cory has 42 feet of fencing around his garden. the garden is rectangular in shape and its length is equal to twice the width minus 3 feet. write a system of equations to find the length and width of the garden. what is the length and width of the garden?

Answer: x= 4/9

Step-by-step explanation:

9x^2-16=0

9x^2 = 16

9x = 4

x= 4/9

Using displacement as a vector quantity, the change or displacement of the car is 3 blocks

Distance is the total movement of an object without any regard to direction. We can define distance as to how much ground an object has covered despite its starting or ending point.  is a vector quantity that refers to "how far out of place an object is"; it is the object's overall change in position. Distance and displacement are two quantities that seem to mean the same but are distinctly different with different meanings and definitions. Distance is the measure of “how much ground an object has covered during its motion” while displacement refers to the measure of “how far out of place is an object.”

The displacement of the car will the change in it's position from starting to it's present position.

This can be calculated mathematically as

2 + 3 - 2 = 5 - 2 = 3

The displacement is 3 blocks.

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The probability that the shipment is accepted is 0.278685

The following problem is a problem of the binomial distribution. Here,

n = 31

p = probability of pills being a defect = 0.08

We need to find the probability that the batch is affected.

This means we need to find

P(X≤1)

PMF of Binomial is given by

P(X = x) = ⁿCₓ pˣ (1-p)ⁿ⁻ˣ

= P(X = 0) + P(X = 1)

=  ³¹C₀ 0.08⁰ 0.92³¹ +  ³¹C₁ 0.08 X  0.92³⁰

= 0.92³⁰(0.92 + 31X0.08)

= 0.92³⁰ X 3.4

=0.278685

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The science of conducting studies to gather, arrange, summarize, analyze, and draw conclusions from data is known as statistics.

Survey responses are analyzed using statistics. Understanding the phrases and ideas is crucial in order to fully comprehend what is being represented (or misrepresented) by a given statement.

Data collection, analysis, presentation, and interpretation are all part of the science of statistics. Much of the early motivation for the subject of statistics came from governmental needs for information on a variety of economic activities and census data. Both theoretical and practical advancements in statistics have been sparked by the current need to transform the vast volumes of data accessible in many application domains into valuable information.

Option B is the proper response, thus.

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The value of c in the equation 5c = 13.5 - 16.5 - 10c is 0.6.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign

In this case, 5c + 16.5 = 13.5 + 10c

Collect the like terms

5c - 10c = 13.5 - 16.5

- 5c = -3.0

Divide

c = -3.0 / -5

c = 0.6

The value of c is 0.6.

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The slope of the line that passes through each pair of points are:

1. -29/3

3. -27/19

5. 2/3

7. -11/3

2. 22/13

4. 1/5

6. 2/3

8. 5/17

The slope of a line that joins two points can be found by using the formula below:

Slope (m) = change in y / change in x

1. Slope (m) of the line that goes through (8, 12) and (11, -17):

Slope (m) = (-17 - 12) / (11 - 8) = -29/3

3. Slope (m) of the line that goes through (-1, -8) and (-20, 19):

Slope (m) = (19 - (-8)) / (-20 - (-1)) = 27/-19

m = -27/19

5. Slope (m) of the line that goes through (2,16) and (8, 20):

Slope (m) = (20 - 16) / (8 - 2) = 4/6

m = 2/3

7. Slope (m) of the line that goes through (11,-6) and (8,5):

Slope (m) = (-6 - 5) / (11 - 8) = -11/3

2. Slope (m) of the line that goes through (2.-11) and (15, 11):

Slope (m) = (-11 - 11) / (2 - 15) = -22/-13

m = 22/13

4. Slope (m) of the line that goes through (5, -18) and (-15, -16):

Slope (m) = (-16 - (-18)) / (-15 - 5) = 2/10

m = 1/5

6. Slope (m) of the line that goes through (9, 10) and (-12,-4):

Slope (m) = (-4 - 10) / (-12 - 9) = -14/-21

m = 2/3

8. Slope (m) of the line that goes through  (11, 8) and (-6, 3):

Slope (m) = (8 - 3) / (11 - (-6)) = 5/17

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According to the point-slope form, the linear equation for the attendance in terms of the price is given as [tex]y=-20p+1490[/tex].

It is given to us that -

If the price of admission was $17, the attendance was about 1150 customers per day

When the price of admission was dropped to $12, attendance increased to about 1250 per day

We have to write a write a linear equation for the attendance in terms of the price.

Let us say that -

Price of admission is given as "p"

and, attendance of customers is given as "q"

It is given to u that -

For p = $17, q = 1150 customers per day

For p = $12, q = 1250 customers per day

We know that the point-slope form of a linear equation can be represented as -

[tex]y-y_{1} =m(x-x_{1} )[/tex] ------ (1)

where,

([tex]x_{1} ,y_{1}[/tex]) = initial coordinates of the point

m = slope of the linear equation = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex] ----- (2)

From the given information, we can represent the points as -

([tex]x_{1} ,y_{1}[/tex]) = (17, 1150)

and, ([tex]x_{2} ,y_{2}[/tex]) = (12, 1250)

Substituting the values of ([tex]x_{1} ,y_{1}[/tex]) and ([tex]x_{2} ,y_{2}[/tex]) in equation (2), we have -

[tex]m = \frac{y_{2} -y_{1} }{x_{2} -x_{1} }\\= > m = \frac{1250-1150}{12-17}\\= > m = \frac{100}{-5} \\= > m = -20[/tex]------ (3)

Now, substituting the values of ([tex]x_{1} ,y_{1}[/tex]) and m from equation (3) in the point-slope form of the linear equation (1), we have

[tex]y-y_{1} =m(x-x_{1} )\\= > y-1150=(-20)(x-17)\\= > y-1150=-20x+340\\= > y=-20x+340+1150\\= > y=-20x+1490[/tex]

In terms of price, p we can write the above linear equation as -

[tex]y=-20p+1490[/tex]

Thus, the linear equation for the attendance in terms of the price is given as [tex]y=-20p+1490[/tex].

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The amount of money in the account after 14 years is $20248.59

From the question, we have the following parameters that can be used in our computation:

Also from the question, we have

V = Pe^{rt}

Where

Substitute the known values in the above equation, so, we have the following representation

V = 8620 * e^(6.1% * 14)

Evaluate the products

So, we have the following representation

V = 8620 * e^(0.854)

Evaluate the exponent

So, we have the following representation

V = 8620 * 2.34902418149

Lastly, evaluate the products

So, we have the following representation

V = 20248.5884444

Approximate

V = 20248.59

This means that the value after 14 years is $20248.59

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Answer:4.50t + 6.75b = 576

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

Point slope form of the new line would be

(y -2) = m (x-3)      from the given formula

From the GIVEN line....its slope, m , is 1/2

      perpendicular slope is  - 1/m = -2    ( this is something you have to remember/learn)

then the NEW Line becomes

(y-2) = -2 ( x-3)       expand and simplify

y-2 = -2x+ 6

y = -2x + 8      Done !

Answer:

y = - 2x + 8

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 )

y = [tex]\frac{1}{2}[/tex] x - 9 ← is in slope- intercept form

with slope m = [tex]\frac{1}{2}[/tex]

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{2} }[/tex] = - 2 , then

y = - 2x + c ← is the partial equation

to find c substitute the point (3, 2 ) into the partial equation

2 = - 2(3) + c = - 6 + c ( add 6 to both sides )

8 = c

y = - 2x + 8 ← equation of perpendicular line

On solving the provided question we can say that the answer is - nnual rate of return will he need to get in order to accomplish his goal if interest is compounded continuously is [tex]A(t) = 2800^e(20)t.[/tex]

Simple interest and compound interest are the two methods for calculating interest. Simple interest is computed on a loan's principle, or initial loan amount. Compound interest is sometimes referred to as "interest on interest" since it is computed using both the principal and the accrued interest from prior periods.

Formula for Monthly Compound Interest. 12 times a year are used to compute interest that is compounded monthly., Formula for Quarterly Compounding. Four times a year are used to compute interest that is compounded quarterly., Formula for Daily Compound Interest., Formula for Annual Compound Interest.

[tex]3300 = 2800e^20t\\ (33/28) = e^20t\\ ln(33/28) = 20t\\ 0.05ln(33/28 = t.[/tex]

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Answer:

The map is displaying 600 miles of land.

Step-by-step explanation:

To find the number of miles of land being displayed on the map, you need to multiply the length of the map in inches by the conversion factor, which is the ratio of inches to miles. In this case, the conversion factor is 2 inches per 200 miles.

So, to find the number of miles of land being displayed on the map, you would do the following calculation: 12 inches * (200 miles / 2 inches) = 600 miles.

Well said. I 100% know what this is.

×

The equation is y = 2.5. And the actual distance in the third case and the distance on the map in the fourth case will be 120 miles and 90 mm, respectively.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

Let 'x' be the distance on the map and 'y' be the actual distance. Then the equation of the line is given as,

(y - 25) = [(50 - 25) / (20 - 10)](x - 10)

y - 25 = 2.5x - 25

y = 2.5x

If x = 48 mm, then the actual distance is given as,

y = 2.5(48)

y = 120 miles

If y = 225 miles, then the distance on the map is given as,

225 = 2.5x

x = 90 mm

The graph is given below.

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if there appears to be a relationship in scatterplot 4,The linear relationship in scatterplot 4 appears to be negative.

When examining scatterplot 4, we can see that as the values of the x-axis increase, the values of the y-axis decrease in a linear relationship. This implies that as the values of the x-axis increase, the values of the y-axis decrease at a constant rate. This indicates a negative linear relationship between the two variables, meaning that as one variable increases, the other variable decreases in a linear fashion.

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The domain of the function is [2, 2) And the range is (3, 3) (along the y -axis).

The domain of a function is the input value for which the function exists while the range is the output value for which the function exists.

The range of a function is defined as the set of all the possible output values that are valid for the given function.

For the graph given, the domain lie across the x-axis.

The range is possible y values. Since we can use negative x values, if we plug in x values for the function, we are going to get positive numbers, as we plug in higher negative numbers, our range is bigger.

The domain of the function is [2, 2) And the range is (3, 3) (along the y -axis).

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Answer:

answer is in explanation

Step-by-step explanation:

The domain of the function is [2, 2) And the range is (3, 3) (along the y -axis).

How to find the domain and range of a function?

The domain of a function is the input value for which the function exists while the range is the output value for which the function exists.

The range of a function is defined as the set of all the possible output values that are valid for the given function.

For the graph given, the domain lie across the x-axis.

The range is possible y values. Since we can use negative x values, if we plug in x values for the function, we are going to get positive numbers, as we plug in higher negative numbers, our range is bigger.

The domain of the function is [2, 2) And the range is (3, 3) (along the y -axis).

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Answer:

=x^2-2x+3x-6

=x(x-2)+3(x-2)

=(x-2) (x+3)

Answer:

[tex] \displaystyle{y' = \dfrac{ - 3x( {x}^{3} + 6) }{( {x}^{3} + 3)^{2} }}[/tex]

Step-by-step explanation:

We can use the quotient rule:

[tex] \displaystyle{y = \frac{u}{v} \to y '= \dfrac{u'v - uv'}{ {v}^{2} }}[/tex]

In this case, u and v both are functions. By applying formula above, we will have:

[tex] \displaystyle{y' = \dfrac{(3 {x}^{2})' ( {x}^{3} + 3) - (3 {x}^{2} )( {x}^{3} + 3)' }{( {x}^{3} + 3)^{2} }}[/tex]

Then apply power rule to derive functions, we have to know that:

[tex] \displaystyle{y = {x}^{n} \to y' = n {x}^{n - 1} } \\ \\ \displaystyle{y = c \to y' = 0 \: \: \: (c \in \mathbb{R})}[/tex]

Therefore, we will have:

[tex] \displaystyle{y' = \dfrac{6x ( {x}^{3} + 3) - (3 {x}^{2} )3 {x}^{2} }{( {x}^{3} + 3)^{2} }}[/tex]

Expand the terms in:

[tex] \displaystyle{y' = \dfrac{6 {x}^{4} + 18x - 9 {x}^{4} }{( {x}^{3} + 3)^{2} }} \\ \\ \displaystyle{y' = \dfrac{ - 3 {x}^{4} + 18x }{( {x}^{3} + 3)^{2} }} \\ \\ \displaystyle{y' = \dfrac{ - 3x( {x}^{3} + 6) }{( {x}^{3} + 3)^{2} }}[/tex]

Hence, that's the answer. You can keep in unfactored form or factored form as you desire!

Amrit's income is £27434.16.

What is the arithmetic operation?

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.

Let the Bethan's income be x

Amrit's income is 32% more than Bethan's income.

So, Amrit's income=x+32%

Amrit and Bethan's combined income is £54868.

According to given question we have

x+x+32%=£54868

2x+32/100=£54868

2x=54868-0.32

2x=54867.68

x=27433.84

Bethan's income=£ 27433.84

Amrit's income

=x+32%

=£ 27433.84+0.32

=£27434.16

Therefore,  Amrit's income is £27434.16.

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The expression when Ahmad thinks of a number, n. He adds 4 then multiplies the result by 3 is 3(n + 4).

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

In this scenario, Ahmad thinks of a number, n. He adds 4 then multiplies the result by 3.

This will be:

= (n + 4) × 3

= 3(n + 4).

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On solving the provided question, we cans ay that by standard deviation, [tex]SE = 0.1590 (approx.)[/tex]

Standard deviation, or variance in a collection of values, is a measure of variation or variance in statistics. A low standard deviation suggests that the values are more likely to be close to the set's mean, whereas a large standard deviation suggests that the values are widely dispersed. Standard deviation, or variance in a collection of values, is a measure of variation or variance in statistics. A low standard deviation suggests that the values are more likely to be close to the set's mean, whereas a large standard deviation suggests that the values are widely dispersed.

By sample standard deviation, we mean standard error. Hence, we have that:

Therefore, Standard deviation[tex]= 0.6929891[/tex]

The sample size [tex](n) = 19.[/tex]

Hence:

[tex]SE = 0.1589826.\\ SE = 0.1590 (approx.)[/tex]

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Test c had 60 items

It is the most accurate statement that can be made about the reliability of these tests.

The reason that objective tests include so many items is to increase the reliability of the test.

Reliability Test

It is the characteristic of a set of test scores that relates to the amount of random error from the measurement process that might be embedded in the scores. Scores that are highly reliable are precise, reproducible, and consistent from one testing occasion to another.

Probability

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

A measure of reliability between two variants of the same test is known as alternate forms reliability. The results of two identical (but distinct) tests are correlated, and a reliability coefficient is computed. If variations in one test's observed results correspond to variations in the scores of an equivalent test, the test is said to be dependable. A psychological test's practise effect which is typical of test-retest reliability, can be mitigated by a survey instrument's alternate-form reliability. The goal is to reword the survey questions in a way that makes them functionally identical, or just rearrange the questions in the first and second surveys of the same respondents.

Test c had 60 items

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Since, Alice ate 5 cookies and 2 carrots for a total of 590 calories; bob ate 3 cookies and 4 carrots for a total of 410 calories. Therefore, In a cookie there are 110 calories.

A calorie is a unit of energy that food and drink provide. we can usually find out how many calories are listed in foods, and wearables like the best fitness trackers let you monitor how many calories you're burning in different activities. Certain foods, such as processed foods, tend to be high in calories. Other foods, such as fresh fruits and vegetables, tend to be low in calories. there is not. Calories are needed to give you enough energy to move, keep warm, grow, work, think, and play. Our circulation and digestion also need to work well with the energy we get from calories.

Let x = calories in cookies.

     y = calories in carrots.

Now, according to the question:

     5x + 2y = 590                   --------------------------------------- (1)

     3x + 4y = 410                    -------------------------------------- (2)

Multiplying equation(1) by 3 and equation(2) by 5:

         15x + 6y = 1770                       ---------------------------(3)

         15x + 20y = 2050                   ---------------------------(4)

Solving we get:

    y = 280/14

or, y = 20 units.

Putting the value of y = 20 in equation (2)

    3x + 4y = 410

⇒  3x + 4 × 20 = 410

⇒ 3x = 410 - 80

⇒ x = 330/3

⇒ x = 110 Units

Therefore, the calories of cookies is 110 units .

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Answer:

3.15

Step-by-step explanation:

In equations, you need to get the variable on one side and the answer on the other. In this instance, you divide both sides by 5.24 so you're left with w = 3.15.

Hope this helps, have an amazing day!

Answer:

d) 3.15

Step-by-step explanation:

Given equation,

→ 5.24w = 16.506

Now the value of w will be,

→ 5.24w = 16.506

→ w = 16.506 ÷ 5.24

→ [ w = 3.15 ]

Thus, the value of w is 3.15.

The probability that an athlete used steroids, given that they tested positive, is approximately 0.5025%.

In order to calculate the probability that an athlete used steroids given the information provided, we need to know the probability that they tested positive. To do this, we can use the formula for conditional probability:

P(A|B) = P(A and B) / P(B)

In this case, we are trying to find the probability that an athlete used steroids (A) given that they tested positive (B). We know that the probability of A is 1% and the probability of B is 0.5%, so we can calculate P(A and B) by multiplying these two probabilities together:

P(A and B) = 1% * 0.5% = 0.005%

Next, we need to calculate P(B), which is the probability that the athlete tested positive. Since we know the false positive rate and the true positive rate of the test, we can use these to calculate P(B) using the formula:

P(B) = P(A and B) + P(not A and B)

P(B) = P(A|B) * P(B) + P(not A|B) * P(B)

P(B) = 0.99 * 0.005% + 0.005 * (1 - 0.005%)

P(B) = 0.00495% + 0.005 * 0.999

P(B) = 0.0099495%

Now that we have P(A and B) and P(B), we can plug these values into the formula for conditional probability to calculate the probability that an athlete used steroids, given that they tested positive:

P(A|B) = P(A and B) / P(B)

P(A|B) = 0.005% / 0.0099495%

P(A|B) = 0.5025%

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The statement that best describes Lucia's claim is at option (b), that is " Lucia's claim is incorrect since not all the rotations that are multiples of 45° carry a square onto itself".

It is given that, Lucia draws a square and plots the center of the square.

Lucia claims that " any rotation about the center of the square that is a multiple of 45° will carry the square onto itself".

To verify this claim, we need to construct a square (ABCD) as shown in the figure.

When the square ABCD is rotated about 45° where we can it is 1 × 45°, the square formed is A'B'C'D' is not the same as the actual one. So, they are not in symmetry after the rotation n this case.

If we rotate again, that is for the second multiple of 45° (2 × 45°), we get a square A''B''C''D''. But, now the square is similar to the actual one. So, they are in symmetry.

This means we can say that, not for all the multiples of 45° rotation, the square does not carry onto itself.

Therefore, we can conclude that "Lucia's claim is incorrect since not all rotations that are multiples of 45' carry a square onto itself".

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Answer: f(x) = -x^2 - 9x - 90

Correct answer is the last one (D)

Step-by-step explanation:

Graph every single one of them using Desmos Graphing Calculator

The following are the answer to each statement;

1. The book is $18

2. Giselle can earn up to $18 pulling weeds for her grandma.

3. Giselle's grandma pays her $1 for every 5 weeds she pulls

4. Giselle does not have to use any of her own money towards the purchase of the book when she pulls 90 weeds.

5. Giselle only needs to pull 18 weeds to not use any of her own money

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Answer:

Step-by-step explanation:

the answer is (6m+1). Hope i helped :)