Antonio is researching the growth of E. coli bacteria cells. The population of cells present at each hour in the table in the chart below. If P represents the size of the population at any time (t), what is the domain in the context of the problem situation?

The missing length of the geometric system of right triangles is equal to 15.833 centimeters.

Herein we find the case of a geometric system formed by ten right triangles, whose missing length can be found by means Pythagorean theorem and trigonometric functions, whose definitions are shown below:

Pythagorean theorem

r = √(x² + y²)

Trigonometric function

cos θ = x / r

Where:

Now we proceed to determine the missing length:

First triangle:

x = 8 / cos 28°

x = 9.061

x' = 9.061 - 2.5

x' = 6.561

Second triangle

x = (6.561 + 3.6) · cos 11°

x = 9.974

x' = 9.974 - 2

x' = 7.974

Third triangle

x = √[(7.974 + 2.9)² - 3.8²]

x = 10.188

x' = 10.188 - 1

x' = 9.188

Fourth triangle

x = (9.188 + 3.2) · cos 43°

x = 9.060

x' = 9.060 - 1

x' = 8.060

Fifth triangle

x = (8.060 + 1) / cos 30°

x = 10.462

Sixth triangle

x = (10.462 + 3.2 + 1.9) · cos 19°

x = 14.714

Seventh triangle

x = (14.714 - 4.8 - 1.1) / cos 46°

x = 12.688

Eighth triangle

x = √[(12.688 + 1.7)² + 3.2²]

x = 14.740

Ninth triangle

x = (14.740 - 2.73) · cos 22°

x = 11.135

x' = 11.135 - 2.24

x' = 8.895

Tenth triangle

x = (8.895 + 6.9) / cos 4°

x = 15.833

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Answer: the first question answer is 16.03 ft

the answer for number two is here too hand the way to get this answer

answer: Elijah is  standing from the base of the monument 159.14 feet

Step-by-step explanation:

see the attached figure to better understand the problem

In the right triangle ABC

----> by TOA (opposite side divided by the adjacent side)

substitute the given values

solve for AC

therefore

Elijah is  standing from the base of the monument 159.14 feet

Answer: Elijah is standing from the base of the monument - 1

And the answer for number 3 is 850.9 feet

The two rectangles are not similar because the scale factor is not the same.

Two objects are said to be comparable if they have the same shape. Therefore, two figures are said to be comparable in mathematics if they share the same shapes, lines, or angles.

If two figures have three sides similar then they will be similar by side-by-side property which is written as SSS.

Given dimension of the rectangle is 2 cm and 4 cm. The dimension of the second rectangle is 6 cm and 4 cm.

The scale factor for the two sides should be,

6 / 2 = 3

4 / 4 = 1

Since the scale factor is not constant so the rectangles are not similar.

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Measures of angles, x = 93° and y = 97°

A cyclic quadrilateral is a quadrilateral with all four vertices on a circle. Also called an inscribed quadrilateral. A circle consisting of all vertices around a polygon is known as the circumcircle.

Given,

Interior angles of quadrilateral

= x° , y° , 83°

Arc angles on the center of circumcircle are 64° and 122°.

angle made by chord on the center is twice to the angle made on the circumference of the circle

64° + 122° = 2x

186° = 2x

x = 186°/2

x = 93°

In cyclic quadrilateral,

Sum of opposite interior angles is 180°

y + 83° = 180°

y = 180° - 83°

y = 97°

Hence, measure of angles x and y are 93° and 97° respectively.

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You can make 8 headbands with all the fabric, which is 12 feet of blue fabric and 4 feet of yellow fabric.

To find out how many headbands you can make with all the fabric, you need to convert the fabric measurements to the same unit and then divide by the amount needed for one headband.

First, convert the 12 feet of blue fabric to yards:
12 feet ÷ 3 = 4 yards

Next, convert the 4 feet of yellow fabric to yards:
4 feet ÷ 3 = 1.333 yards

Now, add the two amounts of fabric together:
4 yards + 1.333 yards = 5.333 yards

Finally, divide the total amount of fabric by the amount needed for one headband:
5.333 yards ÷ 2/3 yard = 8 headbands

Therefore, you can make 8 headbands with all the fabric.

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Answer: 0.75j or 3/4j

Step-by-step explanation:

Using a standard normal distribution table, we can find the closest value to 0.99, which is 2.33. Therefore, the z-score for a 98% confidence interval is 2.33.

To calculate the z-score for a 98% confidence interval, we can use a standard normal distribution table or a calculator with a built-in z-score calculator. To calculate the z-score for a 98% confidence interval, we can use the following formula:

z = invNorm(1 - (1 - confidence level) / 2)

Where "invNorm" is the inverse normal distribution function, and "confidence level" is the level of confidence expressed as a decimal. For a 98% confidence level, we have:

z = invNorm(1 - (1 - 0.98) / 2)

z = invNorm(0.99)

Using the table, we can find the z-score corresponding to a cumulative area of 0.98 by looking up the closest value to 0.98 in the table.

invNorm(0.98) = 2.33.

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The simplified form of the given expression 4.03x + 10x⁶, is [tex]x(4.03x + 10x^5)[/tex]

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation.

Given that an expression 4.03x + 10x⁶

We need to simplify it,

4.03x + 10x⁶

Applying the exponent rule: [tex]a^{b+c}=a^ba^c[/tex]

[tex]x^6=x^5x[/tex]

[tex]=4.03x+10x^5x[/tex]

Factor out common term x,

[tex]=x\left(4.03+10x^5\right)[/tex]

Hence, the simplified form of the given expression 4.03x + 10x⁶, is [tex]x(4.03x + 10x^5)[/tex]

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Answer:

65 m²

Step-by-step explanation:

area of parallelogram = base × height

base = AB = 3 m + 10 m = 13 m

height = 5m

area = 13 m × 5 m

area = 65 m²

(0, 6) and (1, 2) is the solutions to the given system of equation. Option A is correct.

Given the following system of equation

y = x^2 - 5x + 6

y = -4x + 6

Equating both equations, we will have:

x^2 - 5x + 6 = -4x + 6

Collect the like terms

x^2 - 5x + 6+4x - 6 = 0

x^2 - x = 0

x^2 = x

x = 0, 1

If x = 0

y = -4(0) + 6

y = 6

One of the solution is (0, 6)

If x = 1

y = -4(1) + 6

y = 2

The other solution will be (1, 2)

The solution to the given system of equation will be (0, 6) and (1, 2).

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Answer:

s = 9

Step-by-step explanation:

A = s^2

81 = s^2

√81 = s

s = 9

Multiply the denominators and numerators together. GCD(12, 5) = 1, keeping the result fraction to the lowest denominator feasible. To put it another way, six times two fifths equals twelve fifths.

For instance, the fraction bar is the line that separates the digits 4 and 5, and 45 is a fraction. Thus, the numerator is the amount above the fraction bar, and the denominator is the number below the fraction bar. The denominator, or number of pieces out of the total, is represented by a numerator.

The top number in a fraction is referred to as the numerator, while the bottom value is referred to as the denominator. 4/5, for instance, is a fraction. In this case, the numerator is 4 and the denominator is 5.

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Displacement is the length of the straight line drawn from an object’s initial position to the object’s final position

The term "displacement" refers to a change in an object's position. It is a vector quantity with a magnitude and direction. The symbol for it is an arrow pointing from the initial position to the ending position. For instance, if an object shifts from position A to position B, its position changes.

If an object moves with respect to a reference frame, such as when a passenger moves to the back of an airplane or a professor moves to the right with respect to a whiteboard, the object's position changes. This change in location is described as displacement.

The displacement is the shortest distance between an object's initial and final positions. Displacement is a vector. It is visualized as an arrow that points from the initial position to the final position, indicating that it has both a direction and a magnitude.

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Answer:

19/3 (6 1/3)

Step-by-step explanation:

If we divide (1/3) liter of water into four equal cups each cup will (1/12) liter.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, A bottle contains 1/3 liter of water.

Now, If we divide this (1/3) liters of water into 4 equal cups, Each cup will have (1/3)÷4 liters,

= (1/3)×(1/4) liters.

= (1/12) liters.

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There are 168 hours in a week. Therefore, there are approximately 0.536 weeks in 90 hours.

Time conversion is the process of converting a given amount of time from one unit of measurement to another. It involves using conversion factors to change the numerical value of the time while keeping the duration constant.

For example, converting a duration from hours to minutes involves using a conversion factor of 60 minutes per hour. To convert, you multiply the number of hours by 60 to get the equivalent duration in minutes.

To get this answer, you can divide the number of hours (90) by the total number of hours in a week (168):

90 hours ÷ 168 hours/week = 0.536 weeks (rounded to three decimal places)

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The solutions of  y > 3x - 4 are (-5,-3), (-3,4), (0,0) and (0, -4)

A relationship between two expressions or values that are not equal to each other is called 'inequality.

The given equation of the graph is y>3x-4.

We have to check each of the ordered pair is a solution or not.

(-5, -3)

Plug in the values ion inequality

-3>3(-5)-4

-3>-15-4

-3>-19

(-5, -3) is the solution of  y>3x-4.

(-3, 4)

4>-9-4

4>-13, So (-3, 4) is the solution of  y>3x-4.

(-4, 0)

0>-12-4

0>-16, So (-4, 0) is the solution of  y>3x-4.

(0, 0)

0>-4 So (0, 0) is the solution of  y>3x-4.

(1, -7)

-7>-3-4 So (1, -7) is not the solution of  y>3x-4.

(1, 1)

1>3-4

1>-1, so (1, 1) is not the solution of  y>3x-4.

(2, 2)

2>6-4

2>2, so (2, 2) is not the solution of  y>3x-4.

(4, 2)

2>12-4, so (4, 2) is not the solution of  y>3x-4.

Hence, (-5,-3), (-3,4) , (0,0) and (0, -4) are the solutions of  y > 3x - 4.

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Answer:

Step-by-step explanation:6

Multiple regression analysis analyze more than one dependent variable at a time and multicollinearity occurs when the X variables are highly correlated with the Y variable in multiple regression are false. Correct option is D.

The statement (A) that "Multiple regression analysis allows you to analyze more than one dependent (Y) variable at a time" is false. In multiple regression, there is only one dependent variable (Y) that is being predicted by a combination of independent variables (X).

The statement (B) that "Multicollinearity occurs when the X variables are highly correlated with the Y variable in multiple regression" is also false.

Multicollinearity occurs when two or more independent variables (X) are highly correlated with each other, which can cause problems in accurately estimating the effect of each independent variable on the dependent variable.

The statement (C) that "Multicollinearity occurs when two or more of the X variables are highly correlated with one another" is true.

Therefore, the correct answer is (D) "Both A and B are false statements."

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Number of lemon cupcakes in  next 20 cupcakes sold is 1.33.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Given;

carrot cupcakes 8 pumpkin cupcakes 1 lemon cupcakes 6

Now,

For 20 cupcakes

Let the number of lemon cupcakes be x

8+6+1=1lemon

15=1lemon

20=1*20/15lemon

=4/3lemon

Therefore, by algebra the answer will be 1.33lemons

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Answer: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192

Step-by-step explanation:

To find all the factors of a number, multiply all the prime factors of the number in all possible solutions.

Answer:

Surface Area is the space occupied by a two-dimensional flat surface is called the area.

Total surface area is the area including the base(s) and curved part(s).

Calculating Surface Area:

To find the surface area of a shape, we need to find the measurement (in this case, centimeters) of each face/side and add them together.

Volume:

The amount of space an object/3D shape occupies. (Ex: A circle does not have volume, a sphere, however, does.)

Calculating Volume:

Volume = the length times the width times the height. (Volume = length x width x height)

The equation and value of x , the distance of 1 lap around the path at the park is 4.8x + 1.2 = 3.6.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

Florian ran 1.2 miles and walked 4.8 laps around the path at the park for a total distance of 3.6 miles.

As, we know the number of them (4.8) would be multiplied by the variable (x). We also know that 1.2 is the constant.

So, the equation can be framed as

4.8x + 1.2 = 3.6

4.8x = 2.4

x = 0.5

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The question attached here seems to be incomplete the remaining portion is given below:

3.6 x + 1.2 = 4.8; x = 1 mile

4.8 x + 1.2 = 3.6; x = 1 mile

3.6 x + 1.2 = 4.8; x = 0.5 mile

4.8 x + 1.2 = 3.6; x = 0.5 mile

5 x = negative 58

The number of students that have veggies as a snack is equal to 51 students according to the circle graph.

A circle graph is also called a pie chart, and it can be defined as a type of graph that is used for the graphical representation of the proportional relationship between each part to a whole, especially by dividing a circle into various sectors or sections.

Given that, there are 300 students at a school, the number of students that have veggies as a snack can be calculated as follows;

Number of students that had veggies = 17/100 × 300

Number of students that had veggies = 0.17 × 300

Number of students that had veggies = 51 students.

Hence, the number of students that have veggies as a snack is equal to 51 students according to the circle graph.

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The complete question is :-

Refer to the circle graph below. Suppose there are 300 students at York Middle School. Determine the number of students that have veggies as a snack. No Snack 12% Fruit. 23% Chips · 18% Cheese 15% Veggies 17% L Cookies 15%​

Based on this rate of defect, a total of 256 calculators to be defective in all 64 crates are expected to be defective

Mathematically, a proportion is calculated by dividing the number of individuals in a population who have the characteristic of interest by the total number of individuals in the population. For example, if we are interested in the proportion of people in a city who are left-handed, we would count the number of left-handed people in the city and divide it by the total population of the city.

Proportions are commonly used in statistics to describe the prevalence of certain characteristics or outcomes in a population, and they can be used to make comparisons between different populations or subgroups within a population. Proportions are typically expressed as fractions, decimals, or percentages, and they can range from 0 (indicating that none of the population has the characteristic of interest) to 1 (indicating that all of the population has the characteristic of interest).

We can start by finding the proportion of defective calculators in the sample of tested calculators. If 2 out of 12 tested calculators were found to be defective, then the proportion of defective calculators in the sample is:

2/12 = 1/6

This means that, on average, we would expect 1 out of every 6 calculators in the population to be defective.

To find the total number of expected defective calculators in all 64 crates, we need to multiply this proportion by the total number of calculators in the population:

(1/6) * (64 crates) * (144 calculators per crate) = 1536/6 = 256

Therefore, we can expect a total of 256 calculators to be defective in all 64 crates.

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Answer:

B=240-2w

Step-by-step explanation:

.

The statements that must be true are

A. KL = 15

B. JL bisects overline IK

D. JL is the perpendicular bisector of overline IK .

2. JL = 15 units

3. angle IJK = 90

angle JKI = 45

angle kW = 45

The value of x is solved by the information given in the problem

IL = LK

3x = 2x + 5

solving for x

3x - 2x = 5

x = 5

angle IJL = 0.5 angle JIK,

< JIL = < KJL base angles of isosceles triangle

< JIL +  < LJI  + 90 = 180

< LKJ + < KJL + 90 = 180

equating both

< JIL +  < LJI  + 90 = < LKJ + < KJL + 90

< JIL +  < LJI  = < LKJ + < KJL

and  < JIL = < KJL

hence  < LJI  = < LKJ

we can therefore say that

< JIL = < LJI = < LJK = < JKL = 45 degrees

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The constant of proportion is k = 2. An equation that represent the relation is y = 2x. A graph of the equation y = 2x will show 2 units of x values for y on the y–axis. 9 cups of milk are needed for 18 scoops of ice cream

The proportional relationship between the number of scoops of ice cream and the amount of milk can be expressed as:

1 scoop of ice cream = 1/2 cup of milk

we evaluate for k the constant of proportion as follows:

1 = k × 1/2

k = 2 {cross multiplication}

if we represent a scoop of ice cream with y and a cup of milk with x, then we can write the equation that represent the relation as:

y = 2x.

In the graph of y = 2x, for every value of x on the x–axis, there are 2 units of x for y on the y–axis, that is when x = 1, y = 2 or x = 3 then y = 6.

For 18 scoops of ice cream, we will evaluate for the amount of cup of milk as follows:

18 = 2x

x = 18/2 {divide through by 2}

x = 9.

In conclusion, he constant of proportion is k = 2. An equation that represent the relation is y = 2x. A graph of the equation y = 2x will show 2 units of x values for y on the y–axis. 9 cups of milk are needed for 18 scoops of ice cream

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Answer:

1/3

Step-by-step explanation:

constant proportionality = x/y

x1/y1 , x2/y2 , x3/y3 , ....

5/15 , 10/30 , 6/18 , 9/27 , 2/6

= 1/3 , 1/3 , 1/3 , 1/3 , 1/3

since in all the cases x/y = 1/3 ,

Therefore, the contant proportionality in the given table is 1/3

Hope it's helpful..

The domain of f(g(x)) = (-infinity, -4) U [-4, 4) U (4, infinity).

To find the domain of f(g(x)), we first need to find the domain of g(x) and then the domain of f(x).

The domain of g(x) is the set of all real numbers x such that x + 4 >= 0. So, g(x) is defined for all x >= -4.

To find the domain of f(x), we need to exclude the values of x for which f(x) is not defined. In this case, f(x) is not defined for x = 4. Hence, the domain of f(x) is all real numbers except 4, i.e., (-infinity, 4) U (4, infinity).

Therefore, the domain of f(g(x)) is the set of all real numbers x such that g(x) is defined and g(x) belongs to the domain of f(x). This means that f(g(x)) is defined for all x >= -4, except x = 4.

So, the domain of f(g(x)) = (-infinity, -4) U [-4, 4) U (4, infinity).

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