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Graph the function with domain of all the real numbers: f(x) = 5 for x ≥ 3, and f(x) = -6 for x < 3

Answer:

[tex]p = (2.33 \times {10}^{4})( {1.07}^{6} )[/tex]

Answer:

[tex]\frac{1}{6}[/tex]

Step-by-step explanation:

1. You need the same denominator to subtract

2. You can do this by picking the least common multiple of both denominators or multiplying the denominators by each other. In this case, the LCM (least common multiple) and multiply 4*3 or 3*4 is the same thing: 12.

3. But, what you do to the denominator, you do to the numerator:

[tex]\frac{2*4=8}{3*4=12} \\\\\frac{2*3=6}{4*3=12}[/tex]      This leaves the fractions as [tex]\frac{8}{12} -\frac{6}{12} =\frac{2}{12}[/tex].

4. When you subtract fractions, you don't subtract the denominator.

5. You can simplify this fraction by dividing the numerator and denominator by 6: [tex]\frac{2/2}{12/2} =\frac{1}{6}[/tex]

Answer:

In math, number blocks are commonly used as models, where a small square equals 1, a long rectangle equals 10, and a large square equals 100. As models, blocks can be used for addition, subtraction, multiplication, and division. You can represent a problem given by using the correct models.

Answer:

$11.50

Step-by-step explanation:

15% of 10 is 1.5

10-1.5=8.5

20-8.5=11.5

The net pay of Simmons will be $494 after the deductions.

The net pay is defined as the actual amount earned after the deductions of taxes and loan emi etc.

here simmon's total earning is $694

After the deductions the simmon will left with:

694x0.92x0.96x0.88=539.38

Now the insurance premiums are of $45

So the final amount will be

=539.38-45=494.38

Hence net pay of Simmons will be $494 after the deductions.

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There are 10⁷ possible phone numbers from the digit 0 to 9.

Permutations are different ways of arranging objects in a definite order. It can also be expressed as the rearrangement of items in a linear order of an already ordered set.

Here, there are total 10 possible digits (0 to 9) we can use to create 7 digit phone numbers.

For first place there are 10 possible digits.

similarly for second place again 10 possibilities and so on.

So total number of phone number = 10 X 10 X 10 X 10 X 10 X 10 X 10

                                                          = 10⁷

Thus, there are 10⁷ possible phone numbers from the digit 0 to 9.

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Possible phone numbers can be 10 x 9 x 8 x 7 x 6 x 5 x 4 (without repetition) = 10!/3!.

10 10 10 - 10 10 10 10= [tex]10^{7} =1,00,00,000[/tex]. (with repetition)

A numeral system is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner.

There are 7 digit phone number represented with a XXX-XXXX .

So the first x can be 10 different numbers

let us take

10 ___ ___ ____ ____ ____ ____, but which ever number you use, it is then used up.

So then you only have 9 numbers left

10 x 9 x ___ x ___ x ___ x ___ x ___ .

Then, once that number is used it can't be used again, so on

10 x 9 x 8 x 7 x 6 x 5 x 4 (without repetition) = 10!/3!

If the repetition takes place then,

the first place have possibilities of 10 digits

10 __ __ - __ __ ___ __

Now, again repetition is allowed again there are possibilities of 10 digits.

10 10 __- __ __ __ __

and carrying the same way,

10 10 10 - 10 10 10 10= [tex]10^{7} =1,00,00,000[/tex].

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Answer:

2

Step-by-step explanation:

3n+2=8

Collect like terms

3n=8-2

3n=6

Divide both sides by 3

3n÷3=6÷3

n=2

The correct answer is Choice A

[tex] \huge \tt \color{pink}{A}\color{blue}{n}\color{red}{s}\color{green}{w}\color{grey}{e}\color{purple}{r }[/tex]

[tex] \large\underline{ \boxed{ \sf{✰\:Note }}}[/tex]

★ 1st let's know what is the given figure is and it's related concepts for solving !

➣ Given Triangle is a right angled triangle

➣ It is having 3sides let's know what are the name of these sides

➣ 1st AB is know as hypotenuse

➣ 2nd AC and is called Base of the triangle

➣ 3rd BC whích is know as perpendicular of the triangle

➣ Hypotenuse(H):-The side of a right triangle opposite the right angle.

➣ Perpendicular(P):- Exactly upright; extending in a straight line.

➣ Base(B):- it also known as the side opposite to hypotenuse

➣Perpendicular and base are know as the leg of right angled triangle

➣ We can easily find length of one missing side by using a theorem name as "Pythagorean theorem"

➣ Pythagorean theorem :- A mathematical theorem which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of those of the two other sides

★ Note :- The Pythagorean theorem only applies to right triangles.

[tex] \rule{70mm}{2.9pt}[/tex]

★ Writing this theorem mathematically ★

[tex] { \boxed{✫\underline{ \boxed{ \sf{Pythagorean \: theorem \: ⇒ {Hypotenuse }^2={ Base }^2+ {Height }^2}}}✫}}[/tex]

★ Here ★

➣ Base (AC)= 22cm

➣ Perpendicular (height) (BC)= 8cm

[tex] \rule{70mm}{2.9pt}[/tex]

✝ Assumption ✝

➣ let Hypotenuse ( AB ) = "x"

[tex] \boxed{ \rm{ \pink ➛AB^2= AC^2+BC^2}}[/tex]

[tex] \rule{70mm}{2.9pt}[/tex]

✝ let's substitute values ✝

[tex]\rm{ \pink ➛x^2=22 ^2+8^2} \\ \rm{ \pink ➛x^2 = 484+ {64} } \\ \rm{ \pink ➛ {x}^{2} = 548 } \\ \rm{ \pink ➛= {x} = \sqrt{548} } \\ \rm{ \pink ➛ x = 2\sqrt{137} \: or23.4} \\ [/tex]

[tex] \rule{70mm}{2.9pt}[/tex]

Hence Hypotenuse (AB) in the given triangle is of

[tex] { \boxed{✛\underline{ \boxed{ \sf{2\sqrt{137} \: or23.4\green✓}}}✛}}[/tex]

[tex] \rule{70mm}{2.9pt}[/tex]

Hope it helps !

Answer:

the final option

Step-by-step explanation:

the negative sign causes a reflection, the +6 in the parentheses cases a 6 unit shift left and the +3 causes a 3 unit shift up

Answer: the second choice: (0, - 2) and (1, 0).

Explanation:

1) The solution of a graphed system of equations is the points of intersection of the equations.

2) Hence, this method requires to graph each function in one Cartesian coordinate system.

3) To graph the function y = x² + x  - 2, you can follow these steps

      y = (x² + x)  - 2

      y + 1/4 =  (x² + x + 1/4)  - 2

       y + 1/4 = (x + 1/2)²  - 2

       y = (x + 1/2)²  - 2 - 1/4

       y = (x + 1/2)² - 9/4

       Compare with the vertex form y = (x + h)² + k, where the coordinates of the vertex are (h,k). Therefore, the vertex is (1/2, - 9/4).

4) To graph the function y = 2x - 2, you can follow these steps:

The tables show that these points are common to the two functions: (0, - 2) and (1,0).

The graphs are shown in the figure attached.

You can see that the parabola (blue curve) and the line (purple line) intercept each other at those two points ( 0, - 2) and (1,0).

Jesse take 0.4 hours while Mark take 0.23 hours to reach back to home. The statements which should Jesse consider when solving this situation is statement 2.

Pythagoras theorem says that in a right angle triangle, the square of the hypotenuse side is equal to the sum of the square of the other two legs of the right angle triangle.

Jesse and Mark are jogging along the route shown at a rate of 12 miles per hour.

Here, Thus, Florida Avenue is hypotenuse triangular path and the other two sides are Capitol Street and H Street. The distance of  Florida Avenue is,

[tex]1^2+1.75^2=d^2\\1+3.0625=d^2\\4.0625=d^2\\d=\sqrt{4.0625}\\d=2.0156[/tex]

Thus, Jesse walks 2.0156 with 5 miles per hour. Thus, the time taken by him is

[tex]t_J=\dfrac{2.0}{5}\\t_j=0.4\rm\;hr[/tex]

Mark plans to jog back the way they came which is 2.75 miles (1+1.75) long with speed of 12 miles per hour. Thus, the time taken  by him is

[tex]t_M=\dfrac{2.75}{12}\\t_M=0.23\rm\;hr[/tex]

Thus, Jesse take 0.4 hours while Mark take 0.23 hours to reach back to home. The statements which should Jesse consider when solving this situation is statement 2.

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Answer:

about 11,948.05 cubic cm

Step-by-step explanation:

[tex]12 \times \pi( {4.9}^{2} )(13.2) = 11948.05[/tex]

The statement that best describes the relationship between lines s and t is: Lines s and t are parallel.

Parallel lines are as those lines that does not intersect one another despite being equal to each other.

Lines s and t are said to be parallel lines because they are cut by transversal which in turn means that transversal intersect lines s and t to make it parallel lines.

Therefore the statement that best  describes the relationship is :Lines s and t are parallel.

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Answer:

16 cups

Step-by-step explanation:

1 quart = 4 cups

Hey ! there

Answer:

Step-by-step explanation:

In this question we are given that perimeter of a triangle is 84 m , longest side of triangle is 7 meters less than twice the length of shortest side that is x and middle side is 7 meters longer than the shortest side .

And we're asked to find the length of each side of triangle.

So ,

We know that ,

[tex]\underline{\boxed{\frak{Perimeter_{(Triangle)} = Sum \:of\: three\: sides}}}[/tex]

Solution : -

[tex] \longmapsto \qquad x +( x + 7) + (2x - 7) = 84[/tex]

Step 1 : Removing parenthesis and cancelling 7 with -7 :

[tex] \longmapsto \qquad x + x + \cancel{7} + 2x - \cancel{ 7 }= 84[/tex]

Step 2 : Adding like terms on left side :

[tex] \longmapsto \qquad 4x = 84[/tex]

Step 3 : Dividing with 4 on both sides :

[tex] \longmapsto \qquad \dfrac{ \cancel{4}x}{ \cancel{4}} = \cancel{\dfrac{ 84}{4} }[/tex]

On calculating further, We get :

[tex] \longmapsto \qquad \red{\underline{\boxed{\frak{ x = 21 \: m}}}}\quad \bigstar[/tex]

According to question ,

▬▬▬▬▬▬▬▬▬▬▬▬▬▬

▬▬▬▬▬▬▬▬▬▬▬▬▬▬

Verifying : -

Now we are checking our answer by adding all the sides and equating it with given perimeter that is 84 metres .

Therefore , our answer is correct.

Step-by-step explanation:

5

A, d and e are the answer, multiplication/division never changes

6. yes, perpendicular lines are inside of each other always. how ever not all intersecting lines are perpendicular, for they're not 90° degrees.

3. ? (sorry)

4. ??

2. ?

The probability that the collector gets at least one limited edition card if he buys 3 packs is 0.23.

A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. It is given by the formula,

[tex]P(x) = ^nC_x p^xq^{(n-x)}[/tex]

Where,

x is the number of successes needed,

n is the number of trials or sample size,

p is the probability of a single success, and

q is the probability of a single failure.

Given that a box of trading cards contains 24-packs of cards in it. And Only two of those packs contain limited edition cards. Therefore, the probability of finding a limited edition card will be,

[tex]P = \dfrac2{24} = \dfrac{1}{12}[/tex]

The probability of not getting a limited edition card will be,

[tex]q = \dfrac{24-2}{24} = \dfrac{22}{24} = \dfrac{11}{12}[/tex]

Now, using the binomial distribution, the probability can be found.

A.)  The probability that a collector will find both limited edition cards if he buys only 2 packs is

[tex]P(x) = ^nC_x p^xq^{(n-x)}\\\\P(x=2) = ^2C_2 \cdot(\dfrac1{12})^2 \cdot (\dfrac{11}{12})^{(0)}\\\\P(x = 2) = 0.0069 \approx 0.007[/tex]

B.) The probability that he gets at least one limited edition card if he buys 3 packs can be written as,

The probability of at least a limited edition card

= 1 - Probability of not getting any limited edition card

The probability of getting no special edition card will be,

[tex]P(x) = ^nC_x p^xq^{(n-x)}\\\\P(x=0) = ^3C_0 \cdot(\dfrac1{12})^0 \cdot (\dfrac{11}{12})^{(3)}\\\\P(x = 0) = 0.77[/tex]

Now,

The probability of at least a limited edition card

= 1 - Probability of not getting any limited edition card

The probability of at least a limited edition card = 1 - P(x=0) = 1-0.77 = 0.23

Hence,  the probability that the collector gets at least one limited edition card if he buys 3 packs is 0.23.

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so let's notice that, the equation is f(x) in x-terms, meaning the variable "x" is the independent and thus the parabola is a vertical parabola.  Also let's notice that the equation is already in vertex form, keeping in mind that the  axis of symmetry occurs for a vertical parabola at the x-coordinate.

[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ f(x)=2(x-\stackrel{h}{5})^2+\stackrel{k}{8}~\hfill \stackrel{vertex}{(5,8)}~\hfill \stackrel{\textit{equation for axis of symmetry}}{x=5}[/tex]

Answer:

(4,0)

Step-by-step explanation:

standard equation for a circle is (x−h)^2 +(y−k)^2 =r^2

circle center: h, k with radius: r

(x-(+4)^2 + (y-0)^2 = 5

the center is (4, 0)

Answer:

The answer to this one is 0.25

Answer:

see the attachment!

i hope this can help you.

Step-by-step explanation:

the surface area of a figure is always the result of a combination of multiplication(s) of 2 dimensions (side lengths).

and the volume of 3 dimensions (side lengths).

"similar figures" means that they share the same angles. and that there is one scaling factor that applies to all sides (and all other lines like heights).

so, no matter what sides are used to calculate the surface areas and the volumes, it is the same scaling factor used for each of them.

in a multiplication of 2 sides (for the area) the scaling factor is therefore applied twice and hence squared, in a multiplication of 3 sides it is applied 3 times and therefore cubed.

let's call the scaling factor f.

1472 × f³ = 2875

and then

928 × f² = large S.A.

let's use the first to get f :

1472 × f³ = 2875

f³ = 2875 / 1472 = (125 × 23) / (64 × 23) = 125/64

f = 5/4

f² = (5/4)² = 5²/4² = 25/16

large S.A. = 928 × 25/16 = 58 × 25 = 1450 m²

Answer:

6

Step-by-step explanation:

Given :

⇒ The triangles are similar

⇒ The sides are in proportion

===============================================================

Solving :

⇒ [tex]\frac{6}{15+6} = \frac{8}{3x+10}[/tex]

⇒ [tex]\frac{6}{21}= \frac{8}{3x+10}[/tex]

⇒ [tex]\frac{2}{7} = \frac{8}{3x+10}[/tex]

⇒ [tex]\frac{1}{7}=\frac{4}{3x+10}[/tex]

⇒ 1(3x + 10) = 7(4)

⇒ 3x + 10 = 28

⇒ 3x = 18

⇒ x = 6

=============================================================

Solution :

The value of x is 6