The population Of a town in Utah in 1997 was 6000. After two years the population of the town was 145% of the 1997 population. What is the population of the town after two years?
A) 6145
B) 7000
C) 8700
D) 9000

Answer:

{(3, -1), (7, 1), (-6, -1), (9, 1), (2, -1)}

Step-by-step explanation:

Any relation having repetitive x-coordinates, is NOT a function.

{(3, -1), (7, 1), (-6, -1), (9, 1), (2, -1)}, is the set of ordered pairs represents a function. So, the option B is correct.

Here, we have,

A set of ordered pairs represents a function if each input (x-value) is associated with exactly one output (y-value).

Let's examine the given options:

O {(2, -2), (1, 5), (-2, 2), (1, -3), (8, -1)}: This set does not represent a function because the input value 1 is associated with both 5 and -3.

O {(3, -1), (7, 1), (-6, -1), (9, 1), (2, -1)}: This set represents a function since each input value is associated with a unique output value.

O {(6, 8), (5,2), (-2,-5), (1, -3), (-2, 9)}: This set does not represent a function because the input value -2 is associated with both -5 and 9.

O {(-3, 1), (6,3), (3, 2), (-3, -3), (1, -1)}: This set does not represent a function because the input value -3 is associated with both 1 and -3.

Therefore, the set of ordered pairs that represents a function is:

O {(3, -1), (7, 1), (-6, -1), (9, 1), (2, -1)}

Hence, {(3, -1), (7, 1), (-6, -1), (9, 1), (2, -1)}, is the set of ordered pairs represents a function. So, the option B is correct.

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Answer:

1 and 3

AB is the shortest segment in △ABC.

AC = 2AB

Step-by-step explanation:

Enjoy!!

Answer:

1. AB is the shortest segment in △ABC.

3. AC = 2AB

Step-by-step explanation:

edge24

D or B Step-by-step explanation:

Answer:

He could increase the sample size

Step-by-step explanation:

In hypothesis testing, the error associated with the test is affected by a number of factors. The first factor is the level of significance, alpha. This is the probability of type 1 error. The probability of rejecting the null hypothesis when it is indeed true.

The second factor is the size of the sample used. The larger the sample, the smaller the error since the characteristics of the sample will be closer to those of the entire population on which inference is being made

Answer:

B is correct just took the test.

Step-by-step explanation:

Answer:

See attachment.

Step-by-step explanation:

The given function is

[tex]y=0.5\sec(x+\frac{\pi}{3})-2[/tex]

This is the graph of [tex]y=\sec(x)[/tex] that is shifted down 2 units and shifted to the left [tex]\frac{\pi}{3}[/tex] units.

When x=0, [tex]y=0.5\sec(0+\frac{\pi}{3})-2[/tex]

[tex]y=0.5\sec(\frac{\pi}{3})-2[/tex]

[tex]y=1-2=-1[/tex]

The y-intercept is -1.

The correct choice is shown in the attachment

Answer:

The attached graph is the answer

Step-by-step explanation:

* Lets revise the trigonometry translation

- If the equation is y = A sec(B(x + C)) + D

# Amplitude is A

- The Amplitude is the height from the center line to the peak .

  Or we can measure the height from highest to lowest points and

  divide that by 2

# period is 2π/B

- The Period goes from one peak to the next

# phase shift is C (positive is to the left)

- The Phase Shift is how far the function is shifted horizontally

  from the usual position.

# vertical shift is D

- The Vertical Shift is how far the function is shifted vertically from

 the usual position.

- If y = sec(x)

∴ A = 1 , B = 1 , C = 0 , D = 0

- That means the amplitude is 1, the period is 2π, no phase shift

 or vertical shift

* Now lets solve the problem

∵ y = 0.5 sex(x + π/3) - 2

∴ A = 0.5

- The 0.5 tells us it will be half times taller than usual,

 so Amplitude = 0.5

∴ B = 1

- The period is 2π

∴ C = π/3

- The π/3 means it will be shifted to the left by π/3

∴ D = -2

- The -2 tells us the vertical Shift = -2

* Lets calculate the y-intercept

- To find the y-intercept put x = 0

∴ y = 0.5 sec(0 + π/3) - 2

∵ sec(π/3) = 2

∴ y = 0.5(2) - 2 = 1 - 2 = -1

* Now lets look to the graphs to find the correct answer

- Only one graph has y-intercept is -1

- Look to the attached graph

- There is a vertical shift down 2 units

- There is a horizontal shift to the left by π/3 units

- The amplitude is 1/2 ⇒ (-1.5 - -2.5)/2 = 1/2, where -1.5 and -2.5

  are the peak points

- The y-intercept is -1

* The attached graph is the answer

- For more understand look to the attached color graph

- The blue graph is y = sec(x)

- The red graph is y = 0.5 sec(x + π/3) - 2

Answer: Yes, it does. Because each input value has one and only output value.

Step-by-step explanation:

By definition, a relation is a function when each input value has one and only output value.

Then, to know if the table represents a function, you need to observe if each input value (in other words, each value of the variable "x") has only one output value (the output values are the values of the variable "y").

You can observe that each value of "x" has only one value of "y", therefore, you can conclude that the given table represents a function.

a) The answer will be 456976 because you multiply 26 and 4.

b) The answer will be 358800 bacause you multiply 26*25*24*23

Answer:I’m thinking 330 but I’m not sure

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer: 330

Solution:

= (11x10x9x8 / 4x3x2x1)  

= 7920 / 24  

= 330

Answer:

is there an equation?

Answer:

A. ) 125.6 in.

Step-by-step explanation:

Hope I helped :)

Answer:

Step-by-step explanation:

The formula of a circumference of a circle:

[tex]C=d\pi[/tex]

d - diameter

We have d = 40in. Substitute:

[tex]C=40\pi\ in[/tex]

[tex]\pi\approx3.14\to C\approx(40)(3.14)=125.6\ in[/tex]

Answer:42

Step-by-step explanation:

7 multiplied by 6= 42

Insert 6 in the x place and solve

7x

7(6)

^^^The parentheses is the same as saying 7 × 6

so...

42

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

$9426.50

Step-by-step explanation:

let noel's salary = x, robert's salary = y and john's salary = z

y = x - 512.75 ..........(1)

z = 3y = 3(x - 512.75) = 3x - 1538.25 ...............(2)

x + y + z = 47645.25..........................(3)

substitute for y and z

x + (x - 512.75) + (3x - 1538.25) = 47645.25

x + x - 512.75 + 3x - 1538.25 = 47645.25

5x = 47645.75 + 512.75 + 1538.25

5x = 49696.25

divide both sides by 5

x = 9939.25 ..... noel's salary

to get robert's salary substitute x in equation 1

y = 9939.25 - 512.75 = 9426.50

y = $9426.50..... robert's salary

Answer:

5

Step-by-step explanation:

To write the polynomial in standard form you need to write it in descending order of degree.

Standard form is:

5x^3 + 8x^2 + 9

The leading coefficient is the coefficient of the first term, the highest degree term.

Answer: 5

Therefore, the leading coefficient of the polynomial [tex]\(8x^2 + 9 + 5x^3\)[/tex] is [tex]\(5\)[/tex].

To write the polynomial [tex]\(8x^2 + 9 + 5x^3\)[/tex] in standard form, we arrange the terms in descending order of their degree:

[tex]\[ 5x^3 + 8x^2 + 9 \][/tex]

In this polynomial, the term with the highest degree is [tex]\(5x^3\)[/tex]. The coefficient of this term, which is the number multiplied by [tex]\(x^3\)[/tex], is the leading coefficient.

Answer:

There were 18 trials recorded

Step-by-step explanation:

Each dot is a trial, the numbers under them is how long each that trial took.

Hope this helps.

The number of  times trials were recorded during the experiment are:

                                    18

We know that the dot plot is nothing but the representation of outcomes of a experiment where the dots represent the value of each outcome.

and the total number of  dots represent the total number of items which are studied or recorded.

Here, the total number of trials that are recorded is equal to the total number of dots in the dot plot i.e. the total frequency of the set.

The data frequency table is as follows:

      Value            Frequency

       15                      2

        17                      3

        19                      2

        20                     2

        21                       1

        23                       4

        24                        1

         25                       3

 Total frequency= 2+3+2+2+1+4+1+3=18

Hence, the answer is: 18                  

ANSWER

[tex](2x-3y) (4x-y) = 8 {x}^{2} -14xy + 3 {y}^{2} [/tex]

EXPLANATION

We want to expand (2x-3y) (4x-y)

We use the distributive property to obtain,

[tex](2x-3y) (4x-y) = 2x(4x-y) -3y(4x-y)[/tex]

We expand to get,

[tex](2x-3y) (4x-y) = 8 {x}^{2} -2xy -12xy + 3 {y}^{2} [/tex]

Combine the middle terms to obtain,

[tex](2x-3y) (4x-y) = 8 {x}^{2} -14xy + 3 {y}^{2} [/tex]

Answer:

34.5 inches

Step-by-step explanation:

To find the length of the original piece of ribbon, multiply 6.9 inches by 5, obtaining 34.5 inches.

By the way, it appears that your problem statement is not complete.  Nathan thought ... what?  Please be sure to share the entire problem next time.

Answer:

Not sure if this is correct but maybe it is 34?

Answer: [tex]tan(x)=\±\frac{3}{4}[/tex]

Step-by-step explanation:

You know that [tex]sin(x)=\frac{3}{5}[/tex] and you can identify that. Then:

[tex]sin^2(x)=(\frac{3}{5})^2[/tex]

[tex]sin^2(x)=\frac{9}{25}[/tex]

Remember that:

[tex]cos^2(x)=1-sin^2(x)[/tex]

Then [tex]cos^2(x)[/tex] is:

[tex]cos^2(x)=1-\frac{9}{25}\\\\cos^2(x)=\frac{16}{25}[/tex]

Apply square root to both sides to find cos(x):

[tex]\sqrt{cos^2(x)}=\±\sqrt{\frac{16}{25}}\\cos(x)=\±\frac{4}{5}[/tex]

Remember that:

[tex]tan(x)=\frac{sin(x)}{cos(x)}[/tex]

Then, this is:

[tex]tan(x)=\frac{\frac{3}{5}}{\±\frac{4}{5}}[/tex]

[tex]tan(x)=\±\frac{3}{4}[/tex]

Answer:

17

Step-by-step explanation:

2x-8=x+9

x=17

ANSWER

BC=17 units

EXPLANATION

The given triangle is an isosceles triangle.

We have

AC=AB

This implies that,

[tex]x + 9 = 2x - 8[/tex]

Group similar terms and simplify to get:

[tex]2x - x = 9 + 8[/tex]

[tex]x = 17[/tex]

Side BC is x units. But x=17

Therefore BC is 17 units.

Answer:

D

Step-by-step explanation:

Median: Put the list in order from least to greatest.

$20, $20, $23.50, $25, $26.50

$20, $23.50, $25

$23.50 is the median. I took one from each side until I had one left.

Mean: Get the sum of them all and then divide by the number of earnings ( in this case )

$25 + $26.50 = $51.50      $51.50 + $20 = $71.50    $71.50 + $23.50 = $95

$95 + $20 = $115    $115/5 = $23

$23 is the mean.

Mode: Is the one that finds the frequency or in lamen terms it is the number which appears most often.

There's no steps for finding the expect counting how many times that number appeared.

$20 is the mode.

Answer:

He's correct

Step-by-step explanation:

Answer:

f(1) = 2

Step-by-step explanation:

Since y is a function of x, that is;

y = f(x)

f(1) implies the value of y when x = 1.

To obtain this value we draw the vertical line x = 1 and check where the line intersects the graph of f(x).

In this case, the line x = 1 will intersect with the graph of f(x) on the line y = 2. The function f(x) assumes the value 2 between x = 0 and x = 4. Therefore,

f(1) = 2

Answer:

f(1) = 2

Step-by-step explanation:

Answer:

The height of the football is 48 feet after 3 seconds

The first equation y = -16t² + 64t is the best

Step-by-step explanation:

* Lets explain how to solve the problem

- The equation of motion of an object on air without any

 external force is y = ut + 1/2 at², where y is the height of the

 object from the ground, u is the initial velocity, a is the

 acceleration of gravity and t is the time

* Lets solve the problem

- A football is kicked at ground level with an initial velocity of

 64 feet per second

∴ u = 64 feet per seconds

∵ The football is kicked upward

∴ a = -32 feet per seconds²

∵ y = ut + 1/2 at²

∴ y = 64t + 1/2 (-32)t²

∴ y = 64t - 16t²

* We will use the first equation y = -16t² + 64t

∵ y = -16t² + 64t

- We need to find the height of the football after 3 seconds

∵ t = 3 seconds

∴ y = -16(3)² + 64(3)

∴ y = 48

∵ y represents the height of the football

∴ The height of the football is 48 feet after 3 seconds

Answer:

7/13

Step-by-step explanation:

26 cards are red.  2 are black threes.  So the probability that a card is a three or red is 28/52, which reduces to 7/13.

Using the counting principle, Fernando can choose from a total of 35 different watch combinations, as he has 5 watch faces and 7 colored bands which can be selected independently.

The question asks about combinations resulting from 5 watch faces and 7 colored bands, this comes from a mathematical concept known as the counting principle. The counting principle states that if one event can occur in m ways and a second can occur independently of the first in n ways, then the two events together can occur in m × n ways.

So, Fernando can choose from 5 watch faces and 7 colored bands independently. Therefore, the total different combinations of watches he can make is 5 × 7 = 35. Thus, Fernando has 35 different watch combinations to choose from.

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Answer: 1 5/8 or 13/8. They are the same.

Step-by-step explanation to find the amount of books she reads in 4 1/3 says, first you need to find how much she reads in 1 day.

3/4 divided by 2 = 3/4 x 1/2=3/8.

Now you need to multiply 3/8 by 4 1/3 to find how many books she can reed in a day. 4 1/3= 13/3. 13/3 x 3/8= 39/24 = 13/8 = 1 5/8

Answer: 2.888889

Step-by-step explanation:

3/4 book    4 1/3 book

------------- =  ---------------

2 days          x days

4 1/3= 13/3

3/4= 0.75

1.5x= 13/3

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

1.5      1.5

 x=  2.888889 books

Answer:

3603 boxes.

Step-by-step explanation:

Rectangular Prism is actually a cuboid.

Volume of cuboid = length * width * height.

It is given that length = 16.5 m,  width = 18.2 m, and height = 12 m. Therefore:

Volume = 16.5 * 18.2 * 12 = 3603.6 cubic meters.

Volume is actually the capacity of the shape. If the box has the volume of 1 cubic meters, then the number of boxes that can fit in the rectangular prism will be:

Number of boxes to be fit = Volume of Large container/Volume of Small Container.

Number of boxes = 3603.6/1 = 3603 boxes.

Therefore, 3603 boxes will fit the rectangular prism and 0.6 cubic meters will be the spare space!!!

Answer:

-a^2 -4a +3a +12

-a^2 -1a +12

Step-by-step explanation:

Answer: a

hope this helps

Answer:

The answer is A) rotate 540° clockwise about (5, 3) and reflect across the line y = 3 HOPE I HELP :)

Step-by-step explanation:

Answer:

112.81 m.

Step-by-step explanation:

The pole and the tower and their shadows form 2 similar triangles so their corresponding sides are in the smae ratio.

Therefore we have the relation:

1.21 / 48.75 = 2.8 / x   where x is the height of the tower.

Cross multiplying:

x = 2.8 * 48.75 / 1.21

= 112.81 m

Final answer:

To find the height of the tower, we use the proportion 2.8 m / 1.21 m = H / 48.75 m. After cross-multiplication and division, the height of the tower is calculated to be approximately 112.81 meters.

Explanation:

The student's question involves using similar triangles to determine the height of a tower based on the shadow it casts. To solve this problem, we can set up a proportion because the pole and tower will cast shadows at the same angle due to the sun's position. The proportional relationship is formed by the height of the pole over its shadow length being equal to the height of the tower over its shadow length.

Let's designate the height of the tower as H. The proportion will then be:

2.8 m / 1.21 m = H / 48.75 m

Cross-multiplying to solve for H, we get:

2.8 m \\times 48.75 m = H \\times 1.21 m

136.5 m = 1.21 m \\times H

To find H, divide both sides by 1.21 m:

H = 136.5 m / 1.21 m

H = 112.8099 m

So, the height of the tower is approximately 112.81 meters after rounding to two decimal places.

Answer:

n= -3 and n= -6

Step-by-step explanation:

[tex]n^2 = -18 -9n[/tex]

We need to solve this equation to find the value of n.

Rearranging:

[tex]n^2 +9n +18 =0[/tex]

This is a quadratic equation and we can solve by using factorization method.

We need to make factors of 18n^2 such that their sum is equal to 9n.

So solving,

[tex]n^2 + 9n +18 =0\\n^2 + 6n + 3n +18 =0\\n(n+6) + 3(n+6)=0\\(n+3)(n+6) =0\\=> n+3 =0 \,\, and n+6 =0\\n= -3 \,\,and \,\,n=-6[/tex]