The Smiths went to the Cape for a wedding. They left at 11 a.m. They traveled 180 miles and drove at 60 miles per hour. What time did they reach their destination"
O 1:00 p.m.

The output of the equation after transformation is y=3x^2 - 1.

According to the statement

We have to find that the mathematical transformation.

So, For this purpose, we know that the

A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure.

From the given information:

The details are:

y=3x^2 + 2 translated down three units

According to this it is clear that the there is decrease of the 3 numbers.

Then the equation become:

y=3x^2 + 2

After transformation of the 3 units then:

y=3x^2 + 2 -3

y=3x^2 - 1

Then the output gets the y=3x^2 - 1.

So, The output of the equation after transformation is y=3x^2 - 1.

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The time that you will arrive in Nashville is 1:33.

From the information given, the person leaves Knoxville at 11:13, and the journey takes 2 hours and 20 minutes.

Therefore the time when the person will arrive will be the addition of the time given.

This will be:

= 11:13 + 2:20

= 1:33

Therefore, the person will arrive by 1:33.

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By solving inequality  [tex]x[/tex] ∈ [tex][-2,3)[/tex]

What is inequality?

A declaration of the relation in terms of greater, greater than or equal to, smaller, or less than or equal to between two numbers or algebraic expressions is known as inequality.

[tex]4\leq 3x+10 < 19[/tex]

Rearranging the above equation

[tex]\left \{ {{4\leq 3x+10} \atop {3x+10} < 19} \right.[/tex]

Subtracting 10 from the above equation

[tex]\left \{ {{4-10\leq 3x+10-10} \atop {3x+10-10 < 19-10}} \right[/tex]

[tex]\left \{ {{-6\leq 3x} \atop {3x < 9}} \right.[/tex]

Dividing the above equation by 3

[tex]\left \{ {{\frac{-6}{3}\leq \frac{3x}{3} } \atop {\frac{3x}{3} < \frac{3}{3} }} \right.[/tex]

[tex]\left \{ {{-2\leq x} \atop {x < 3}} \right[/tex]

[tex]-2\leq x < 3[/tex]

Therefore, by solving inequality we get  [tex]x[/tex] ∈ [tex][-2,3)[/tex]

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Answer:

Do you mean GCF? If so, it is 10.

If you mean factors that they have in common it is: 1,2,5 and 10.

Step-by-step explanation:

Factors of 70: 1,2,5,7,10,14,35,70

Factors of 110: 1,2,5,10,11,22,55,110

GCF is 10

Answer:

10

Step-by-step explanation:

The value of the middle integer is 26

From the question, we are to determine the middle integer

From the given information,

"The sum of the squares of three consecutive positive integers is 2030"

Let the first integer be x,

Then the middle integer will be x + 1

and the third integer will be x + 2

Thus,

x² + (x +1)² + (x +2)² = 2030

x² + x² + 2x + 1 + x² + 4x + 4 = 2030

3x² + 6x + 5 = 2030

3x² + 6x + 5 - 2030 = 0

3x² + 6x - 2025 = 0

x² + 2x - 675= 0

Solve quadratically

x² + 27x - 25x - 675 = 0

x(x + 27) -25(x + 27) = 0

(x - 25)(x + 27) = 0

x - 25 = 0 and x + 27 = 0

x = 25 and x = -27

Since x is a positive integer,

x = 25

Thus,

The middle integer,

x + 1

= 25 + 1

= 26

Hence, the value of the middle integer is 26

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Considering the definition of an inequality, the correct answer is option (C): the inequality 15×S + 35≤ 137 describes the scenario.

An inequality is the existing inequality between two algebraic expressions, connected through the signs:

An inequality contains one or more unknown values ​​called unknowns.

Solving an inequality consists of finding all the values ​​of the unknown for which the inequality relation holds.

In this case, you know that

Being "S" the number of shirts that Lisa buys, the inequality that expresses the previous relationship is

15×S + 35≤ 137

Finally, the correct answer is option (C): the inequality 15×S + 35≤ 137 describes the scenario.

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option B. g(x)=-2, x<-2, option D. g(x)=-2x+6, x>1 and option E. g(x)=x/2+1 represent a piece of the function in given graph.

The graph of a function is a collection of all ordered pairs of the relation. These are usually represented as points in a Cartesian coordinate system. It is a relationship between an independent variable and a dependent variable. The graph of a function f is the set of all points in the plane of the form (x, f(x)). We could also define the graph of f to be the graph of the equation y = f(x).

Reasons are given below:

In first option that is g(x)=-2x, -2<x<0, we can see a negative sign which indicates that the graph should be downward (negative slope). Also, g(x)=-2x has no y-intercept therefore g(x)=-2x, -2<x<0 does not represent a piece of the function in given graph.

In second option that is g(x)=-2, x<-2, we can see a negative sign and no y-intercept which indicates that it is a horizontal line parallel to x-axis. Also given that x is less than -2, therefore the line should move away from y-axis to the left where lies more negative values. The given data matches the slope given in third quadrant. Hence, it represents a piece of function in given graph.

In third option that g(x)=x-2, -2<x<1, we can see that the function indicates that it has y-intercept at y=-2 and a slope of value 1(positive) which means it should move in upward direction and must cut y-axis at y=-2. The given data does not match with the graph given. Hence, it does not represent a piece of function in the given graph.

In fourth option that is g(x)=-2x+6, x>1, we can see negative sign therefore it should be downward and +6 indicates that it is  with y-intercept too. Hence the given data matches with the graph given and therefore it represents a piece of the function in the given graph.

In fifth option that is g(x)=x/2+1, -2<x<1. As we can see, x lies between -2 and 1, to understand let us assume x=2 then x/2=2/2=1. Therefore, the slope can start at x=1 and extend till -2. Hence, it represents a piece of the function in the given graph.

Therefore, Functions g(x)=-2, x<-2, g(x)=-2x+6, x>1 and g(x)=x/2+1 represent a piece of the function in the given graph.

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Step-by-step explanation:

the line is perpendicular to

y = 2x.

and it goes through the point (1, 2).

the point-slope form looks like

y - y1 = a(x - x1)

"a"being the slope, and (x1, y1) being a point on the line.

the slope-intercept form is

y = ax + b

"a" is again the slope, "b" is the y-intercept (the y value when x = 0).

as you can see, we need the slope of the new line in both cases.

then we will start with the point-slope form, and transform it into the slope-intercept form.

the slope of a line is generally the ratio (y coordinate change / x coordinate change) when going from one point on the line to another.

it is always the factor of x.

we can see it is 2 for the original line. that means 2/1.

a perpendicular slope is turning the x and y values upside down, and is flipping the sign.

so, in our case it is

-1/2

so, starting with the new slope and the point to create the point-slope form :

y - 2 = -1/2 × (x - 1)

and from there we transform into the slope-intercept form :

2y - 4 = -x + 1

2y = -x + 5

y = (-x + 5)/2 = -1/2 x + 5/2 = -1/2 × (x - 5)

all of the expressions in the last line are valid forms to write it.

The value of the linear equation after multiplying is 8/xX.

According to the statement

We have to find that the value of the statement.

So, For this purpose, we know that the

The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line.

From the given information:

The equation is a:

7+1/X (1/x)

Here we know that the X and x are the different variables.

Then

7+1/X (1/x)

Now add the terms which are possible then

8/X (1/x)

Now, multiply the terms which are possible to multiply

Then the equation become

8/xX.

So, The value of the linear equation after multiplying is 8/xX.

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The Ferris wheel in discuss which has 15 cars that are equally spaced around the circumference as described rotates 24° between successive cars being at the bottom.

It follows from the task content that the Ferris wheel in discuss has 15 cars spaced around it.

Since the Ferris wheel in discuss is circular and has a total angle measure of 360.

Hence, the total angle rotated between successive cars can therefore be evaluated as;

Angle rotated = 360°/15

= 24°.

Ultimately, The Ferris wheel in discuss which has 15 cars that are equally spaced around the circumference as described rotates 24° between successive cars being at the bottom.

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The answers are given below:-

a) The exponential function is: [tex]y(t) = 500e^{-0.0117593}[/tex]

b) The rule is: [tex]y(t) = y(0)(\dfrac{358}{500})^{\frac{t}{8}[/tex]

c) The half-life of the element is of 16.599 days.

The mathematical expression  [tex]f(x) = e^x[/tex] denotes the exponential function. The phrase typically refers to the positive-valued function of a real variable, unless otherwise specified.

Following t days, the substance's amount's exponential function is given by:

[tex]y(t) = y(0)e^{-kt}[/tex]

For this problem, we have that:

y(0) = 500, y(8) = 358.

Hence we can solve for k as follows:

[tex]y(t) = y(0)e^{-kt}[/tex]

[tex]358=500e^{-8k}[/tex]

[tex]e^{-8k}=\dfrac{358}{500}[/tex]

[tex]lne^-8k}=ln0.716[/tex]

-8k = ln(0.716)

k = -ln(0.716)/8

k = 0.041759389.

Hence:

[tex]y(t) = 500e^{-0.0117593}[/tex]

For item b, 358/500 of the material is what is left over after each 8-day period, therefore f(t) = t/8, and the rule is as follows:

[tex]y(t) = y(0)(\dfrac{358}{500})^{\frac{t}{8}[/tex]

For item c, using the rule from item a, we have to find t for which y(t) = 0.5y(0), hence:

[tex]y(t) = y(0)e^{-0.0117593}[/tex]

[tex]0.5y(0)=y(0)e^{-0.0117593[/tex]

[tex]e^{-0.0117593}=0.5[/tex]

[tex]lne^{-0.0117593}=ln0.5[/tex]

-0.041759389t = ln(0.5)

t = -ln(0.5)/0.041759389

t = 16.599.

The half-life of the element is of 16.599 days.

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Answer:

w = 20m

l = 60m

Step-by-step explanation:

P = 2l + 2w

We know the perimeter = 160 and we know that l = 3w, so write what we know and solve for w.

P = 2l x 2w

160 = 2(3w) + 2w

160 = 6w + 2w

160 = 8w

Divide both sides by 8

20 = w

Now we can figure out the length, which is 3(w) or 3 x 20 = 60

Answer:

w = 20m, l = 60m

Step-by-step explanation:

The determination of the net income for each of the following separate situations is as follows:

                      Situation A     Situation B      Situation C

Net income     $21,800          $2,400           $31,400

The formula for determining the net income (loss) for the year is:

Net Income (loss) = Ending Equity - Beginning Equity - Additional stock + Dividend Paid).

                    Beginning of year        End of year

Total assets     $ 53,200                  $ 84,000

Total liabilities $ 23,600                  $ 36,600

Situation A:

Common Stock issued = $4,600

Dividend paid = $8,600

                    Beginning of year        End of year

Total assets     $ 53,200                  $ 84,000

Total liabilities $ 23,600                  $ 36,600

Equity               $29,600                    $47,400

Common Stock issued                          4,600

Dividend paid                                       (8,600)

Net Income = Ending Equity - Beginning Equity - Additional stock + Dividend Paid)

$21,800 ($47,400 - $29,600 - 4,600 + 8,600)

Common Stock issued = $15,400

                    Beginning of year        End of year

Total assets     $ 53,200                  $ 84,000

Total liabilities $ 23,600                  $ 36,600

Equity               $29,600                    $47,400

Common Stock issued                        15,400

Dividend paid                                      

Net Income = Ending Equity - Beginning Equity - Additional stock + Dividend Paid)

$2,400 ($47,400 - $29,600 - 15,400)

Dividends paid = $13,600

                    Beginning of year        End of year

Total assets     $ 53,200                  $ 84,000

Total liabilities $ 23,600                  $ 36,600

Equity               $29,600                    $47,400

Common Stock issued                        

Dividend paid                                    $13,600

Net Income = Ending Equity - Beginning Equity - Additional stock + Dividend Paid)

$31,400 ($47,400 - $29,600 + 13,600)

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Answer:

100

Step-by-step explanation:

first let's convert 240 mins to hours

240/60 = 4

now let's find approximately how many pages per hour

200/4 = 50

so, in one hour she approximately read 50 pages

let's say she reads 25 pages per hour

25(4)= 100

The amount of the 1167 rupees he have to pay every month according to the interest rate.

According to the statement

We have to find that the monthly repayments.

So, For this purpose, we know that the

Interest rate is the annual rate that is charged for borrowing , expressed as a single percentage number that represents the actual yearly cost of funds over the term of a loan.

From the given information:

A couple buys furniture for R50 000. They put down a cash deposit of 20% and pay off the balance using a higher purchase agreement, over 4years. The institution charges interest of 10% p.a and monthly Insurance fee of R75.00.

Then

A couple buys furniture =  50,000

cash deposit of 20% = 20% of 50,000

cash deposit = 20/100*50,000

cash deposit = 0.2*50,000

cash deposit = 10000

Left money on which company put interest of 10% =50000 - 10,000

Left money on which company put interest of 10% = 40,000

Then

interest amount per year = 10% of  40,000

interest amount per year = 10/100*40,000

interest amount per year = 0.1*40,000

interest amount per year = 4000

It means interest paid by the customer in 4 years = 4000*4

It means interest paid by the customer in 4 years = 16000

Then

Total money he pays with interest rate in 4 years = 16000 +40,000

Total money he pays with interest rate = 56000

Then

The money he have to pay every month in 4 years = 56000/48

The money he have to pay every month in 4 years = 1167.

So, The amount of the 1167 rupees he have to pay every month according to the interest rate.

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Answer:

There are thirteen 4 card hands are possible with a 52 card deck.

Answer:

Thirteen 4 card hands are possible with a 52 card deck

Answer:

z+5

Step-by-step explanation:

the word more indicates addition

Answer:

0.035

Step-by-step explanation:

hope this helps :)

The sampling method used to get the sample is  Systematic sampling.

The variable type of color of cars around the gym is qualitative.

Sampling is the process of choosing a subset of people (a statistical sample) from a statistical population in order to estimate characteristics of the entire population. It is used in statistics, quality control, and survey technique. Statisticians try to get samples that are typical of the population under consideration.

The different sampling methods used are:

Now the given sample of the residents that were selected was every eighth car . Hence  Systematic sampling is used.

Disclaimer: Missing question stem: Identify the sampling method(simple , stratified, cluster, systemic).

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Answer:

-2,-1.5,-1,-0.5 etc

Step-by-step explanation:

The smaller the negative value the greater the value compared to other negative value carrying a negative sign.

The size of the game file written in standard form is 350000 kilobytes

The given parameters are:

Size of the file = 3.1 x 10E4 kilobytes

Patch = 40000 kilobytes

The size of the game file written in standard form is then calculated as

Size = Size of the file + Patch

This gives

Size = 3.1 x 10E4 kilobytes + 40000 kilobytes

Rewrite as

Size = 310000 kilobytes + 40000 kilobytes

Evaluate the sum

Size = 350000 kilobytes

Hence, the size of the game file written in standard form is 350000 kilobytes

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Answer:

b is the answer

Step-by-step explanation:

b is the answer

The mistake is that in both numbers 0.304 and 0.340, 4 is in the tenth position following the point.

The combination of numerical variables and operations expressed by the addition, subtraction, multiplication, and division signs is known as a mathematical expression. A place-value system gives a number's specific location within a series a value.

Karin's softball batting average is 0.304, whereas Cheryl's is 0.340. They have the same average, according to Karin.

Because the numbers 0.340 and 4 are in the tenth position, as opposed to 0.304 and 4, the values are different from one another.

He made a mistake in his estimation because both averages are equal.

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Answer:

$840.77

Step-by-step explanation:

Answer:  a

Step-by-step explanation:

Every six powers of ten, the cycle repeats. In other words, a repeating decimal with a denominator of 7 can have a repeating cycle that is up to six digits long.

The repeating cycle of a repeating decimal for the rational number with a denominator of 7 can be determined by considering the factors of the denominator.

In this case, the denominator is 7, which is a prime number. The length of the repeating cycle can be determined by examining the powers of 10 modulo 7.

To find the length of the repeating cycle, we need to find the smallest positive integer "n" for which 10ⁿ - 1 is divisible by 7. In other words, we are looking for the smallest "n" such that 10ⁿ ≡ 1 (mod 7).

Let's calculate the powers of 10 modulo 7:

10¹ ≡ 3 (mod 7)

10² ≡ 2 (mod 7)

10³ ≡ 6 (mod 7)

10⁴ ≡ 4 (mod 7)

10⁵ ≡ 5 (mod 7)

10⁶ ≡ 1 (mod 7)

As you can see, the cycle repeats every 6 powers of 10. This means that the repeating cycle of a repeating decimal with a denominator of 7 can be up to six digits long.

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Answer:

1.25

Step-by-step explanation:

=2.75/2.2

=1.25

it is answer .it think answer give some help

The values of the unknown variables a,b,c,d,e and f is 8, 7, -3, 6, 1, and 2 respectively.

The code is 2 ( 7 + 6 ) + 8 ( 1 - ( - 3 ) ).

1.given that

[tex] x^4 . x^a = {x}^{12}[/tex]

we know the formula

[tex] a^m . a^n = {a}^{m+n}[/tex]

so, [tex] {x}^{(4+a)} = {x}^{12}[/tex]

if bases are equal then Powers will be equals.

then 4 + a = 12

a = 12 - 4

a = 8.

2. given that.

[tex] (y^b)/(y^5)= y^2[/tex]

we know the formula

[tex] a^m/a^n = {a}^{(m-n)}[/tex]

so, [tex] {y}^{(b-5)} = y^2[/tex]

when bases are equal then Powers will be equal.

b - 5 = 2

b = 2 + 5

b = 7

3.given that

[tex] 3^c = (1)/(27)[/tex]

so, [tex] 3^c = ( 1/3)^3 [/tex]

[tex] 3^c = {( 3/1)}^{-3} [/tex]

if bases are equal then Powers will be equals.

then c = -3.

4.given that

[tex] (m^3)^2 = m^d[/tex]

we know the formula

[tex] (a^m)^n = {a}^{m.n}[/tex]

[tex] m^6 = m^d[/tex]

if bases are equal then Powers will be equals.

then d = 6

5. given that

[tex] 7^0 = e[/tex]

e = 1

6. given that

[tex] {4}^{(-2) }. {4}^{9}. {4}^{(-5)} = 4^f[/tex]

we know the formula

[tex] a^m . a^n = {a}^{(m+n)}[/tex]

so, [tex] {4}^{(-2+9-5)} = 4^f[/tex]

if bases are equal then Powers will be equals.

then -7+9 = f

f = 2.

Hence, the values of the unknown variables a,b,c,d,e and f is 8, 7, -3, 6, 1, and 2 respectively.

The code is

f ( b + d ) + a ( e - c )

2 ( 7 + 6 ) + 8 ( 1 - ( - 3 ) ).

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The scale factor used to dilate triangle XYZ so as to form X'Y'Z' is a scale factor of 5/4.

Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, rotation, translation and dilation.

Triangle X'Y'Z' is the image of triangle XYZ after a dilation by a scale factor.

Given that XZ = 4; X'Z' = 5

Hence:

Scale factor = X'Z'/XZ = 5/4

The scale factor used to dilate triangle XYZ so as to form X'Y'Z' is a scale factor of 5/4.

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