Which expression is equivalent to (4y²) ³ (3y²)?
O 12y8
12y12
192y8
192y12

Option A.  [tex]Y = 3(2)^{X}[/tex]

Here, looking at the graph we can see that when x = 0, the value of y will be 3. Thus, (0, 3) is a solution to the given function.

Putting x = 0 in the given options, we see that

A. y = 3(1) = 3 (as anything raised to the power is 1)

B. y = 2(1) = 2

C. y = 4(1) = 4

D. y = 3(1) = 3

Thus, we can eliminate option B and C as (0, 3) does not satisfy these equations.

Now, if we take x = 1, from the graph we can see that the value of y will be 6.

Substituting x = 1 in the remaining two options, we get

A. y = 3(2) = 6

D. y = 3(4) = 12

Thus, D is also eliminated.

Option A, y = 3(2)^x is the correct answer.

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Answer:

let the number be x and y

Step-by-step explanation:

x+y=12

x-y=-4

here,

(a) The 2nd letter to be a vowel (a, e, i, o, u) = 69000

(b) Exactly one vowel = 159600

An open sound is represented by a vowel, which is a letter. The English language has six vowels: a, e, I o, u, and occasionally y. Y can function as a consonant or a vowel depending on the context, as in the word story or yes. Vowels are a representation of open, frictionless vocal sounds.

4 letter word to be formed

Total Alphabets = 26

Repeated letters are not allowed

(a) 4 letter word, Consonant - C, vowel - V

Second letter to be a vowel

C or V = 25, V = 5, C or V = 24, C or V = 23

Number of word can form = 25 × 5 × 24 × 23 = 69000

(b) 4 letter word, in this exactly one vowel.

Number of words

V(5) × C(21) × C(20) × C(19)

C(21) × V(5) × C(20) × C(19)

C(21) × C(20) × V(5) × C(19)

C(21) × C(20) × C(19) × V(5)

Total number of words formed = 4 [5×21×20×19] = 159600

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Step-by-step explanation:

Fact 1: Alternate angles are equal.

Angles, (5x-11)° and (3x+17)° are ALTERNATE angles and so,

(5x-11)° = (3x+17)°

5x - 3x = 17 + 11

2x = 28

x = 28 ÷ 2

x = 14

NB: x does NOT have the degree sign because it's NOT an angle on its own, but rather within the bracket/part of the calculation to get the angle degree.

Fact 2: Opposite angles are equal.

Y° and (3x+17)° are OPPOSITE angles

y = (3x+17)°

y = (3x14) + 17

y= 42 + 17

y = 59°

Hope this helps!

Answer:

16^6

Step-by-step explanation:

Farfalla produces 2,400 kites every year.

The number of factories Farfalla owns around the globe = 3;

The number of kites produced by original factory every year = 600;

The number of kites produced by each of other 2 factories every year = 900;

Then the total kites produced by both other factories will be = 2 × 900 = 1800;

Now, the number of kites Farfalla produces every year is = 600 + 1800 = 2400;

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Answer:

56

Step-by-step explanation:

The mode of a data set is the number that appears the most, which in this situation would be 56

:D

Answer:

the place value of 7 is =70.000000

Step-by-step explanation:

The number of mini bottles required is;  68 mini bottles

We are told that a mini bottle of water contains 8 ounces of water.

Now, we are told that you require 4¹/₄ = 4.25gallons of water.

Now from conversions, we know that;

1 gallon = 128 ounces

Thus; 4.25 gallons = 4.25 * 128 = 544 ounces

Since a mini bottle of water contains 8 ounces of water, then we can say that;

Number of mini bottles required is;

544/8 = 68 mini bottles

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Answer:

-2 < x < 1

Step-by-step explanation:

Given inequality:

[tex]1 < x+3 < 4[/tex]

[tex]\textsf{If $a < u < b$ \;then\; $a < u$ \;and \;$u < b$}:[/tex]

Case 1

[tex]\implies 1 < x+3[/tex]

[tex]\implies 1-3 < x+3-3[/tex]

[tex]\implies -2 < x[/tex]

[tex]\implies x > -2[/tex]

Case 2

[tex]\implies x+3 < 4[/tex]

[tex]\implies x+3-3 < 4-3[/tex]

[tex]\implies x < 1[/tex]

Combine the intervals:

[tex]-2 < x < 1[/tex]

Answer:

3611/5000

Step-by-step explanation:

The speed from slowest to the fastest is Julio; Elana; Kevin; Lorena.

Given that a table shows the distance traveled by 4 cyclists as shown in attached images.

Speed ​​is defined as . The rate at which an object changes position in any direction. Speed ​​is measured as the ratio between distance and time traveled.

Firstly, we will calculate the speed of Elena.

The given distance is 20(1/2) mi or it can be written as 41/2mi and the time is 2(1/4) hr or 9/4hr.

Now, substitute the values in speed formula that is

Speed=Distance/Time

Speed=(41/2)/(9/4)

Speed=(41/2)×(4/9)

Speed=82/9 mi/hr.

Now, we will calculate its speed of Julio.

The given distance is 12(1/4) mi or it can be written as 49/4mi and the time is 1(1/2) hr or 3/2hr.

Now, substitute the values in speed formula that is

Speed=Distance/Time

Speed=(49/4)/(3/2)

Speed=(49/4)×(2/3)

Speed=49/6 mi/hr.

Further, we will calculate the speed of Kevin.

The given distance is 20(2/3) mi or it can be written as 62/3mi and the time is 1(2/3) hr or 5/3hr.

Now, substitute the values in speed formula that is

Speed=Distance/Time

Speed=(62/3)/(5/3)

Speed=(62/3)×(3/5)

Speed=62/5 mi/hr.

Furthermore, we will calculate the speed of Lorena.

The given distance is 33(1/4) mi or it can be written as 133/4mi and the time is 2(1/3) hr or 7/3hr.

Now, substitute the values in speed formula that is

Speed=Distance/Time

Speed=(133/4)/(7/3)

Speed=(133/4)×(3/7)

Speed=57/4 mi/hr.

Hence, the speeds from slowest to fastest from the given table is Julio; Elana; Kevin; Lorena.

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Answer:$472,500

Step-by-step explanation: I did $350,000 multiplied by 4.5% and got 15750 and then multiplied 15750 by 30 and then got $472,500

Answer:

56.52m is the circumference. The area is 254.34[tex]m^{2}[/tex]

Step-by-step explanation:

The equation for the circumference of a circle is c=2πr with r being the radius. So 2(3.14)(9)=56.52m. The area equation for a circle is A=π[tex]r^{2}[/tex] so it would be (3.14)(9)^2 or (3.14)(81) which equals 254.34[tex]m^{2}[/tex]

Answer:

Step-by-step explanation:

first we can turn these mixed fractions into normal numbers so

1.42<.336 FALSE

.54>1.357 false

.615>.96 false

1.16>1.83 TRUE

Answer:

 A.  width = x - 4.5

 B.  111 = 2(x + (x -4.5))

Step-by-step explanation:

A. The width is 4.5 meters shorter than x, so is x -4.5.

__

B. The perimeter is twice the sum of length and width. It is 111 meters, so an equation for it could be ...

 111 = 2(x + (x -4.5))

The amount Jasmin was paid altogether was $210

From the question, we are to determine how much Jasmin was paid altogether

From the given information,

The Smith family pay her $10 an hour.

and

She babysat for the Smith family for 12 hours

Thus,

The amount she was paid by the Smith family is 12 × $10 = $120

Also,

The Johnson family pay her $15 an hour

and

She babysat for the Johnson family for 6 hours

Thus,

The amount she was paid by the Johnson family is 6 × $15 = $90

Therefore,

The amount she was paid altogether = $120 + $90

The amount she was paid altogether = $210

Hence, the amount Jasmin was paid altogether was $210

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Answer:

Step-by-step explanation:

The angles lie on a straight line summing to total 180 degrees.

Form an equation:

m∠1 + m∠2 = 180

2x + x + 72 = 180

and solve:

3x + 72 = 180

3x = 180 - 72

3x = 108

x = 36

Answer:

see below

Step-by-step explanation:

We are here given a straight line which is splitted into two parts by a line , such that it makes two angles.

Also we know that the angle measure of a straight line is 180° . Therefore; here the sum of angles 1 and 2 will be 180° .

So that,

==> angle 1 + angle 2 = 180°

==> 2x + x + 72° = 180°

==> 3x = 180° - 72°

==> 3x = 108°

==> x = 108°/3

==> x = 36° .

The equation which we used to solve the problem is ,

==> Equation = 2x + x + 72° = 180°

For finding the individual angels substitute the value of x into their expressions , as ;

==> angle 1 = 2x = 2(36°) = 72°

==> angle 3 = x + 72° = 36° + 72° = 108° .

And we are done!

If two hundred liters of a punch that contains 35% fruit juice is mixed with 300 liters of another punch and the resulting fruit punch is 20% fruit juice, then the percent of fruit juice in 300 liters of punch is calculated to be 10%.

The percentage of fruit juice in 300 liters of punch can be calculated by forming a linear equation.

A linear equation also termed a first-degree equation is an equation with one or more variables that have the highest power of one.

A linear equation for this problem can be given as:

the volume of the first punch × percentage of fruit juice in the first punch + the volume of the second punch × percentage of fruit juice in the second punch = total volume × total percentage of fruit juice

Consider x = percentage of unknown fruit juice

Now add the given values in the equation:

200 × 35 + 300(x) = 500 × 20

7000 + 300(x) = 10000

300(x) = 10000 - 7000

300(x) = 3000

x = 3000 / 300

x = 10%

Hence, the percentage of fruit juice in 300 liters of punch is calculated to be 10%.

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Answer:

3000

Step-by-step explanation:

If it was 3500 then it would've been 4000. However, since 3458 is below 3500 it's 3000. Hope this helps. Good luck!

Answer:4.12

Step-by-step explanation:

The branch of statistical studies called descriptive statistics summarizes important aspects of a data set is true.

It is required to find the statement.

A statement is a declarative sentence that is either true or false but not both. A statement is sometimes called a proposition. The key is that there must be no ambiguity. To be a statement, a sentence must be true or false, and it cannot be both.

Given:

The branch of statistical studies called descriptive statistics summarizes important aspects of a data set.

Descriptive statistics refers to the summary of important aspects of a data set.

Therefore, the branch of statistical studies called descriptive statistics summarizes important aspects of a data set is true.

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$22,150  is the total assets .

What is total assets?

Total asset =  Saving account balance + current value of automobile + video equipment + personal computer + cash in checking account + household possessions + value of stock investment

        = $1990 + $9800 + $2600 + $1700 + $550 + $4400 + $ 1110

       =  $22,150

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x-2y=8

Step-by-step explanation:

x=8+2y

The gradient is 2

Answer:

gradient = [tex]\frac{1}{2}[/tex] , y- intercept = - 4

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope (gradient) and c is the y- intercept )

given

x - 2y = 8 ( subtract x from both sides )

- 2y = - x + 8 ( divide through by - 2 )

y = [tex]\frac{1}{2}[/tex] x - 4 ← in slope- intercept form

with gradient m = [tex]\frac{1}{2}[/tex] and y- intercept c = - 4

Answer:

Step-by-step explanation:

sub equation 1 into 2

2-5x=x²-2x-8

0=x²-2x+5x-8-2

0=x²+3x-10

0=(x-2)(x+5)

x=2 or x=-5

sub x into equation 1

y=2-5(2)                            or        y=2-5(-5)

y=-8                                              y=27

Which graph results when f(x) = (8)* is first reflected across the y-axis and then across the x-axis?

Option 1 for Question 1

Option 1 for Question 2

Option 3 for Question 3

Option 1 for Question 4

Option 1 to Question 5

1) We subtract from any sequence to find the common difference d. For instance, =(-4) - (-15) = -4+15 = 11. Hence, choice 1. The answer for the sequence is (11).

2) In case a sequence is

The sequence's eighth term, then, will be = 25-24 = 1. Therefore, choice 1 is right.

Question #3: Any arithmetic series has the following explicit rule

As a result, choice three is right.

4. Reggie started off with 195 cards, and each week, 16 more cards are added.

In light of this query

There are 16 common differences in the sequence.

The order is going to be

the amount of cards will be after the 12th week.

Therefore, choice 1 is right.

5th query: If the sequence is

Then

and

The usual difference is 7-3 = 4.

Therefore

Choice 1. is the right response.

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Answer:

Step-by-step explanation:

a=number of products

product profit=49,60-7,45=42,15

115000+1200=42,15xa

127000=42,15xa

a=3013