During the holiday, students went swimming in a local rectangular pool. The pool measures 20 feet by 35 feet. It is surrounded by a patio that is uniform width. Find the width of the patio if the total area of the pool and patio is 1350 sqr feet. Write a quadratic equation to solve the problem.

Answer:  Yes to all 3 questions

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Explanation:

VLT = vertical line test

HLT = horizontal line test

The given curve passes the VLT since it's not possible to draw a single vertical line through more than one point on the blue curve. Therefore, we have a function. Any input (x) leads to exactly one output (y).

The curve also passes the HLT through similar reasoning (use a horizontal line this time of course). This tells us the function is one-to-one. Each input leads to a unique output.

The keyword "unique" is important in the previous paragraph. It's needed to help set up the inverse. Since this curve passes the HLT, we know the inverse exists and it is a function. The inverse itself will pass the VLT.

Note: recall you reflect the given curve over the line y = x to form the inverse curve.

Since the side length is three units, the specified rectangular prism's volume will be 27 units.

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity. The capacity of an object is measured by its volume. For instance, a cup's capacity is stated to be 100 ml if it can hold 100 ml of water in its brim. The quantity of space occupied by a three-dimensional object can also be used to describe volume.

Here,

Length of side=3 units

Volume=(side)³

=3³ unit

=27 unit³

The length of side is 3 unit, so the volume of the given rectangular prism will be 27 unit.

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Answer:

B) 69.6

Step-by-step explanation:

Answer:

(x+9)(x+9)

Step-by-step explanation:

Let's factor x2+18x+81

x2+18x+81

hope this help xxx

Answer:

32 Packs

Step-by-step explanation:

Ms Hoblin will need to buy 452/14 = <<452/14=32>>32 packs of prizes.

Alternatively, you could divide 452 by 14 and then round up to the nearest whole number to determine the number of packs that she needs to buy. In this case, 452/14 = 32.64, so she would need to buy 33 packs of prizes.

The test statistic of the proportion is given as follows:

z = 4.47.

The equation that gives the test statistic for a proportion is given as follows:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

In which:

In the context of this problem, the values of these parameters are given as follows:

[tex]p = 0.06, n = 724, \overline{p} = \frac{72}{724} = 0.0994[/tex]

Hence the test statistic for the proportion is calculated as follows:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

[tex]z = \frac{0.0994 - 0.06}{\sqrt{\frac{0.06(0.94)}{724}}}[/tex]

z = 4.47.

Meaning that the first option is correct.

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In linear equation,(10/21) glasses of water does she drink, in glae per hour.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.    

                                   Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

3/4 of hour she drinks (2/3) of a glass

So, in 1 hour she drinks (2/3)×(5/14) of a glass

So, in 1 hour she drinks (10/21) glasses of water.

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Answer:

smallest angle = 35

Step-by-step explanation:

the 3 angles lying on the straight line AOB sum to 180° , then

3a + 8 + 60 - a + 4a - 38 = 180 , that is

6a + 30 = 180 ( subtract 30 from both sides )

6a = 150 ( divide both sides by 6 )

a = 25

Then

3a + 8 = 3(25) + 8 = 75 + 8 = 83°

60 - a = 60 - 25 = 35°

4a - 38 = 4(25) - 38 = 100 - 38 = 62°

the smallest angle is 35°

you can either graph it or solve it algebraically

move the parts of the equation to fit the sctructure of y = mx + b

2x + 4y = 20

4y = -2x + 20

divide by 4 on both sides to get 'y' by itself

y = -2/4x + 20/4

y = -1/2x + 5

this equation tells you the 'y intercept' and the slope

slope; -1/2

y intercept; 5

1.. Plane R and plane P intersect at AB.

2.. 3 points that are collinear are A, D and B.

3. Planes can be named indicating three points that are on the same plane yet not on the same line.

4. Coplanar points are three or more points that lie on the same plane.

What is Coplanar points?

When three points that are not on the same line can be used to describe a plane, it is said to be a plane. Line AB is the point where planes P and R intersect. Plane P is horizontal and Plane R is vertical. These two planes intersect at this point, so line AB is shared by both planes.

A, D, and B are the three collinear points. This occurs when three or more points are all aligned in a single straight line, as the name collinear suggests.

Three locations that are on the same plane but not on the same line might be termed as a plane. These points are not collinear, to put it another way. DBG or FAD are two ways to represent Plane R.

Three or more points on the same plane are referred to as coplanar points. Since planes are typically flat surfaces, any three or more points located there are considered coplanar points. The four coplanar points ACDE are located on plane P.

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The equations that are true for x = -2 and x = 2 are x^2 - 4 = 0 and 2(x - 2)^2 = 0.

For x = -2, the equation x^2 - 4 = 0 becomes (-2)^2 - 4 = 0, which simplifies to 4 - 4 = 0, and therefore this equation is true when x = -2.

Similarly, for x = 2, the equation 2(x - 2)^2 = 0 becomes 2((2 - 2)^2) = 0, which simplifies to 2(0)^2 = 0, and therefore this equation is also true when x = 2.

The other equations, x^2 = -4, 3x^2 + 12 = 0, and 4x^2 = 16, are not true for x = -2 or x = 2. For example, for x = -2, the equation 3x^2 + 12 = 0 becomes 3(-2)^2 + 12 = 0, which simplifies to -24 + 12 = -12, and therefore this equation is not true when x = -2. Similarly, for x = 2, the equation 4x^2 = 16 becomes 4(2)^2 = 16, which simplifies to 16 = 16, and therefore this equation is true when x = 2. However, since the problem asks for equations that are true for both x = -2 and x = 2, the equation 4x^2 = 16 is not a correct answer because it is only true when x = 2.

Do not reject H0 there is not sufficient evidence at a 0.05 significance level to warrant rejection of the claim that the four vehicle size categories have the same mean force on the left femur in crash tests.

What is Null hypothesis?

A statistical hypothesis known as a null hypothesis asserts that no statistical significance can be found in a collection of provided observations. Using sample data, hypothesis testing is performed to judge a theory' veracity. It is sometimes referred to as just "the null," and its symbol is H0.

from given outpout

Null hypothesis

H0:u1=u2=u3=u4

Alternative Hypothesis

H1: not all means are equal

Test statistic =F=0.49

P value=0.691

Pvalue>0.05 alpha level of significance

We fail to reject null hypothesis

Conclusion =

Do not reject H0 there is not sufficient evidence at a 0.05 significance level to warrant rejection of the claim that the four vehicle size categories have the same mean force on the left femur in crash tests.

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Answer:

the answer is d

Step-by-step explanation:

x is -2 and y is

Answer:

0

Step-by-step explanation:

4(8x–1) = 2(2x–2)

32x–4 = 4x–4

32x–4x = –4+4

28x = 0

x=0/28

x= 0

Answer:

x=0

Step-by-step explanation:

4(8x-1)=2(2x-2)

Step 1)  32x-4=4x-4

Step 2) 28x=0

Step 3) x=[tex]\frac{0}{28\\}[/tex]

Step 4) x=0

Thus, the probability of the electron being in a spherical shell at distance (a) from the proton is e^(-a/a0), at distance (b) is e^(-b/a0), and at distance (c) is e^(-c/a0).

Probability is a metric for determining the possibility or chance of an event happening. It is a mathematical concept that measures the unpredictability of an occurrence and is frequently stated as a decimal or fraction. For example, if the probability of flipping a coin and obtaining heads is 0.5, there is a 50% chance of flipping heads. The number of favorable outcomes to the total number of potential outcomes is used to compute probability. In other words, it is the number of ways an event may occur divided by the total number of conceivable outcomes. Probability is used to make predictions and take wise decisions in a variety of disciplines, including mathematics, science, finance, and engineering.

How to solve?

If we assume the electron is in a hydrogen 1s orbital, the probability density function is given by the square of the 1s wavefunction, which is:

p(r) = (1/πa0^3) e^(-r/a0)

P(r, r+δr) = ∫p(r')dV = ∫p(r')4πr'^2dr'

For the given distances (a), (b), and (c), the probabilities are:

P(a) = ∫p(r')4πr'^2dr' = (1/πa0^3) ∫e^(-r'/a0)4πr'^2dr' = (1/πa0^3) * 4π * a0^3 * e^(-a/a0) = e^(-a/a0)

P(b) = e^(-b/a0)

P(c) = e^(-c/a0)

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Derivative of log(tanhx) = 2cossec(2x)

Let us assume y = log (tan hx)

On differentiating both sides ,

[tex] \frac{dy}{dx \: } = \frac{d \: log(tanhx)}{dx} [/tex]

[tex] \frac{dy}{dx} = \frac{d log( \tan(hx) ) }{d \tan(hx).d \tan(hx) } \times dx[/tex]

[tex] \frac{dy}{dx} = \frac{1}{ \tan(hx) \times \sec( {h}^{2x} ) } [/tex]

[tex] \frac{dy}{dx} = \frac{ \cos(hx) }{ \sin(hx) } \times \frac{1 }{ \cos(h {}^{2} ) } [/tex]

[tex] \frac{dy}{dx} = \frac{2}{2 \sin(hx). \cos(hx) } [/tex]

[tex] \frac{dy}{dx} = \frac{2}{ \sin(h)(2x) } [/tex]

dy/dx = 2 cos sec (2x)

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the point of intersection of the given function will be (-1,5).

What is a function?

A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.

The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.

the functions f(x) = (x+6)(x+2) and g(x) = x + 6

Equating them with each other

(x+6)(x+2) = x + 6

x+2 = 1

x = -1

f(-1) = 5

So the point of intersection of the given function will be (-1,5).

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Step-by-step explanation:

James and Bethany Morrison are celebrating their 10th anniversary by having a reception at a local reception hall. They have budgeted $3,500 for their reception. If the reception hall charges a $50 cleanup fee plus $32 per person, find the greatest number of people that they may invite and still stay within their budget. James and Bethany can invite at most people to the reception. (Round down to the nearest whole person).

3,500 = 32p + 50

subtract 50 from both sides:

3,450 = 32p

divide both sides by 32:

p = 107.8125

because you cannot invite part of a person, round down to 107 people.

Answer:

107

Step-by-step explanation:

You have $3,450 to work with and you divide that by 32, which is the cost per person, and you come up with 107.8... You can round up to 108, but you risk(because you are) being over budget.

The number of small boxes and large boxes for the given linear equation condition purchased is 10 and 7 respectively.

What is a linear equation?

Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.

According to the question, a builder needs to purchase nails in order to construct a house.

Both small and large boxes of nails are provided. There are 50 nails in each small box and 350 in each large box.

The contractor purchased 3 more small boxes than large boxes, hence it is assumed that he purchased an 'x' number of large boxes.

He purchased (x+3) small boxes.

So, 50(x+3) + 350(x) = 2950.

50x + 150 + 350x  = 2950.

400x = 2950 - 150.

400x = 2800.

x = 7.

∴ The no. of large boxes he purchased is 7.

∴ The no. of small boxes he purchased is 10.

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The system of linear inequalities to model the situation is 10x + 20y ≤ 100 and y > 2x

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

Using the following representations:

We have the following system of inequalities from the given statements

10x + 20y ≤ 100

y > 2x

Hence, the system of inequalities is 10x + 20y ≤ 100 and y > 2x

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Answer:

t=2/f-5

Step-by-step explanation:

The true option regarding the relationship between a catalyst and a chemical reaction is D. Each reaction has its own unique catalyst.

A catalyst is a substance that accelerates the rate of a chemical reaction without affecting the end product. They only have an effect on the rate of the reaction, not the yield.

Catalysts offer an alternative reaction pathway with lower activation energy than uncatalyzed reactions. It raises the frequency of collision and, as a result of the increased collision, lowers the activation energy of the reaction.

A chemical reaction is a process that converts one or more substances, known as reactants, to one or more different substances, known as products. Chemical elements or compounds are examples of substances.

A chemical reaction rearranges the constituent atoms of the reactants to produce various products. The properties of the products differ from the properties of the reactants. It is distinct from physical changes, which include state changes such as ice melting to water and water evaporating to vapor.

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Answer:

2n + 1 = 157

2n = 157 - 1

2n = 156

n = 156/2

n = 78

Step-by-step explanation:

hope this helps

Answer: nope

Step-by-step explanation:

According to the given statement 16% is the probability that the person is age 48 or older.

A metric of a data set's deviation from the mean is referred to as "standard deviation" (or ""). While a high standard deviation indicates that the numbers are more spread, a smaller standard deviation suggests that the data are clustered around the mean.

After calculating the z-score, we will look up the value in the table on page (718–719).

We will employ the equation, to determine the z-score.

z= x−μ / σ

How is x=48

μ=41

σ=7 the z-score is,

z = 48 - 47 /7

z = 7 / 7

z = 1

The value for z=1 in the table is 0.84130, meaning that the region below the curve represents people who are 48 years of age and older. However, we are looking at the area that represents people who are 48 years of age and older, hence,

1−0.8413

=0.1587≈0.16

=16%

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The complete question is-

The distribution of ages of licensed drivers shopping at the Kalish County Mall is normally distributed with mean 41 and standard deviation 7. A person will be selected at random. Round your answers to the nearest hundredth. What is the probability that the person is age 48 or older?

Answer:

6

Step-by-step explanation:

1) Total-Amount left

112-64=48

So now we know how much money she spent on the carne asada fries. Now let's get on with the next step.

2) Amount Spent/Cost for carne asada fries

48/8=6

So they bought 6 carne asada fries

I hope this helps!!!

When the actual selling price is $20, the store manager is showing a $18 item with a $2 price tag.

One can calculate the percentage by dividing the value by the total value and multiplying the result by 100. (Value/Total Value)100% is the formula for calculating percentages.

To convert a decimal number, such as 0.57, to a percentage, just multiply it by 100. Therefore, 0.57 times 100 equals 57. Therefore, 0.57 is a percentage that equals 57%. Another example is 0.03 x 100 = 3%. Percentages are just fractions with a denominator of 100. To show that a number is a percentage, we place the percent sign (%) next to it.

For instance, if you properly answered 75 out of 100 questions on a test, you would have received a 75% grade (75/100).

Here,

Item cost is $18.

Price to Sell = 18 + 11% ×18

= $19.98

= $20

The store manager is displaying an item that cost $18 for a selling price of $2 when the true selling price is $20.

So,

When the actual selling price is $20, the store manager is showing a $18 item with a $2 price tag.

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Each shirt = $2.99, each pair of slacks = $5.99, and each sports coat = $6.99.

Total refers to a whole or full amount, and the verb "to total" means to combine two numbers or to destroy anything. In mathematics, you add integers to get the total; the outcome is the total. The result of adding 8 and 8 is 16.

Let shirts equal SH, Slacks equal S, and sports coats equal SC.

2SH+2S equals 17.96.

6SH+3S+2SC=49.89

5SH+1SC=21.94

We'll use them to address

6SH+3S+2SC=49.89

-6SH-6S=--53.88, multiplying by -3 to eliminate SH.

-3S+2SC=-3.99

-30SH-6SC=-131.64, multiplying the third by -6 to eliminate SH

30SH+15S+10SC=249.45,multiplying by 5 to eliminate SH.

15S + 4SC = 117.81

Now 15S + 4SC = 117.81  and -3S+2SC=-3.99

S = $5.99

As a result, we may calculate SH as $2.99 and use the value of S and SH we get SC = $6.99

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The domain and range of the equations for the three cars using the hypothetical condition that x represents additional gas added to the tank are;

Car #1

Domain; 0 ≤ x < ∞

Range; 607.8 ≤ y < ∞

Car #2

Domain; 0 ≤ x < ∞

Range; 568 ≤ y < 0

Car #3

Domain; 0 ≤ x < x

Range; 528.4 ≤ y < ∞

An equation is a statement that indicates that two expressions be equivalent by joining them with an equals sign.

The specified equations for three cars are;

Car #1: y = 28·x + 607.6

Car #2: y = 80·x + 568

Car #3: y = 20·x + 528.4

The domain of a function is the set of possible input values (x-values) of the function

The range is the set of possible output values (y-values) of the function

Let y represent the number of miles driven and let x represent the additional gas added to the car, we get;

The domain of car #1

The additional number of gallons of gas car #1 can drive receive has a domain of 0 ≤ x < ∞

The range for car #1

The total number of miles car #1 can drive = 607.6 ≤ y < ∞

The domain for car #2

The additional amount of gas car #2 receives is; 0 ≤ x < ∞

The range for car #2

The distance car #2 can drive is; 568 ≤ y < ∞

The domain for car #3

The additional volume of gas car #3 receives is; 0 ≤ x < ∞

The range of the function for car #3

The number of miles car #3 can drive is; 528.4 ≤ y < ∞

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