Use properties of exponents to simplify the expression. First, express the
answer in exponential form. Then, evaluate the expression.
(1^3) ^4

The function is called an exponential function became the exponent is a variable.

The function is called an exponential function became the exponent is a variable.

An exponential function is a Mathematical function in the form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.

So, here given a fill in the blank statement, we need to find the words to be filled in the blanks,

So, the whole statement is =

The function is called an exponential function became the exponent is a variable.

The function y = 3ˣ is an exponential function because it is having a power which is a variable.

The graph of the same is attached to the solution.

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The hypothesis will be that "If a kid wears braces, then the kid will have a straight teeth".

It should be noted that a hypothesis means a proposed explanation based on reasoning and evidence.

In this case, the hypothesis will be that "If a kid wears braces, then the kid will have a straight teeth".

The conclusion is that kids who wear braces will have straight teeth.

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The total tax rate and the sales tax will be given below.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Total selling price (TSP), State tax rate (STR), City tax rate (CTR), Total tax rate (TTR) and Sales tax (ST).

The table complete table is given below.

Item                            TSP            STR        CTR           TTR              ST

Clothing                     $81.39            3%        0%            3%            $2.44

Cell phone               $159.95           5%        0%            5%            $7.99

MP3 player               $195.55          4%         2%            6%           $11.73

Computer                $1599.75      4.88%     1.50%       6.38%      $102.06

Take-out                   $49.85         8.13%    2.50%      10.63%        $5.29

Pickup truck          $38,526.42    6.50%    1.25%        7.75%     $2985.79

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The number of boys signed up to play basketball this year is 560.

Given that, the number of boys who played basketball last year = 320.

We need to find the number of boys signed up to play basketball this year.

In mathematics, a percentage is a number or ratio expressed as a fraction of 100.

Now, the number of boys signed up to play basketball this year = 175 per cent of what it was last year.

So, the number of boys signed up to play basketball this year = 175% of 320

[tex]=\frac{175}{10} \times 320=1.75 \times 320=560[/tex]

Therefore, the number of boys signed up to play basketball this year is 560.

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The area of the deck that surrounds the hot tub is 17.93 m²

The area is the amount of space within the perimeter of a 2D shape.

radius = 3/2 = 1.5 m

Area of deck,

=Area of square - area of circle

= side side- πr²

=5*5 - 3.14* 1.5*1.5

= 25- 7.065

=  17.93 m²

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The difference between Palomas and Antons' points on the English test is of 14 points.

When two numbers can be written in the form as p:q , they are said to be in Ratio.

It is given that

The ratio of Michaels point to Paloma point is 12 :11

The ratio of Michaels point to Anton's Point is 4:3

Let Paloma's point be x

then Michaels point will be 12x/11

and Anton's points will be

(12x/11 ) / Anton's points = 4 /3

Anton's points = 9x/11

It is given that the sum of the points of the three students is 224

so

x + (12x/11)+ (9x/11) = 224

32x /11 = 224

x = 77

Paloma's points = 77

Anton's Points = 9x/11 = 63

The difference between Palomas and Antons' points on the English test

=77 -63

= 14 points.

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Answer:

x • (2xt + 7y)

Step-by-step explanation:

1. ((5xy-((x2)•t))+2xy)+(3x2•t)

2. Pull out like factors :

  2x2t + 7xy  =   x • (2xt + 7y)

Final result

x • (2xt + 7y)

Answer:

[tex]7xy + {x}^{2} t[/tex]

Step-by-step explanation:

[tex](5xy + 2xy) + ( - 2 {x}^{2} t + 3 {x}^{2}t) [/tex]

By analytical methods and algebraic handling and on the basis that x is increased by 25 %, we conclude that the variable x² is increased by 18.75 %.

In this case we have a linear variable x, whose increase is described by the following expression:

y = x · (1 + r/100)     (1)

Where r is the increase rate.

If we square (1), then we find that:

y² = x² · (1 + r/100)² = (1 + r'/100)     (2)

Where r' is the equivalent increase rate.

(1 + r/50 + r²/10000) = (1 + r'/100)

r'/100 = r/50 + r²/10000

r' = r/2 + r²/100

If we know that r = 25, then the equivalent increase rate is:

r' = 25/2 + 25²/100

r' = 18.75

By analytical methods and algebraic handling and on the basis that x is increased by 25 %, we conclude that the variable x² is increased by 18.75 %.

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Based on the data, it is found that "being female" and "earning over $50,000" are not independent events. the correct answer is option D.

Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Two events, A and B are independent, if:

P(A [tex]\cap[/tex] B) = P(A) P(B)

In this problem, the events are:

Out of the 1000 people, 450 are female, hence:

P(A) = [tex]\dfrac{450}{1000}[/tex] = 0.45

850 earn over $50,000, hence:

P(B) = [tex]\dfrac{850}{1000}[/tex] = 0.85

375 are women who earn over $50,000, hence:

P(A [tex]\cap[/tex] B)  = [tex]\dfrac{375}{1000}[/tex] = 0.375

The multiplication of the probabilities is:

P(A [tex]\cap[/tex] B)  = 0.45(0.85} = 0.3825

Therefore based on the data, it is found that "being female" and "earning over $50,000" are not independent events. the correct answer is option D.

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Answer:

The answer is B

Step-by-step explanation:

By proportion , 3 : 2.91 = 2: x . then you write it in fraction

Answer:

(-2,-9)

(-1,8)

(0,-5)

(1,0)

(2,7)

Step-by-step explanation:

Shape F has a perimeter of 180mm and an area of 2196mm² is similar to shape G with perimeter 300mm then area of shape is 6100mm².

As given,

Shapes F and G are similar

Perimeter of shape F=180mm

Area of shape F=2196mm²

Perimeter of shape G=300mm

Let xmm²be the area of shape G

Square of ratio of perimeter of similar shape =Ratio of area of similar shape

⇒(180 /300)² =(2196/x)

⇒9/25=2196/x

⇒x=(2196×25)/9

⇒x=6100mm²

Therefore, shape F has a perimeter of 180mm and an area of 2196mm² is similar to shape G with perimeter 300mm then area of shape is 6100mm².

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Answer:

A

Step-by-step explanation:

y = - 2x + 5 → (1)

y = x² + 3x + 9 → (2)

substitute y = x² + 3x + 9 into (1)

x² + 3x + 9 = - 2x + 5 ( subtract - 2x + 5 from both sides )

x² + 5x + 4 = 0 ← in standard form

(x + 1)(x + 4) = 0 ← in factored form

equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = - 1

x + 4 = 0 ⇒ x = - 4

substitute these values into (1) for corresponding values of y

x = - 1 : y = - 2(- 1) + 5 = 2 + 5 = 7 ⇒ (- 1, 7 )

x = - 4 : y = - 2(- 4) + 5 = 8 + 5 = 13 ⇒ (- 4, 13 )

Answer:

so first we have to divide each side by 38

4.5miles=0.1

45miles=1 hour

Hope This Helps!!!

Answer:

D

Step-by-step explanation:

The volume of a cylinder is pi * r^2 * h

A) V = 3.14 * (0.7/2)^2 * 6.2 = 2.4 m^2

B) V = 3.14 * (0.9/2)^2 * 3.4 = 2.2 m^2

C) V = 3.14 * (1.2/2)^2 * 6.8 = 7.7 m^2

D) V = 3.14 * (1.4/2)^2 * 6.2 = 9.5 m^2

None of the equations are parallel or perpendicular to the line jk.

The equation of a line can be interpreted as follows:

y = mx + b

where

Therefore,

Parallel lines have the same slope(m).

Perpendicular line follows the principle below:

Therefore, let's find equation of jk

(-5, 5)(1, -5)

m = -5 - 5 / 1 + 5 = -10 / 6 = - 5 / 3

using (1, -5)

-5 = - 5 / 3 (1) + b

b = -5 + 5 / 3 = -15 + 5 / 3 = -10 / 3

Therefore,

y = -5 / 3 x - 10 / 3

m = - 5 / 3

6x + 10y = 11

10y = -6x + 11

y = - 6 / 10 x + 11 / 10

y = - 3 / 5 x + 11 / 10

hence, m = - 3 / 5

5x - 3y = 8

3y = 5x - 8

y = 5 / 3 x - 8/3

m = 5 / 3

The equation

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For the spider man the discount is of rs600, for the doll the discount is of rs1,000.

We know that the price of the spider-man is rs3,000, and we apply a discount of the 20%.

So the amount of discount for that toy is the 20% of rs3,000, which gives:

(20%/100%)*rs3,000 = rs600

So the amount discounted for the spider-man is rs600.

For the case of the doll, we know that its cost is rs5,000, the amount discounted is:

(20%/100%)*rs5,000 = rs1,000

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Answer:

( -10.5 , 0 ) and ( 0 , -21 )

Step-by-step explanation:

→ Determine where a line intersects

x and y intercept

→ Set x equal to 0 to find y - intercept

( 0 , -21 )

→ Set y equal to 0 to find x intercept

0 = -2x - 21

→ Add 21 to both sides

21 = -2x

→ Divide both sides by -2

-10.5 = x

Answer:

i. {1,2,3,4,5,6,7,9}

ii. {1,3,5}

iii. {1,2,3,4,5,6,8,10}

Step-by-step explanation:

U= {1,2,3,4,5,6,7,8,9,10}

A= {1,3,5,7,9}

B= {1,2,3,4,5,6}

A U B = {1,2,3,4,5,6,7,9}

A n B = { 1,3,5}

A (prime) U B =

A(prime)= {2,4,6,8,10}

Therefore A(prime)= {1,2,3,4,5,6,8,10}

Answer:

30

Step-by-step explanation:

4 cups x 60 hours a min x 2 hours of lunch ÷ 16 cups per gallon = 30 gallons

The answer is 30 gallons.

Firstly, convert the hours to minutes so you know how many minutes you're working with. 2*60=120 minutes.

Then, multiply 120 with 4 to get the number of tea (in cups) that is poured. 120*4=480 cups.

Finally, divide 480 cups with 16 cups to find out the number of gallons poured. 480/16 equals 30 gallons.

Hope this helped.

The answer is 45


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

Answer:

integers include negative numbers, whole numbers are only 0 and positive numbers.

Step-by-step explanation:

whole numbers are very similar to integers as they do not have a decimal place although whole numbers are from 0, 1, 2, 3.... and so on whereas integers include negative numbers as well. So all whole numbers are integers but not all integers are whole numbers.

Answer:

10√7

Step-by-step explanation:

you can simplify the second radical and break it up into

√4 * √7 which then simplifies to 2√7 which you then multiply by 3. 4√7 + 3(2√7) which becomes 4√7 + 6√7 and then you just add the numbers Infront to get 10√7

The value of the expression Z² + Q² is 4321

The radius of the chocolate spheres is given as:

r = 2

The maximum number of chocolates that can fit in a spherical capsule is calculated as:

Max = R³/r³

Where:

R represents the radius of the sphere.

For the spherical capsule whose radius is 8 inches, we have:

Z = 8³/2³

Evaluate

Z = 64

For the spherical capsule whose radius is 5 inches, we have:

Q = 5³/2³

Evaluate

Q = 15.625

Remove decimal

Q = 15

So, we have:

Z² + Q² = 64² + 15²

Evaluate the exponent

Z² + Q² = 4096 + 225

Evaluate the sum

Z² + Q² = 4321

Hence, the value of Z² + Q² is 4321

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Answer:

8.49 × 10⁻³

Explanation:

Standard form of a number: A. × 10ᵇ

(where 'A' is the number, b is the exponent over 10)

For the number "0.00849​", move the decimal point 3 places right so the exponent of 10 is -3.

Standard form: 8.49 × 10⁻³

Other examples of standard/scientific forms are:   standard forms

i) 0.043, move the decimal point 2 places right = 4.3 × 10⁻²

ii) 4030, move the decimal point 3 places left = 4.03 × 10³

Answer:

when a number is given in that manner you have to take that decimal between two whole numbers.

and that is the main reason why I took that decimal from 0.0 to 8.49 and since it went towards the right my answer is going to be 8.49 *10 raised to negative 3.

This is not a syllogism. Hence option B is correct.

A logical structure for a formal argument that includes a major, minor, and conclusion.

This syllogism cannot be concluded without a given statement.

You'll need wrapping paper if you're going to wrap Holly's present. To get wrapping paper, you must visit a store.

Therefore, you will wrap Holly's present if you visit the store. This isn't a syllogism

Hence option B is correct.

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Answer:

This is not a syllogism

Step-by-step explanation:

I took the quiz. :)

Tristan needs to make at least 10 visits to the movie theater to earn his first free movie ticket.

Let v be the number of visits Tristan makes to the movie theater.

He receives 25 rewards points just for signing up, and he earns 8.5 points for each visit. So, the total rewards points he will have is

25+8.5v.

He needs at least 110 points for a free movie ticket. Therefore, we can write the inequality:

25+8.5v≥110

To solve for v, we can subtract 25 from both sides of the inequality and then divide by 8.5:

8.5v≥85

v≥85/8.5

v≥10

So, Tristan needs to make at least 10 visits to the movie theater to earn his first free movie ticket.

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Answer:

8

Step-by-step explanation:

To one decimal place:

[tex]2 \sqrt{10} = 6.3[/tex]

[tex]10 \sqrt{2} = 14.1[/tex]

So there are eight integers between 2√10 and 10√2: 7, 8, 9, 10, 11, 12, 13, and 14.