Pat and Rich drove to the beach
last weekend. It took them twice as
long to get back as it did to drive
there. If they spent 9 hours traveling
to and from the beach, how long
did it take them to drive each way?

The equation of the line that is parallel to this line and passes through the point (-4,-6) is y = 7x + 22

The equation of the line that is perpendicular to this line and passes through the point (-4,-6) is y = -(1/7)x - 46/7

An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.

The slope intercept form of a line is:

y = mx + b

where m is the slope and b is the y intercept

Two lines are parallel if they have the same slope and are perpendicular if the product of their slope is -1.

Given the line:

y = 7x - 3

The slope is 7. The line parallel to this line would also have a slope of 7, while the line perpendicular have a slope of -1/7

The equation of the line that is parallel to this line and passes through the point (-4,-6) is:

y - (-6) = 7(x - (-4))

y = 7x + 22

The equation of the line that is perpendicular to this line and passes through the point (-4,-6) is:

y - (-6) = (-1/7)(x - (-4))

y = -(1/7)x - 46/7

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The value of the sum of the series is are 234 and 10200

In an arithmetic series, the sum of the first "n" terms (Sn) is given by the formula:

Sn = n/2 * (a1 + an)

Where "a1" is the first term and "an" is the nth term.

For the first series, we have

In this series, a1=3 , an=36 , n=12

Plugging these values into the formula, we get:

Sn = 12/2 * (3 + 36)

Sn = 234

For the second series, we have

In this series, a1=3 , d = 2 , n=100

So, we have

an = a + (n - 1)d = 3 + 99 * 2 = 201

Plugging these values into the formula, we get:

Sn = 100/2 * (3 + 201)

Sn = 10200

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The only table that represents both a linear and proportional relationship is table 4

A proportional relationship is a mathematical relationship between two variables in which their ratio is always equal.

In the first table, we see that the proportion of y to x are;

-4/-2 = 2

-3/0 = undefined

-2/2 = -1

Second table shows that;

0/-1 = 0

2/0 = undefined

4/1 = 4

Third table shows that;

-4/-1 = 4

-1/0 = undefined

2/1 = 2

Fourth table shows that;

-1/-3 = 1/3

0/0 = 0

1/3 = 1/3

Looking at the tables. the only one that is a proportional relationship is table 4

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Answer:

The only table that represents both a linear and proportional relationship is table 4

How to identify a proportional relationship?

A proportional relationship is a mathematical relationship between two variables in which their ratio is always equal.

In the first table, we see that the proportion of y to x are;

-4/-2 = 2

-3/0 = undefined

-2/2 = -1

Second table shows that;

0/-1 = 0

2/0 = undefined

4/1 = 4

Third table shows that;

-4/-1 = 4

-1/0 = undefined

2/1 = 2

Fourth table shows that;

-1/-3 = 1/3

0/0 = 0

1/3 = 1/3

Looking at the tables. the only one that is a proportional relationship is table 4

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Step-by-step explanation:

Answer:

Step-by-step explanation

y≥  2x + 3 is -6,2

Answer:

Mixed number: 1  3/8

Improper fraction: 11/8

Step-by-step explanation:

The first circle is 1 whole  1 = 8/8

The second circle is 3/8 *

8/8 + 3/8 = 11/8

----------------------

If you want to write a mixed number as improper fraction just multiply the whole number by the denominator and add the numerator's fraction.

1  3/8 Mixed number

1x8=8

8+3=11

11/8 Improper fraction

-----------------------

* the second circle is not divided into 4 parts. It is divided into 8 equal parts. Each part is 1/8. There are three shaded parts which means 3/8.

----------------------

I hope this helps!

The graph of function g(x) is given by the following option:

First graph.

(right below the text).

A translation happens when either a figure or a function are moved horizontally or vertically.

The four translation rules for functions are given as follows:

The definition of function g(x) for this problem is given as follows:

g(x) = f(x) + 2.

Meaning that it underwent a translation of 2 units up, hence the first graph is correct, as the values of x remain constant, just the values of y are increased by two for each point on the graph.

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The equation of line having a slope of 2 and passing through the point (1,4) is y = 2x + 2.

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Given that the line has a gradient of 2 and passes through the point (1, 4).

Plug the given values into the point-slope formula and solve for y.

y - y₁ = m( x - x₁ )

y - 4 = 2( x - 1 )

y - 4 = 2x - 2

Add 4 to both sides of the equation

y - 4 + 4 = 2x - 2 + 4

y = 2x - 2 + 4

y = 2x + 2

Therefore, the equation of the line is y = 2x + 2.

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Answer: The area of the base of the triangular pyramid is given as 15.6 in² and each side of the base is 6 in, so we can use the formula for the area of an equilateral triangle to find the height of the base:

A = (s^2 * sqrt(3)) / 4

where s is the side length of the triangle. Plugging in the values, we get:

15.6 = (6^2 * sqrt(3)) / 4

Solving for the height of the base, h:

h = (4 * 15.6) / (6^2 * sqrt(3)) = 4 / sqrt(3)

Next, we can use the Pythagorean theorem to find the height of the pyramid, since the slant height is given:

h^2 + (base/2)^2 = slant height^2

where base is the length of one side of the base of the pyramid. Plugging in the values, we get:

h^2 + (6/2)^2 = 8^2

Solving for h:

h = sqrt(64 - 9) = sqrt(55)

Finally, the surface area of the pyramid can be found using the formula:

SA = base area + (perimeter * slant height) / 2

where perimeter is the total length of the sides of the base. Plugging in the values, we get:

SA = 15.6 + (3 * 6 * 8) / 2 = 15.6 + 36 = 51.6 in²

So, the surface area of the triangular pyramid is 51.6 in².

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

Solve the given equation for y

3x+9y = 18

9y = -3x + 18       divide by 9

y = - 1/3 x + 2     done

Answer:

1

Step-by-step explanation:

Y intercept is 1

Y intercept is the point where the line crosses the y axis (point where x=0, you see the line crosses y axis at 1). Thus even if you put 0 in equation 9^x you will get 9^0 and anything power of 0 is 1.

Answer:

4 4/10 is greater.

Step-by-step explanation:

4 = 40/10

then:

4 4/10 = 4 + 4/10 = 40/10 + 4/10 = (40+4)/10 = 44/10

Then:

44 > 32

44 is greater.

Answer:

Sunrise: 95x5+25 = 500

Bright Eyes: 110x5= 550

Sunrise Will be 50$ Cheaper

oops sorry did my math wrong

Answer: Sunrise Hotel is cheaper by $50

Step-by-step explanation:

First, you do $95 x 5 nights = $475, and then add $25 and get $500 per night (Sunrise).

Then multiply $110 and 5 nights and get $550 per night (Bright Eyes).

Lastly, subtract $550 and $500 and get $50.

The required decimal that is greater than the decimals shown in the diagram are 0.5, 0.32, and 0.4. Options B, C, and D are correct.

Decimal value is defined as showing the place value of the digits in a decimal number. If any proportion of the digit is lower than 1 it would be represented after the dot right to the absolute value,

here,
The decimal value is shown in the image,
= 31 / 100

= 0.31

From the options,
0.31 > 0.1
0.31 < 0.5
0.31 < 0.32
0.31 < 0.4

Thus, the required decimal that is greater than the decimals shown in the diagram are 0.5, 0.32, and 0.4. Options B, C, and D are correct.

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Answer:

Well, it depends, but I'd reckon kilograms.

Step-by-step explanation:

2.2 pounds is approximately 0.998 kg, which can be rounded off to 1 kg. However, you really do have to be precise, you may measure it in grams (that's, 998 grams).

So, the most appropriate way is to use 1 kilogram, as a hailstone can be considered quite heavy and we may not be keen on looking for a really precise measurements, as they're measured in hundreds of grams!
Hope this helps :)

The total number of students in the class given the percentage of unhappy students is 263 students.

Percentage of unhappy students= 7.23%

Number of unhappy students= 19

Total number of students in class= x

Number of unhappy students = Percentage of unhappy students × Total number of students in class

19 = 7.23% × x

19 = 0.0723 × x

19 = 0.0723x

divide both sides by 0.0723

x = 19/0.0723

x = 262.7939142461964

Approximately,

x = 263 students

Therefore, there are 263 students in the class.

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Step-by-step explanation:

The average speed is 42 km/hr.

To calculate the average speed, you divide the total distance by the time it took to travel that distance:

189 km / 4.5 hours = 42 km/hr

[tex]\texttt{speed}=\dfrac{d}{t}[/tex]

distance = 189 km

time = 4.5 hours

[tex]\texttt{speed}=\dfrac{189}{4.5}[/tex]

[tex]\fbox{speed = 42 km/hr}[/tex]

The exponential grows at the same rate as the quadratic in the interval

0 ≤ x ≤ 1.

The average Rate of Change function is defined as the average rate at which one quantity is changing with respect to something else changing. In simple terms, an average rate of change function is a process that calculates the amount of change in one item divided by the corresponding amount of change in another.

The average rate of change of a function A = [tex](f(a) - f(b))/(b-a)[/tex]

Given an exponential function, say f(x), such that f(0) = 1 and f(1) = 2.

A quadratic function, say g(x), such that g(0) = 0 and g(1) = 1.

The rate of change of a function f(x) over an interval a ≤ x ≤ b is given by

[tex](f(a) - f(b))/(b-a)[/tex].

Thus, the rate of change (growth rate) of the exponential function, f(x) over the interval 0 ≤ x ≤ 1 is given by

 = (2-1)/1 = 1

Similarly, the rate of change (growth rate) of the quadratic function, g(x) over the interval 0 ≤ x ≤ 1 is given by

=(1 - 0)/1  = 1

Therefore, the exponential grows at the same rate as the quadratic in the interval 0 ≤ x ≤ 1.

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For a dozen cookies, 0.75 cups of sugar are needed in total.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

given, A cookie recipe calls for 1.5 cups of sugar for two dozen cookies.

Since,

For two dozen of cookies, there are a total of 1.5 cups of sugar required.

In 2 dozen cookies, required sugar = 1.5 cups

In 1 dozen cookies, required sugar = 1.5/2 cups

In 1 dozen cookies, required sugar = 0.75 cups

Therefore, The total number of cups of sugar required for one dozen cookies is 0.75.

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Factor Trees are diagrams that show the prime factorization of a number by breaking it down into smaller factors until only prime numbers are left.

Here are the factor trees for the numbers you provided:

8:

8

/

2 4

/

2 2

20:

20

/

2 10

/

2 5

27:

27

/

3 9

/

3 3

36:

36

/

2 18

/

2 9

/

3 3

72:

72

/

2 36

/

2 18

/

2 9

/

3 3.

To solve this, I used the process of prime factorization. Prime factorization is the process of finding the prime numbers that multiply together to form a given number.

The steps I followed to solve this problem are:

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The total number of hours for Jim to drive 900 miles is given by the proportion A = 25 hours

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the number of hours for Jim to drive 900 miles be A

Now , the number of hours = 5 hours

The total distance traveled by Jim in 5 hours = 180 miles

Now , the distance traveled by Jim = 900 miles

And , the proportion will be

A / 900 = 5 / 180

Multiply both sides of the equation by 900 , we get

A = ( 5 x 900 ) / 180

On simplifying the equation , we get

A = 5 x 5

A = 25 hours

Hence , the number of hours is 25 hours

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The radius is the center of circle to its edge or half of a diameter so half of 4/5 is 0.4 since 0.8 / 2 = 0.4.

To find the volume we need to do the equation π r² h.

So, π x 0.4^2 x 10 = 5.02654825.

Round 5.02654825 to the nearest hundredth and it is 5.03.

Volume is 5.03.

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The amount invested at 10% by $568.65 and investment rate is -

amount invested at 13%. is $5275

amount invested at 10%.  is $1171

Compound interest is when you earn interest on both the money you've saved and the interest you earn.

Formula:

A = P(1 + {r}/{n})^{n.t}

here, we have,

Let x represent the amount invested at 13%.

Let y represent the amount invested at 10%.

$6,446 is invested, part at 13 % and the rest at 11%.

This means that

x + y = 6,446

The formula for determining simple interest is expressed as

I = PRT/100

Where

I represents interest paid on the loan.

P represents the principal or amount taken as loan

R represents interest rate

T represents the duration of the loan in years.

Considering the amount invested at 13%,

P = x

R = 13%

T =1 year

I = (x × 13 × 1)/100 = 0.13x

Considering the amount invested at 10%,

P = y

R =10%

T = 1 year

I = (x × 10 × 1)/100 = 0.10y

If the interest earned from the amount invested at

13% exceeds the interest earned from the amount invested at

10% 10 % by $568.65, it means that

0.13x - 0.10y = 568.65,- - -- - - - - -1

Substituting x = 6,446 - y into equation 1, it becomes

0.13(6,446- y) - 0.10y =568.65

i.e. y= 1171

solving, we get,

x=5275

y= 1171

amount invested at 13%. is $5275

amount invested at 11%.  is $1171

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The equations are 4x - y - 2 = 0 and x + 3y + 6 = 0. The solution has been obtained using two-point form.

What is two-point form?

One of the crucial forms for algebraically representing a straight line is the two-point form. Each and every point on a line fulfils the equation for that line, making it the representation of the entire line.

We are given two lines on the graph

Both the lines meet on the y-axis at (0,-2)

This means (0,-2) is the common solution.

Another point of the steeper line is (1,2)

Another point of the flatter line is (3,-3)

Now, as we know the two points of the line, using the two-point form, we get

[tex]\frac{y - y_{1}}{x-x_{1} } = \frac{y_{2} - y_{1}}{x_{2} -x_{1} }[/tex]

⇒ (y+2)/(x-0) = (2+2)/(1-0)

⇒ y+2 = 4x

⇒ y = 4x-2

⇒ 4x - y - 2 = 0

Similarly,

⇒ (y+3)/(x-3) = (-2+3)/(0-3)

⇒ (y+3)/(x-3) = -1/3

⇒ (y+3) = -(x-3)/3

⇒ y+3 = -x/3 + 1

⇒ y = -x/3 - 2

⇒x + 3y + 6 = 0

Hence, the equations are 4x - y - 2 = 0 and x + 3y + 6 = 0.

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Since there are multiple questions so, the question answered above is attached below

The variance for waiting times for patients who are discharged after receiving treatment is more, so waiting times for patients who are discharged after receiving treatment is more variable.

In probability and statistics, variance is the actual value of the squared variation of a stochastic process from its mean value. Informally, variance calculates the degree to which a random group of numbers deviates from the mean value.

Another essential tool, the measurement of variance is equal to the square of the standard deviation.

Since the variance for waiting times for patients who are discharged after receiving treatment is more, so waiting times for patients who are discharged after receiving treatment is more variable.

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Answer: i don't know give me more info

Step-by-step explanation:

Answer:

13 since the second power (-3) is doubled.