[/tex]

The second piece of information we are given is that there are 12 more blue tiles than red tiles in the box.

This can be written as:

[tex]\text{B = R}+12[/tex]

We can solve this system of equations by substituting the second equation into the first equation and solving for R.

Substituting [tex]\text{B = R}+12[/tex] into the first equation, we get:

[tex]\dfrac{\text{R}}{\text{R}}+12 =\dfrac{3}{5}[/tex]

We can then simplify this equation to get:

[tex]\text{R} = 15[/tex]

Thus, there are 15 red tiles in the box.

the required number of packages of bias binding for the tablecloth is 2.

As the rectangular tablecloth measures 73 in. by 46 in., the perimeter of the tablecloth can be calculated by the following formula:

Perimeter of the tablecloth = 2(Length + Width)= 2(73 + 46)= 2(119)= 238 inches

Therefore, the length of the bias binding required to sew around the tablecloth will be equal to the perimeter of the tablecloth. The length of the bias binding available in a single package is 13 feet, which is equal to 156 inches.Therefore, the number of packages required can be calculated as:

Number of packages of bias binding required= Length of bias binding required / Length of bias binding in a package= 238 / 156= 1.52

Therefore, 1.52 packages of bias binding will be needed for the tablecloth. However, we cannot purchase a fractional part of a package. Therefore, we need to round up the decimal to the nearest whole number. Hence, 2 packages of bias binding are required for the tablecloth.

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The probability that team A wins the best-of-three series over team B is 3/16.

If team A is the underdog and has a probability of 1/4 of winning every game it plays against team B,

The probability that it wins the best-of-three series over team B :

Let us first begin by determining the probability of team A winning two games in a row. Since each game is independent, we can use multiplication to calculate the probability of winning two games in a row:

P(Team A wins 2 in a row) = P(Team A wins Game 1) x P(Team A wins Game 2)

Using the probability given in the problem, we can substitute:

P(Team A wins 2 in a row) = (1/4) x (1/4) = 1/16

Now we must determine the probability of team A winning two games in the series. There are three ways that Team A could win the series:

Winning the first two games;

Winning the second two games;

Winning the first and third games.

Assuming that each of these scenarios is equally probable, the probability of team A winning the series is the sum of the probabilities of these scenarios:

P(Team A wins series) :

= P(Team A wins first two games) + P(Team A wins second two games) + P(Team A wins first and third games)P(Team A wins series)

= (1/16) + (1/16) + (1/16)P(Team A wins series)

= 3/16

Therefore, the probability that team A wins the best-of-three series over team B is 3/16.

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Answer:

2,525 FEET

Step-by-step explanation:

The answer of the given question based on the  exponential function is the exponential function that goes through the points (0,4) and (4,0.25) is: f(x) = 4(0.5)ˣ.

An equation is a statement that two expressions are equal. It contains an equal sign (=) which separates the two expressions, and it can include variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponents, and roots.

The general form of exponential function is:

f(x) = a(b)ˣ

where a is the initial value, b is the base, and x is the independent variable.

We can use the two given points to form a system of equations and solve for the values of a and b.

Using the point (0,4):

f(0) = a(b)⁰ = a = 4

Using the point (4,0.25):

f(4) = a(b)⁴ = 0.25

Now we can substitute a = 4 into the second equation and solve for b:

4(b)⁴ = 0.25

(b)⁴ = 0.25/4 = 1/16

b = (1/16)⁽¹/⁴⁾ = 0.5

Therefore, the exponential function that goes through the points (0,4) and (4,0.25) is: f(x) = 4(0.5)ˣ

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The terms and properties of operations that complete the statement and reasons for the equivalent expressions are;

3. Same

4.The properties of operations to write the equivalent expressions are; (-4), (-4) Distributive property

(-4), (-4), Associative property

(-4), (-3) Distributive property

5. When x = 2, and y = -5 -28·x + 12·y is -116 = -116

Equivalent expressions are expressions that have the same value for the values of the input variable.

3. The completed statement is presented as follows;

Equivalent expressions evaluate to the same value when a given set of values of x and y are substituted into both expressions.

4. The expressions in the question can be expanded to collect like terms as follows;

Expression; -28·x + 12·y

The common factor of 28 and 12 is 4, therefore, we get;

-28·x + 12·y = (4 × (-7))·x + (4 × 3)·y

To make the coefficient of the leading term positive, we get;

-28·x + 12·y = (-4 * 7)·x + (-4 * (-3))·y; Distributive property

Factoring the algebraic expression on the right, where the common factor is -4, we get;

(-4 * 7)·x + (-4 * (-3))·y = -4 × (7·x) + -4 × (-3·y);  Associative property

= -4 × ((7·x) + (-3·y));

Therefore; -28·x + 12·y = -4 × (7·x + -3·y); Distributive property

5. Evaluation of the left and right side of the expression, where; x = 2, and y = 5, we get;

-28 × 2 + 12 × -5 = -116

(-4) × ((7 × 2) + (-3 × -5)) = -4 × 29 = -116

The completed equations are therefore;

-28·x + 12·y = -4 × (7·x + -3·y)

-28 × 2 + 12 × (-5) = -4 × (7 × 2 + -3 × (-5))

-116 = -116

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Answer:

4³, 8², and 2⁶ are all equivalent to 64¹

Answer:

A, C, F

Step-by-step explanation:

A. 4 x 4 x 416 x 4= 64

C. 8 x 8 = 64

F. 2x2=4x2= 8x2=16x2=32 x 2= 64